pydrake.multibody.plant

Bindings for MultibodyPlant and related classes.

pydrake.multibody.plant.AddMultibodyPlant(*args, **kwargs)

Overloaded function.

AddMultibodyPlant(config: pydrake.multibody.plant.MultibodyPlantConfig, builder: pydrake.systems.framework.DiagramBuilder) -> tuple

Adds a new MultibodyPlant and SceneGraph to the given builder. The plant’s settings such as time_step are set using the given config.

AddMultibodyPlant(plant_config: pydrake.multibody.plant.MultibodyPlantConfig, scene_graph_config: pydrake.geometry.SceneGraphConfig, builder: pydrake.systems.framework.DiagramBuilder) -> tuple

Adds a new MultibodyPlant and SceneGraph to the given builder. The plant’s settings such as time_step are set using the given plant_config. The scene graph’s settings are set using the given scene_graph_config.

pydrake.multibody.plant.AddMultibodyPlantSceneGraph(*args, **kwargs)

Overloaded function.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder, plant: pydrake.multibody.plant.MultibodyPlant, scene_graph: pydrake.geometry.SceneGraph = None) -> tuple

Adds a MultibodyPlant and a SceneGraph instance to a diagram builder, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter plant:: Plant to be added to the builder.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder and plant must be non-null.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder, time_step: float, scene_graph: pydrake.geometry.SceneGraph = None) -> tuple

Makes a new MultibodyPlant with discrete update period time_step and adds it to a diagram builder together with the provided SceneGraph instance, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter time_step:: The discrete update period for the new MultibodyPlant to be added. Please refer to the documentation provided in MultibodyPlant::MultibodyPlant(double) for further details on the parameter time_step.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder must be non-null.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder_[AutoDiffXd], plant: pydrake.multibody.plant.MultibodyPlant_[AutoDiffXd], scene_graph: pydrake.geometry.SceneGraph_[AutoDiffXd] = None) -> tuple

Adds a MultibodyPlant and a SceneGraph instance to a diagram builder, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter plant:: Plant to be added to the builder.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder and plant must be non-null.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder_[AutoDiffXd], time_step: float, scene_graph: pydrake.geometry.SceneGraph_[AutoDiffXd] = None) -> tuple

Makes a new MultibodyPlant with discrete update period time_step and adds it to a diagram builder together with the provided SceneGraph instance, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter time_step:: The discrete update period for the new MultibodyPlant to be added. Please refer to the documentation provided in MultibodyPlant::MultibodyPlant(double) for further details on the parameter time_step.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder must be non-null.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder_[Expression], plant: pydrake.multibody.plant.MultibodyPlant_[Expression], scene_graph: pydrake.geometry.SceneGraph_[Expression] = None) -> tuple

Adds a MultibodyPlant and a SceneGraph instance to a diagram builder, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter plant:: Plant to be added to the builder.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder and plant must be non-null.

AddMultibodyPlantSceneGraph(builder: pydrake.systems.framework.DiagramBuilder_[Expression], time_step: float, scene_graph: pydrake.geometry.SceneGraph_[Expression] = None) -> tuple

Makes a new MultibodyPlant with discrete update period time_step and adds it to a diagram builder together with the provided SceneGraph instance, connecting the geometry ports.

Note

Usage examples in add_multibody_plant_scene_graph “AddMultibodyPlantSceneGraph”.

Parameter builder:: Builder to add to.
Parameter time_step:: The discrete update period for the new MultibodyPlant to be added. Please refer to the documentation provided in MultibodyPlant::MultibodyPlant(double) for further details on the parameter time_step.
Parameter scene_graph:: (optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition:: builder must be non-null.

pydrake.multibody.plant.ApplyMultibodyPlantConfig(config: pydrake.multibody.plant.MultibodyPlantConfig, plant: pydrake.multibody.plant.MultibodyPlant) → None

Applies settings given in config to an existing plant. The time_step is the one value in config that cannot be updated – it can only be set in the MultibodyPlant constructor. Consider using AddMultibodyPlant() or manually passing config.time_step when you construct the MultibodyPlant.

This method must be called pre-Finalize.

Raises: RuntimeError if plant is finalized or if time_step is changed. –

pydrake.multibody.plant.CalcContactFrictionFromSurfaceProperties(*args, **kwargs)

Overloaded function.

CalcContactFrictionFromSurfaceProperties(surface_properties1: pydrake.multibody.plant.CoulombFriction, surface_properties2: pydrake.multibody.plant.CoulombFriction) -> pydrake.multibody.plant.CoulombFriction

Given the surface properties of two different surfaces, this method computes the Coulomb’s law coefficients of friction characterizing the interaction by friction of the given surface pair. The surface properties are specified by individual Coulomb’s law coefficients of friction. As outlined in the class’s documentation for CoulombFriction, friction coefficients characterize a surface pair and not individual surfaces. However, we find it useful in practice to associate the abstract idea of friction coefficients to a single surface. Please refer to the documentation for CoulombFriction for details on this topic.

More specifically, this method computes the contact coefficients for the given surface pair as:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

where the operation above is performed separately on the static and dynamic friction coefficients.

Parameter surface_properties1:: Surface properties for surface 1. Specified as an individual set of Coulomb’s law coefficients of friction.
Parameter surface_properties2:: Surface properties for surface 2. Specified as an individual set of Coulomb’s law coefficients of friction.

Returns: the combined friction coefficients for the interacting surfaces.

CalcContactFrictionFromSurfaceProperties(surface_properties1: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd], surface_properties2: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]) -> pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]

Given the surface properties of two different surfaces, this method computes the Coulomb’s law coefficients of friction characterizing the interaction by friction of the given surface pair. The surface properties are specified by individual Coulomb’s law coefficients of friction. As outlined in the class’s documentation for CoulombFriction, friction coefficients characterize a surface pair and not individual surfaces. However, we find it useful in practice to associate the abstract idea of friction coefficients to a single surface. Please refer to the documentation for CoulombFriction for details on this topic.

More specifically, this method computes the contact coefficients for the given surface pair as:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

where the operation above is performed separately on the static and dynamic friction coefficients.

Parameter surface_properties1:: Surface properties for surface 1. Specified as an individual set of Coulomb’s law coefficients of friction.
Parameter surface_properties2:: Surface properties for surface 2. Specified as an individual set of Coulomb’s law coefficients of friction.

Returns: the combined friction coefficients for the interacting surfaces.

CalcContactFrictionFromSurfaceProperties(surface_properties1: pydrake.multibody.plant.CoulombFriction_[Expression], surface_properties2: pydrake.multibody.plant.CoulombFriction_[Expression]) -> pydrake.multibody.plant.CoulombFriction_[Expression]

Given the surface properties of two different surfaces, this method computes the Coulomb’s law coefficients of friction characterizing the interaction by friction of the given surface pair. The surface properties are specified by individual Coulomb’s law coefficients of friction. As outlined in the class’s documentation for CoulombFriction, friction coefficients characterize a surface pair and not individual surfaces. However, we find it useful in practice to associate the abstract idea of friction coefficients to a single surface. Please refer to the documentation for CoulombFriction for details on this topic.

More specifically, this method computes the contact coefficients for the given surface pair as:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

where the operation above is performed separately on the static and dynamic friction coefficients.

Parameter surface_properties1:: Surface properties for surface 1. Specified as an individual set of Coulomb’s law coefficients of friction.
Parameter surface_properties2:: Surface properties for surface 2. Specified as an individual set of Coulomb’s law coefficients of friction.

Returns: the combined friction coefficients for the interacting surfaces.

pydrake.multibody.plant.ConnectContactResultsToDrakeVisualizer(builder: pydrake.systems.framework.DiagramBuilder, plant: drake::multibody::MultibodyPlant<double>, scene_graph: pydrake.geometry.SceneGraph, lcm: pydrake.lcm.DrakeLcmInterface = None, publish_period: Optional[float] = None) → pydrake.systems.lcm.LcmPublisherSystem: MultibodyPlant-connecting overload.

class pydrake.multibody.plant.ContactModel

Enumeration for contact model options.

Members:

kHydroelastic : Contact forces are computed using the Hydroelastic model. Contact

between unsupported geometries will cause a runtime exception.

kPoint : Contact forces are computed using a point contact model, see

compliant_point_contact.

kHydroelasticWithFallback : Contact forces are computed using the hydroelastic model, where

possible. For most other unsupported colliding pairs, the point model from kPoint is used. See geometry::QueryObject::ComputeContactSurfacesWithFallback for more details.

kHydroelasticsOnly : Legacy alias. TODO(jwnimmer-tri) Deprecate this constant.

kPointContactOnly : Legacy alias. TODO(jwnimmer-tri) Deprecate this constant.

__init__(self: pydrake.multibody.plant.ContactModel, value: int) → None

kHydroelastic = <ContactModel.kHydroelastic: 0>

kHydroelasticsOnly = <ContactModel.kHydroelastic: 0>

kHydroelasticWithFallback = <ContactModel.kHydroelasticWithFallback: 2>

kPoint = <ContactModel.kPoint: 1>

kPointContactOnly = <ContactModel.kPoint: 1>

property name

property value

class pydrake.multibody.plant.ContactResults

A container class storing the contact results information for each contact pair for a given state of the simulation.

This class is immutable, so can be efficiently copied and moved.

Note

This class is templated; see ContactResults_ for the list of instantiations.

__init__(self: pydrake.multibody.plant.ContactResults) → None: Constructs an empty ContactResults.

hydroelastic_contact_info(self: pydrake.multibody.plant.ContactResults, i: int) → pydrake.multibody.plant.HydroelasticContactInfo: Retrieves the ith HydroelasticContactInfo instance. The input index i must be in the range [0, num_hydroelastic_contacts()) or this method throws.

num_hydroelastic_contacts(self: pydrake.multibody.plant.ContactResults) → int: Returns the number of hydroelastic contacts.

num_point_pair_contacts(self: pydrake.multibody.plant.ContactResults) → int: Returns the number of point pair contacts.

plant(self: pydrake.multibody.plant.ContactResults) → drake::multibody::MultibodyPlant<double>: Returns the plant that produced these contact results. In most cases the result will be non-null, but default-constructed results might have nulls.

point_pair_contact_info(self: pydrake.multibody.plant.ContactResults, i: int) → pydrake.multibody.plant.PointPairContactInfo: Retrieves the ith PointPairContactInfo instance. The input index i must be in the range [0, num_point_pair_contacts()) or this method throws.

SelectHydroelastic(self: pydrake.multibody.plant.ContactResults, selector: Callable[[pydrake.multibody.plant.HydroelasticContactInfo], bool]) → pydrake.multibody.plant.ContactResults

Returns a selective copy of this object. Only HydroelasticContactInfo instances satisfying the selection criterion are copied; all other contacts (point_pair and deformable) are unconditionally copied.

Parameter selector:: Boolean predicate that returns true to select which HydroelasticContactInfo.

Note

It uses deep copy (unless the operation is trivially identifiable as being vacuous, e.g., when num_hydroelastic_contacts() == 0).

template pydrake.multibody.plant.ContactResults_: Instantiations: ContactResults_[float], ContactResults_[AutoDiffXd], ContactResults_[Expression]

class pydrake.multibody.plant.ContactResults_[AutoDiffXd]

A container class storing the contact results information for each contact pair for a given state of the simulation.

This class is immutable, so can be efficiently copied and moved.

__init__(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd]) → None: Constructs an empty ContactResults.

hydroelastic_contact_info(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd], i: int) → pydrake.multibody.plant.HydroelasticContactInfo_[AutoDiffXd]: Retrieves the ith HydroelasticContactInfo instance. The input index i must be in the range [0, num_hydroelastic_contacts()) or this method throws.

num_hydroelastic_contacts(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd]) → int: Returns the number of hydroelastic contacts.

num_point_pair_contacts(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd]) → int: Returns the number of point pair contacts.

plant(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd]) → drake::multibody::MultibodyPlant<Eigen::AutoDiffScalar<Eigen::Matrix<double, -1, 1, 0, -1, 1> > >: Returns the plant that produced these contact results. In most cases the result will be non-null, but default-constructed results might have nulls.

point_pair_contact_info(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd], i: int) → pydrake.multibody.plant.PointPairContactInfo_[AutoDiffXd]: Retrieves the ith PointPairContactInfo instance. The input index i must be in the range [0, num_point_pair_contacts()) or this method throws.

SelectHydroelastic(self: pydrake.multibody.plant.ContactResults_[AutoDiffXd], selector: Callable[[pydrake.multibody.plant.HydroelasticContactInfo_[AutoDiffXd]], bool]) → pydrake.multibody.plant.ContactResults_[AutoDiffXd]

Returns a selective copy of this object. Only HydroelasticContactInfo instances satisfying the selection criterion are copied; all other contacts (point_pair and deformable) are unconditionally copied.

Parameter selector:: Boolean predicate that returns true to select which HydroelasticContactInfo.

Note

It uses deep copy (unless the operation is trivially identifiable as being vacuous, e.g., when num_hydroelastic_contacts() == 0).

class pydrake.multibody.plant.ContactResults_[Expression]

A container class storing the contact results information for each contact pair for a given state of the simulation.

This class is immutable, so can be efficiently copied and moved.

__init__(self: pydrake.multibody.plant.ContactResults_[Expression]) → None: Constructs an empty ContactResults.

hydroelastic_contact_info(self: pydrake.multibody.plant.ContactResults_[Expression], i: int) → pydrake.multibody.plant.HydroelasticContactInfo_[Expression]: Retrieves the ith HydroelasticContactInfo instance. The input index i must be in the range [0, num_hydroelastic_contacts()) or this method throws.

num_hydroelastic_contacts(self: pydrake.multibody.plant.ContactResults_[Expression]) → int: Returns the number of hydroelastic contacts.

num_point_pair_contacts(self: pydrake.multibody.plant.ContactResults_[Expression]) → int: Returns the number of point pair contacts.

plant(self: pydrake.multibody.plant.ContactResults_[Expression]) → drake::multibody::MultibodyPlant<drake::symbolic::Expression>: Returns the plant that produced these contact results. In most cases the result will be non-null, but default-constructed results might have nulls.

point_pair_contact_info(self: pydrake.multibody.plant.ContactResults_[Expression], i: int) → pydrake.multibody.plant.PointPairContactInfo_[Expression]: Retrieves the ith PointPairContactInfo instance. The input index i must be in the range [0, num_point_pair_contacts()) or this method throws.

SelectHydroelastic(self: pydrake.multibody.plant.ContactResults_[Expression], selector: Callable[[pydrake.multibody.plant.HydroelasticContactInfo_[Expression]], bool]) → pydrake.multibody.plant.ContactResults_[Expression]

Returns a selective copy of this object. Only HydroelasticContactInfo instances satisfying the selection criterion are copied; all other contacts (point_pair and deformable) are unconditionally copied.

Parameter selector:: Boolean predicate that returns true to select which HydroelasticContactInfo.

Note

It uses deep copy (unless the operation is trivially identifiable as being vacuous, e.g., when num_hydroelastic_contacts() == 0).

class pydrake.multibody.plant.ContactResultsToLcmSystem

Bases: pydrake.systems.framework.LeafSystem

A System that encodes ContactResults into a lcmt_contact_results_for_viz message. It has a single input port with type ContactResults<T> and a single output port with lcmt_contact_results_for_viz.

Although this class can be instantiated on all default scalars, its functionality will be limited for T = symbolic::Expression. If there are any symbolic::Variable instances in the expression, attempting to evaluate the output port will throw an exception. The support is sufficient that a systems::Diagram with a ContactResultsToLcmSystem can be scalar converted to symbolic::Expression without error, but not necessarily evaluated.

Constructing instances

Generally, you shouldn’t construct ContactResultsToLcmSystem instances directly. We recommend using one of the overloaded contact_result_vis_creation “ConnectContactResultsToDrakeVisualizer()” functions to add contact visualization to your diagram.

How contacts are described in visualization

In the visualizer, each contact between two bodies is uniquely characterized by two triples of names: (model instance name, body name, geometry name). These triples help distinguish contacts which might otherwise be ambiguous (e.g., contact with two bodies, both called “box” but part of different model instances).

ContactResultsToLcmSystem gets the model instance and body names from an instance of MultibodyPlant, but geometry names are not available from the plant. By default, ContactResultsToLcmSystem will generate a unique name based on a geometry’s unique id (e.g., “Id(7)”). For many applications (those cases where each body has only a single collision geometry), this is perfectly acceptable. However, in cases where a body has multiple collision geometries, those default names may not be helpful when viewing the visualized results. Instead, ContactResultsToLcmSystem can use the names associated with the id in a geometry::SceneGraph instance. The only method for doing this is via the contact_result_vis_creation “ConnectContactResultsToDrakeVisualizer()” functions and requires the diagram to be instantiated as double valued. If a diagram with a different scalar type is required, it should subsequently be scalar converted.

u0→

ContactResultsToLcmSystem

→ y0

__init__(self: pydrake.multibody.plant.ContactResultsToLcmSystem, plant: drake::multibody::MultibodyPlant<double>) → None

Constructs an instance with default geometry names (e.g., “Id(7)”).

Parameter plant:: The MultibodyPlant that the ContactResults are generated from.
Precondition:: The plant parameter (or a fully equivalent plant) connects to this system’s input port.
Precondition:: The plant parameter is finalized.

get_contact_result_input_port(self: pydrake.multibody.plant.ContactResultsToLcmSystem) → pydrake.systems.framework.InputPort

get_lcm_message_output_port(self: pydrake.multibody.plant.ContactResultsToLcmSystem) → pydrake.systems.framework.OutputPort

class pydrake.multibody.plant.CoulombFriction

Parameters for Coulomb’s Law of Friction, namely:

Static friction coefficient, for a pair of surfaces at rest relative to each other.
Dynamic (or kinematic) friction coefficient, for a pair of surfaces in relative motion.

These coefficients are an empirical property characterizing the interaction by friction between a pair of contacting surfaces. Friction coefficients depend upon the mechanical properties of the surfaces’ materials and on the roughness of the surfaces. They are determined experimentally.

Even though the Coulomb’s law coefficients of friction characterize a pair of surfaces interacting by friction, we associate the abstract idea of friction coefficients to a single surface by considering the coefficients for contact between two identical surfaces. For this case of two identical surfaces, the friction coefficients that describe the surface pair are taken to equal those of one of the identical surfaces. We extend this idea to the case of different surfaces by defining a combination law that allow us to obtain the Coulomb’s law coefficients of friction characterizing the pair of surfaces, given the individual friction coefficients of each surface. We would like this combination law to satisfy:

The friction coefficient of two identical surfaces is the friction coefficient of one of the surfaces.
The combination law is commutative. That is, surface A combined with surface B gives the same results as surface B combined with surface A.
For two surfaces M and N with very different friction coefficients, say μₘ ≪ μₙ, the combined friction coefficient should be in the order of magnitude of the smallest friction coefficient (in the example μₘ). To understand this requirement, consider rubber (high friction coefficient) sliding on ice (low friction coefficient). We’d like the surface pair to be defined by a friction coefficient close to that of ice, since rubber will easily slide on ice.

These requirements are met by the following ad-hoc combination law:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

See CalcContactFrictionFromSurfaceProperties(), which implements this law. More complex combination laws could also be a function of other parameters such as the mechanical properties of the interacting surfaces or even their roughnesses. For instance, if the rubber surface above has metal studs (somehow making the surface “rougher”), it will definitely have a better grip on an ice surface. Therefore this new variable should be taken into account in the combination law. Notice that in this example, this new combination law model for tires, will have a different set of requirements from the ones stated above.

Note

This class is templated; see CoulombFriction_ for the list of instantiations.

__init__(*args, **kwargs)

Overloaded function.

__init__(self: pydrake.multibody.plant.CoulombFriction) -> None

Default constructor for a frictionless surface, i.e. with zero static and dynamic coefficients of friction.

__init__(self: pydrake.multibody.plant.CoulombFriction, static_friction: float, dynamic_friction: float) -> None

Specifies both the static and dynamic friction coefficients for a given surface.

Raises

RuntimeError if any of the friction coefficients are negative or –
if dynamic_friction > static_friction (they can be equal.) –

dynamic_friction(self: pydrake.multibody.plant.CoulombFriction) → float: Returns the coefficient of dynamic friction.

static_friction(self: pydrake.multibody.plant.CoulombFriction) → float: Returns the coefficient of static friction.

template pydrake.multibody.plant.CoulombFriction_: Instantiations: CoulombFriction_[float], CoulombFriction_[AutoDiffXd], CoulombFriction_[Expression]

class pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]

Parameters for Coulomb’s Law of Friction, namely:

Static friction coefficient, for a pair of surfaces at rest relative to each other.
Dynamic (or kinematic) friction coefficient, for a pair of surfaces in relative motion.

These coefficients are an empirical property characterizing the interaction by friction between a pair of contacting surfaces. Friction coefficients depend upon the mechanical properties of the surfaces’ materials and on the roughness of the surfaces. They are determined experimentally.

Even though the Coulomb’s law coefficients of friction characterize a pair of surfaces interacting by friction, we associate the abstract idea of friction coefficients to a single surface by considering the coefficients for contact between two identical surfaces. For this case of two identical surfaces, the friction coefficients that describe the surface pair are taken to equal those of one of the identical surfaces. We extend this idea to the case of different surfaces by defining a combination law that allow us to obtain the Coulomb’s law coefficients of friction characterizing the pair of surfaces, given the individual friction coefficients of each surface. We would like this combination law to satisfy:

The friction coefficient of two identical surfaces is the friction coefficient of one of the surfaces.
The combination law is commutative. That is, surface A combined with surface B gives the same results as surface B combined with surface A.
For two surfaces M and N with very different friction coefficients, say μₘ ≪ μₙ, the combined friction coefficient should be in the order of magnitude of the smallest friction coefficient (in the example μₘ). To understand this requirement, consider rubber (high friction coefficient) sliding on ice (low friction coefficient). We’d like the surface pair to be defined by a friction coefficient close to that of ice, since rubber will easily slide on ice.

These requirements are met by the following ad-hoc combination law:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

See CalcContactFrictionFromSurfaceProperties(), which implements this law. More complex combination laws could also be a function of other parameters such as the mechanical properties of the interacting surfaces or even their roughnesses. For instance, if the rubber surface above has metal studs (somehow making the surface “rougher”), it will definitely have a better grip on an ice surface. Therefore this new variable should be taken into account in the combination law. Notice that in this example, this new combination law model for tires, will have a different set of requirements from the ones stated above.

__init__(*args, **kwargs)

Overloaded function.

__init__(self: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]) -> None

Default constructor for a frictionless surface, i.e. with zero static and dynamic coefficients of friction.

__init__(self: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd], static_friction: pydrake.autodiffutils.AutoDiffXd, dynamic_friction: pydrake.autodiffutils.AutoDiffXd) -> None

Specifies both the static and dynamic friction coefficients for a given surface.

Raises

RuntimeError if any of the friction coefficients are negative or –
if dynamic_friction > static_friction (they can be equal.) –

dynamic_friction(self: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd: Returns the coefficient of dynamic friction.

static_friction(self: pydrake.multibody.plant.CoulombFriction_[AutoDiffXd]) → pydrake.autodiffutils.AutoDiffXd: Returns the coefficient of static friction.

class pydrake.multibody.plant.CoulombFriction_[Expression]

Parameters for Coulomb’s Law of Friction, namely:

Static friction coefficient, for a pair of surfaces at rest relative to each other.
Dynamic (or kinematic) friction coefficient, for a pair of surfaces in relative motion.

These coefficients are an empirical property characterizing the interaction by friction between a pair of contacting surfaces. Friction coefficients depend upon the mechanical properties of the surfaces’ materials and on the roughness of the surfaces. They are determined experimentally.

Even though the Coulomb’s law coefficients of friction characterize a pair of surfaces interacting by friction, we associate the abstract idea of friction coefficients to a single surface by considering the coefficients for contact between two identical surfaces. For this case of two identical surfaces, the friction coefficients that describe the surface pair are taken to equal those of one of the identical surfaces. We extend this idea to the case of different surfaces by defining a combination law that allow us to obtain the Coulomb’s law coefficients of friction characterizing the pair of surfaces, given the individual friction coefficients of each surface. We would like this combination law to satisfy:

The friction coefficient of two identical surfaces is the friction coefficient of one of the surfaces.
The combination law is commutative. That is, surface A combined with surface B gives the same results as surface B combined with surface A.
For two surfaces M and N with very different friction coefficients, say μₘ ≪ μₙ, the combined friction coefficient should be in the order of magnitude of the smallest friction coefficient (in the example μₘ). To understand this requirement, consider rubber (high friction coefficient) sliding on ice (low friction coefficient). We’d like the surface pair to be defined by a friction coefficient close to that of ice, since rubber will easily slide on ice.

These requirements are met by the following ad-hoc combination law:

Click to expand C++ code...

μ = 2μₘμₙ/(μₘ + μₙ)

See CalcContactFrictionFromSurfaceProperties(), which implements this law. More complex combination laws could also be a function of other parameters such as the mechanical properties of the interacting surfaces or even their roughnesses. For instance, if the rubber surface above has metal studs (somehow making the surface “rougher”), it will definitely have a better grip on an ice surface. Therefore this new variable should be taken into account in the combination law. Notice that in this example, this new combination law model for tires, will have a different set of requirements from the ones stated above.

__init__(*args, **kwargs)

Overloaded function.

__init__(self: pydrake.multibody.plant.CoulombFriction_[Expression]) -> None

Default constructor for a frictionless surface, i.e. with zero static and dynamic coefficients of friction.

__init__(self: pydrake.multibody.plant.CoulombFriction_[Expression], static_friction: pydrake.symbolic.Expression, dynamic_friction: pydrake.symbolic.Expression) -> None

Specifies both the static and dynamic friction coefficients for a given surface.

Raises

RuntimeError if any of the friction coefficients are negative or –
if dynamic_friction > static_friction (they can be equal.) –

dynamic_friction(self: pydrake.multibody.plant.CoulombFriction_[Expression]) → pydrake.symbolic.Expression: Returns the coefficient of dynamic friction.

static_friction(self: pydrake.multibody.plant.CoulombFriction_[Expression]) → pydrake.symbolic.Expression: Returns the coefficient of static friction.

class pydrake.multibody.plant.DeformableBodyId

Uniquely identifies a deformable body. It is valid before and after Finalize().

__init__(*args, **kwargs)

static get_new_id() → pydrake.multibody.plant.DeformableBodyId: Generates a new identifier for this id type. This new identifier will be different from all previous identifiers created. This method does not make any guarantees about the values of ids from successive invocations. This method is guaranteed to be thread safe.

get_value(self: pydrake.multibody.plant.DeformableBodyId) → int: Extracts the underlying representation from the identifier. This is considered invalid for invalid ids and is strictly enforced in Debug builds.

is_valid(self: pydrake.multibody.plant.DeformableBodyId) → bool: Reports if the id is valid.

class pydrake.multibody.plant.DeformableModel

Bases: pydrake.multibody.plant.PhysicalModel

DeformableModel implements the interface in PhysicalModel and provides the functionalities to specify deformable bodies. Unlike rigid bodies, the shape of deformable bodies can change in a simulation. Each deformable body is modeled as a volumetric mesh with persisting topology, changing vertex positions, and an approximated signed distance field. A finite element model is built for each registered deformable body that is used to evaluate the dynamics of the body.

Warning

This feature is considered to be experimental and may change or be removed at any time, without any deprecation notice ahead of time.

__init__(self: pydrake.multibody.plant.DeformableModel, arg0: drake::multibody::MultibodyPlant<double>) → None

(Internal only) Constructs a DeformableModel to be owned by the given MultibodyPlant. This constructor is only intended to be called internally by MultibodyPlant.

Precondition:: plant != nullptr.
Precondition:: Finalize() has not been called on plant.

AddFixedConstraint(self: pydrake.multibody.plant.DeformableModel, body_A_id: pydrake.multibody.plant.DeformableBodyId, body_B: pydrake.multibody.tree.RigidBody, X_BA: pydrake.math.RigidTransform, shape: pydrake.geometry.Shape, X_BG: pydrake.math.RigidTransform) → pydrake.multibody.tree.MultibodyConstraintId

Defines a fixed constraint between a deformable body A and a rigid body B. Such a fixed constraint is modeled as distance holonomic constraints:

p_PᵢQᵢ(q) = 0 for each constrained vertex Pᵢ

where Pᵢ is the i-th vertex of the deformable body under constraint and Qᵢ is a point rigidly affixed to the rigid body B. To specify the constraint, we put the reference mesh M of the deformable body A in B’s body frame with the given pose X_BA and prescribe a shape G with pose X_BG in B’s body frame. All vertices Pᵢ in M that are inside (or on the surface of) G are subject to the fixed constraints with Qᵢ being coincident with Pᵢ when M is in pose X_BA. p_PᵢQᵢ(q) denotes the relative position of point Qᵢ with respect to point Pᵢ as a function of the configuration of the model q. Imposing this constraint forces Pᵢ and Qᵢ to be coincident for each vertex i of the deformable body specified to be under constraint.

Parameter body_A_id:: The unique id of the deformable body under the fixed constraint.
Parameter body_B:: The rigid body under constraint.
Parameter X_BA:: The pose of deformable body A’s reference mesh in B’s body frame
Parameter shape:: The prescribed geometry shape, attached to rigid body B, used to determine which vertices of the deformable body A is under constraint.
Parameter X_BG:: The fixed pose of the geometry frame of the given shape in body B’s frame.

Returns

the unique id of the newly added constraint.

Raises

RuntimeError if no deformable body with the given body_A_id –
has been registered. –
RuntimeError unless body_B is registered with the same –
multibody plant owning this deformable model. –
RuntimeError if shape is not supported by –
QueryObject::ComputeSignedDistanceToPoint() Currently, supported –
shapes include Box, Capsule, Cylinder, Ellipsoid, HalfSpace, and –
Sphere. –
RuntimeError if Finalize() has been called on the multibody plant –
owning this deformable model. –
RuntimeError if this DeformableModel is not of scalar type –
double. –
RuntimeError if no constraint is added (i.e. no vertex of the –
deformable body is inside the given shape with the given –
poses) –

GetBodyId(self: pydrake.multibody.plant.DeformableModel, geometry_id: pydrake.geometry.GeometryId) → pydrake.multibody.plant.DeformableBodyId

Returns the DeformableBodyId associated with the given geometry_id.

Raises

RuntimeError if the given geometry_id does not correspond to a –
deformable body registered with this model. –

GetDiscreteStateIndex(self: pydrake.multibody.plant.DeformableModel, id: pydrake.multibody.plant.DeformableBodyId) → pydrake.systems.framework.DiscreteStateIndex

Returns the discrete state index of the deformable body identified by the given id.

Raises

RuntimeError if MultibodyPlant::Finalize() has not been called –
yet. or if no deformable body with the given id has been –
registered in this model. –

GetGeometryId(self: pydrake.multibody.plant.DeformableModel, id: pydrake.multibody.plant.DeformableBodyId) → pydrake.geometry.GeometryId

Returns the GeometryId of the geometry associated with the body with the given id.

Raises: RuntimeError if no body with the given id has been registered. –

GetReferencePositions(self: pydrake.multibody.plant.DeformableModel, id: pydrake.multibody.plant.DeformableBodyId) → numpy.ndarray[numpy.float64[m, 1]]

Returns the reference positions of the vertices of the deformable body identified by the given id. The reference positions are represented as a VectorX with 3N values where N is the number of vertices. The x-, y-, and z-positions (measured and expressed in the world frame) of the j-th vertex are 3j, 3j + 1, and 3j + 2 in the VectorX.

Raises

RuntimeError if no deformable body with the given id has been –
registered in this model. –

num_bodies(self: pydrake.multibody.plant.DeformableModel) → int: Returns the number of deformable bodies registered with this DeformableModel.

RegisterDeformableBody(self: pydrake.multibody.plant.DeformableModel, geometry_instance: pydrake.geometry.GeometryInstance, config: pydrake.multibody.fem.DeformableBodyConfig, resolution_hint: float) → pydrake.multibody.plant.DeformableBodyId

Registers a deformable body in this DeformableModel with the given GeometryInstance. The body is represented in the world frame and simulated with FEM with linear elements and a first order quadrature rule that integrates linear functions exactly. See FemModel for details. Returns a unique identifier for the added geometry.

Parameter geometry_instance:: The geometry to be registered with the model.
Parameter config:: The physical properties of deformable body.
Parameter resolution_hint:: The parameter that guides the level of mesh refinement of the deformable geometry. It has length units (in meters) and roughly corresponds to a typical edge length in the resulting mesh for a primitive shape.
Precondition:: resolution_hint > 0.

Raises

RuntimeError if this DeformableModel is not of scalar type –
double. –
RuntimeError if Finalize() has been called on the multibody plant –
owning this deformable model. –

SetWallBoundaryCondition(self: pydrake.multibody.plant.DeformableModel, id: pydrake.multibody.plant.DeformableBodyId, p_WQ: numpy.ndarray[numpy.float64[3, 1]], n_W: numpy.ndarray[numpy.float64[3, 1]]) → None

Sets wall boundary conditions for the body with the given id. All vertices of the mesh of the deformable body whose reference positions are inside the prescribed open half space are put under zero displacement boundary conditions. The open half space is defined by a plane with outward normal n_W. A vertex V is considered to be subject to the boundary condition if n̂ ⋅ p_QV < 0 where Q is a point on the plane and n̂ is normalized n_W.

Parameter id:: The body to be put under boundary condition.
Parameter p_WQ:: The position of a point Q on the plane in the world frame.
Parameter n_W:: Outward normal to the half space expressed in the world frame.
Precondition:: n_W.norm() > 1e-10.

Warning

Be aware of round-off errors in floating computations when placing a vertex very close to the plane defining the half space.

Raises

RuntimeError if Finalize() has been called on the multibody plant –
owning this deformable model or if no deformable body with the –
given id has been registered in this model. –

class pydrake.multibody.plant.DiscreteContactApproximation

The type of the contact approximation used for a discrete MultibodyPlant model.

kTamsi, kSimilar and kLagged are all approximations to the same contact model – Compliant contact with regularized friction, refer to mbp_contact_modeling “Contact Modeling” for further details. The key difference however, is that the kSimilar and kLagged approximations are convex and therefore our contact solver has both theoretical and practical convergence guarantees — the solver will always succeed. Conversely, being non-convex, kTamsi can fail to find a solution.

kSap is also a convex model of compliant contact with regularized friction. There are a couple of key differences however: - Dissipation is modeled using a linear Kelvin–Voigt model, parameterized by a relaxation time constant. See accessing_contact_properties “contact parameters”. - Unlike kTamsi, kSimilar and kLagged where regularization of friction is parameterized by a stiction tolerance (see set_stiction_tolerance()), SAP determines regularization automatically solely based on numerics. Users have no control on the amount of regularization.

How to choose an approximation

The Hunt & Crossley model is based on physics, it is continuous and has been experimentally validated. Therefore it is the preferred model to capture the physics of contact.

Being approximations, kSap and kSimilar introduce a spurious effect of “gliding” in sliding contact, see [Castro et al., 2023]. This artifact is 𝒪(δt) but can be significant at large time steps and/or large slip velocities. kLagged does not suffer from this, but introduces a “weak” coupling of friction that can introduce non-negligible effects in the dynamics during impacts or strong transients.

Summarizing, kLagged is the preferred approximation when strong transients are not expected or don’t need to be accurately resolved. If strong transients do need to be accurately resolved (unusual for robotics applications), kSimilar is the preferred approximation.

References

[Castro et al., 2019] Castro A., Qu A., Kuppuswamy N., Alspach A., Sherman M, 2019. A Transition-Aware Method for the Simulation of Compliant Contact with Regularized Friction. Available online at https://arxiv.org/abs/1909.05700.
[Castro et al., 2022] Castro A., Permenter F. and Han X., 2022. An Unconstrained Convex Formulation of Compliant Contact. Available online at https://arxiv.org/abs/2110.10107.
[Castro et al., 2023] Castro A., Han X., and Masterjohn J., 2023. A Theory of Irrotational Contact Fields. Available online at https://arxiv.org/abs/2312.03908

Members:

kTamsi : TAMSI solver approximation, see [Castro et al., 2019].

kSap : SAP solver model approximation, see [Castro et al., 2022].

kSimilar : Similarity approximation found in [Castro et al., 2023].

kLagged : Approximation in which the normal force is lagged in Coulomb’s law,

such that ‖γₜ‖ ≤ μ γₙ₀, [Castro et al., 2023].

__init__(self: pydrake.multibody.plant.DiscreteContactApproximation, value: int) → None

kLagged = <DiscreteContactApproximation.kLagged: 3>

kSap = <DiscreteContactApproximation.kSap: 1>

kSimilar = <DiscreteContactApproximation.kSimilar: 2>

kTamsi = <DiscreteContactApproximation.kTamsi: 0>

property name

property value

class pydrake.multibody.plant.DiscreteContactSolver

The type of the contact solver used for a discrete MultibodyPlant model.

Note: the SAP solver only fully supports scalar type double. For scalar type AutoDiffXd, the SAP solver throws if any constraint (including contact) is detected. As a consequence, one can only run dynamic simulations without any constraints under the combination of SAP and AutoDiffXd. The SAP solver does not support symbolic calculations.

References

[Castro et al., 2019] Castro, A.M, Qu, A., Kuppuswamy, N., Alspach, A., Sherman, M.A., 2019. A Transition-Aware Method for the Simulation of Compliant Contact with Regularized Friction. Available online at https://arxiv.org/abs/1909.05700.
[Castro et al., 2022] Castro A., Permenter F. and Han X., 2022. An Unconstrained Convex Formulation of Compliant Contact. Available online at https://arxiv.org/abs/2110.10107.

Members:

kTamsi : TAMSI solver, see [Castro et al., 2019].

kSap : SAP solver, see [Castro et al., 2022].

__init__(self: pydrake.multibody.plant.DiscreteContactSolver, value: int) → None

kSap = <DiscreteContactSolver.kSap: 1>

kTamsi = <DiscreteContactSolver.kTamsi: 0>

property name

property value

class pydrake.multibody.plant.ExternallyAppliedSpatialForce

Note

This class is templated; see ExternallyAppliedSpatialForce_ for the list of instantiations.

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForce) → None

property body_index: The index of the body that the force is to be applied to.

property F_Bq_W: A spatial force applied to Body B at point Bq, expressed in the world frame.

property p_BoBq_B: A position vector from Body B’s origin (Bo) to a point Bq (a point of B), expressed in B’s frame.

template pydrake.multibody.plant.ExternallyAppliedSpatialForce_: Instantiations: ExternallyAppliedSpatialForce_[float], ExternallyAppliedSpatialForce_[AutoDiffXd], ExternallyAppliedSpatialForce_[Expression]

class pydrake.multibody.plant.ExternallyAppliedSpatialForce_[AutoDiffXd]

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForce_[AutoDiffXd]) → None

property body_index: The index of the body that the force is to be applied to.

property F_Bq_W: A spatial force applied to Body B at point Bq, expressed in the world frame.

property p_BoBq_B: A position vector from Body B’s origin (Bo) to a point Bq (a point of B), expressed in B’s frame.

class pydrake.multibody.plant.ExternallyAppliedSpatialForce_[Expression]

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForce_[Expression]) → None

property body_index: The index of the body that the force is to be applied to.

property F_Bq_W: A spatial force applied to Body B at point Bq, expressed in the world frame.

property p_BoBq_B: A position vector from Body B’s origin (Bo) to a point Bq (a point of B), expressed in B’s frame.

class pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer

Bases: pydrake.systems.framework.LeafSystem

Concatenates multiple std::vector<>’s of ExternallyAppliedSpatialForce<T>.

u0→

...→

u(N-1)→

ExternallyAppliedSpatialForceMultiplexer

→ y0

Note

This class is templated; see ExternallyAppliedSpatialForceMultiplexer_ for the list of instantiations.

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer, num_inputs: int) → None

Constructor.

Parameter num_inputs:: Number of input ports to be added.

template pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer_: Instantiations: ExternallyAppliedSpatialForceMultiplexer_[float], ExternallyAppliedSpatialForceMultiplexer_[AutoDiffXd], ExternallyAppliedSpatialForceMultiplexer_[Expression]

class pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer_[AutoDiffXd]

Bases: pydrake.systems.framework.LeafSystem_[AutoDiffXd]

Concatenates multiple std::vector<>’s of ExternallyAppliedSpatialForce<T>.

u0→

...→

u(N-1)→

ExternallyAppliedSpatialForceMultiplexer

→ y0

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer_[AutoDiffXd], num_inputs: int) → None

Constructor.

Parameter num_inputs:: Number of input ports to be added.

class pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer_[Expression]

Bases: pydrake.systems.framework.LeafSystem_[Expression]

Concatenates multiple std::vector<>’s of ExternallyAppliedSpatialForce<T>.

u0→

...→

u(N-1)→

ExternallyAppliedSpatialForceMultiplexer

→ y0

__init__(self: pydrake.multibody.plant.ExternallyAppliedSpatialForceMultiplexer_[Expression], num_inputs: int) → None

Constructor.

Parameter num_inputs:: Number of input ports to be added.

class pydrake.multibody.plant.HydroelasticContactInfo

A class containing information regarding contact and contact response between two geometries attached to a pair of bodies. This class provides the output from the Hydroelastic contact model and includes:

The shared contact surface between the two geometries, which includes

the virtual pressures acting at every point on the contact surface. - The spatial force from the integrated tractions that is applied at the centroid of the contact surface.

The two geometries, denoted M and N (and obtainable via contact_surface().id_M() and contact_surface().id_N()) are attached to bodies A and B, respectively.

When T = Expression, the class is specialized to not contain any member data, because ContactSurface doesn’t support Expression.

Note

This class is templated; see HydroelasticContactInfo_ for the list of instantiations.

__init__(*args, **kwargs)

contact_surface(self: pydrake.multibody.plant.HydroelasticContactInfo) → pydrake.geometry.ContactSurface: Returns a reference to the ContactSurface data structure. Note that the mesh and gradient vector fields are expressed in the world frame.

F_Ac_W(self: pydrake.multibody.plant.HydroelasticContactInfo) → pydrake.multibody.math.SpatialForce: Gets the spatial force applied on body A, at the centroid point C of the surface mesh M, and expressed in the world frame W. The position p_WC of the centroid point C in the world frame W can be obtained with contact_surface().centroid().

template pydrake.multibody.plant.HydroelasticContactInfo_: Instantiations: HydroelasticContactInfo_[float], HydroelasticContactInfo_[AutoDiffXd], HydroelasticContactInfo_[Expression]

class pydrake.multibody.plant.HydroelasticContactInfo_[AutoDiffXd]

A class containing information regarding contact and contact response between two geometries attached to a pair of bodies. This class provides the output from the Hydroelastic contact model and includes:

The shared contact surface between the two geometries, which includes

the virtual pressures acting at every point on the contact surface. - The spatial force from the integrated tractions that is applied at the centroid of the contact surface.

The two geometries, denoted M and N (and obtainable via contact_surface().id_M() and contact_surface().id_N()) are attached to bodies A and B, respectively.

When T = Expression, the class is specialized to not contain any member data, because ContactSurface doesn’t support Expression.

__init__(*args, **kwargs)

contact_surface(self: pydrake.multibody.plant.HydroelasticContactInfo_[AutoDiffXd]) → pydrake.geometry.ContactSurface_[AutoDiffXd]: Returns a reference to the ContactSurface data structure. Note that the mesh and gradient vector fields are expressed in the world frame.

F_Ac_W(self: pydrake.multibody.plant.HydroelasticContactInfo_[AutoDiffXd]) → pydrake.multibody.math.SpatialForce_[AutoDiffXd]: Gets the spatial force applied on body A, at the centroid point C of the surface mesh M, and expressed in the world frame W. The position p_WC of the centroid point C in the world frame W can be obtained with contact_surface().centroid().

class pydrake.multibody.plant.HydroelasticContactInfo_[Expression]

A class containing information regarding contact and contact response between two geometries attached to a pair of bodies. This class provides the output from the Hydroelastic contact model and includes:

The shared contact surface between the two geometries, which includes

the virtual pressures acting at every point on the contact surface. - The spatial force from the integrated tractions that is applied at the centroid of the contact surface.

The two geometries, denoted M and N (and obtainable via contact_surface().id_M() and contact_surface().id_N()) are attached to bodies A and B, respectively.

When T = Expression, the class is specialized to not contain any member data, because ContactSurface doesn’t support Expression.

__init__(*args, **kwargs)

class pydrake.multibody.plant.MultibodyPlant

Bases: pydrake.systems.framework.LeafSystem

MultibodyPlant is a Drake system framework representation (see systems::System) for the model of a physical system consisting of a collection of interconnected bodies. See multibody for an overview of concepts/notation.

actuation→

applied_generalized_force→

applied_spatial_force→

model_instance_name[i]_actuation→

model_instance_name[i]_desired_state→

geometry_query→

MultibodyPlant

→ state

→ body_poses

→ body_spatial_velocities

→ body_spatial_accelerations

→ generalized_acceleration

→ net_actuation

→ reaction_forces

→ contact_results

→ model_instance_name[i]_state

→ model_instance_name[i]_generalized_acceleration

→ model_instance_name[i]_generalized_contact_forces

→ model_instance_name[i]_net_actuation

→ geometry_pose

→ deformable_body_configuration

The ports whose names begin with model_instance_name[i] represent groups of ports, one for each of the model_instances “model instances”, with i ∈ {0, …, N-1} for the N model instances. If a model instance does not contain any data of the indicated type the port will still be present but its value will be a zero-length vector. (Model instances world_model_instance() and default_model_instance() always exist.)

The ports shown in green are for communication with Drake’s geometry::SceneGraph “SceneGraph” system for dealing with geometry.

MultibodyPlant provides a user-facing API for:

mbp_input_and_output_ports “Ports”:

Access input and output ports. - mbp_construction “Construction”: Add bodies, joints, frames, force elements, and actuators. - mbp_geometry “Geometry”: Register geometries to a provided SceneGraph instance. - mbp_contact_modeling “Contact modeling”: Select and parameterize contact models. - mbp_state_accessors_and_mutators “State access and modification”: Obtain and manipulate position and velocity state variables. - mbp_parameters “Parameters” Working with system parameters for various multibody elements. - mbp_working_with_free_bodies “Free bodies”: Work conveniently with free (floating) bodies. - mbp_kinematic_and_dynamic_computations “Kinematics and dynamics”: Perform systems::Context “Context”-dependent kinematic and dynamic queries. - mbp_system_matrix_computations “System matrices”: Explicitly form matrices that appear in the equations of motion. - mbp_introspection “Introspection”: Perform introspection to find out what’s in the MultibodyPlant.

**** Model Instances

A MultiBodyPlant may contain multiple model instances. Each model instance corresponds to a set of bodies and their connections (joints). Model instances provide methods to get or set the state of the set of bodies (e.g., through GetPositionsAndVelocities() and SetPositionsAndVelocities()), connecting controllers (through get_state_output_port() and get_actuation_input_port()), and organizing duplicate models (read through a parser). In fact, many MultibodyPlant methods are overloaded to allow operating on the entire plant or just the subset corresponding to the model instance; for example, one GetPositions() method obtains the generalized positions for the entire plant while another GetPositions() method obtains the generalized positions for model instance.

Model instances are frequently defined through SDFormat files (using the model tag) and are automatically created when SDFormat files are parsed (by Parser). There are two special multibody::ModelInstanceIndex values. The world body is always multibody::ModelInstanceIndex 0. multibody::ModelInstanceIndex 1 is reserved for all elements with no explicit model instance and is generally only relevant for elements created programmatically (and only when a model instance is not explicitly specified). Note that Parser creates model instances (resulting in a multibody::ModelInstanceIndex ≥ 2) as needed.

See num_model_instances(), num_positions(), num_velocities(), num_actuated_dofs(), AddModelInstance() GetPositionsAndVelocities(), GetPositions(), GetVelocities(), SetPositionsAndVelocities(), SetPositions(), SetVelocities(), GetPositionsFromArray(), GetVelocitiesFromArray(), SetPositionsInArray(), SetVelocitiesInArray(), SetActuationInArray(), HasModelInstanceNamed(), GetModelInstanceName(), get_state_output_port(), get_actuation_input_port().

**** System dynamics

The state of a multibody system x = [q; v] is given by its generalized positions vector q, of size nq (see num_positions()), and by its generalized velocities vector v, of size nv (see num_velocities()).

A MultibodyPlant can be constructed to be either continuous or discrete. The choice is indicated by the time_step passed to the constructor – a non-zero time_step indicates a discrete plant, while a zero time_step indicates continuous. A systems::Simulator “Simulator” will step a discrete plant using the indicated time_step, but will allow a numerical integrator to choose how to advance time for a continuous MultibodyPlant.

We’ll discuss continuous plant dynamics in this section. Discrete dynamics is more complicated and gets its own section below.

As a Drake systems::System “System”, MultibodyPlant implements the governing equations for a multibody dynamical system in the form ẋ = f(t, x, u) with t being time and u external inputs such as actuation forces. The governing equations for the dynamics of a multibody system modeled with MultibodyPlant are [Featherstone 2008, Jain 2010]:

Click to expand C++ code...

q̇ = N(q)v
(1)    M(q)v̇ + C(q, v)v = τ

where M(q) is the mass matrix of the multibody system (including rigid body mass properties and reflected_inertia “reflected inertias”), C(q, v)v contains Coriolis, centripetal, and gyroscopic terms and N(q) is the kinematic coupling matrix describing the relationship between q̇ (the time derivatives of the generalized positions) and the generalized velocities v, [Seth 2010]. N(q) is an nq x nv matrix. The vector τ ∈ ℝⁿᵛ on the right hand side of Eq. (1) is the system’s generalized forces. These incorporate gravity, springs, externally applied body forces, constraint forces, and contact forces.

**** Discrete system dynamics

We’ll start with the basic difference equation interpretation of a discrete plant and then explain some Drake-specific subtleties.

Note

We use “kinematics” here to refer to quantities that involve only position or velocity, and “dynamics” to refer to quantities that also involve forces.

By default, a discrete MultibodyPlant has these update dynamics:

x[0] = initial kinematics state variables x (={q, v}), s s[0] = empty (no sample yet)

s[n+1] = g(t[n], x[n], u[n]) record sample x[n+1] = f(t[n], x[n], u[n]) update kinematics yd[n+1] = gd(s) dynamic outputs use sampled values yk[n+1] = gk(x) kinematic outputs use current x

Optionally, output port sampling can be disabled. In that case we have:

x[n+1] = f(t[n], x[n], u[n]) update kinematics yd[n+1] = gd(g(t, x, u)) dynamic outputs use current values yk[n+1] = gk(x) kinematic outputs use current x

We’re using yd and yk above to represent the calculated values of dynamic and kinematic output ports, resp. Kinematic output ports are those that depend only on position and velocity: state, body_poses, body_spatial_velocities. Everything else depends on forces so is a dynamic output port: body_spatial_accelerations, generalized_acceleration, net_actuation, reaction_forces, and contact_results.

Use the function SetUseSampledOutputPorts() to choose which dynamics you prefer. The default behavior (output port sampling) is more efficient for simulation, but use slightly-different kinematics for the dynamic output port computations versus the kinematic output ports. Disabling output port sampling provides “live” output port results that are recalculated from the current state and inputs whenever changes occur. It also eliminates the sampling state variable (s above). Note that kinematic output ports (that is, those depending only on position and velocity) are always “live” – they are calculated as needed from the current (updated) state.

The reason that the default mode is more efficient for simulation is that the sample variable s records expensive-to-compute results (such as hydroelastic contact forces) that are needed to advance the state x. Those results are thus available for free at the start of step n. If instead we wait until after the state is updated to n+1, we would have to recalculate those expensive results at the new state in order to report them. Thus sampling means the output ports show the results that were calculated using kinematics values x[n], although the Context has been updated to kinematics values x[n+1]. If that isn’t tolerable you should disable output port sampling. You can also force an update to occur using ExecuteForcedEvents().

See output_port_sampling “Output port sampling” below for more practical considerations.

Minor details most users won’t care about:

The sample variable s is a Drake Abstract state variable. When it is

present, the plant update is performed using an Unrestricted update; when it is absent we are able to use a Discrete update. Some Drake features (e.g. linearization of discrete systems) may be restricted to systems that use only Discrete (numeric) state variables and Discrete update. - The sample variable s is used only by output ports. It does not affect the behavior of any MultibodyPlant “Calc” or “Eval” functions – those are always calculated using the current values of time, kinematic state, and input port values.

**** Output port sampling

As described in mbp_discrete_dynamics “Discrete system dynamics” above, the semantics of certain MultibodyPlant output ports depends on whether the plant is configured to advance using continuous time integration or discrete time steps (see is_discrete()). This section explains the details, focusing on the practical aspects moreso than the equations.

Output ports that only depend on the [q, v] kinematic state (such as get_body_poses_output_port() or get_body_spatial_velocities_output_port()) do not change semantics for continuous vs discrete time. In all cases, the output value is a function of the kinematic state in the context.

Output ports that incorporate dynamics (i.e., forces) do change semantics based on the plant mode. Imagine that the get_applied_spatial_force_input_port() provides a continuously time-varying input force. The get_body_spatial_accelerations_output_port() output is dependent on that force. We could return a snapshot of the acceleration that was used in the last time step, or we could recalculate the acceleration to immediately reflect the changing forces. We call the former a “sampled” port and the latter a “live” port.

For a continuous-time plant, there is no distinction – the output port is always live – it immediately reflects the instantaneous input value. It is a “direct feedthrough” output port (see SystemBase::GetDirectFeedthroughs()).

For a discrete-time plant, the user can choose whether the output should be sampled or live: Use the function SetUseSampledOutputPorts() to change whether output ports are sampled or not, and has_sampled_output_ports() to check the current setting. When sampling is disabled, the only state in the context is the kinematic [q, v], so dynamics output ports will always reflect the instantaneous answer (i.e., direct feedthrough). When sampling is enabled (the default), the plant state incorporates a snapshot of the most recent step’s kinematics and dynamics, and the output ports will reflect that sampled state (i.e., not direct feedthrough). For a detailed discussion, see mbp_discrete_dynamics “Discrete system dynamics”.

For a discrete-time plant, the sampled outputs are generally much faster to calculate than the feedthrough outputs when any inputs ports are changing values faster than the discrete time step, e.g., during a simulation. When input ports are fixed, or change at the time step rate (e.g., during motion planning), sampled vs feedthrough will have similar computational performance.

Direct plant API function calls (e.g., EvalBodySpatialAccelerationInWorld()) that depend on forces always use the instantaneous (not sampled) accelerations.

Here are some practical tips that might help inform your particular situation:

(1) If you need a minimal-state representation for motion planning, mathematical optimization, or similar, then you can either use a continuous-time plant or set the config option use_sampled_output_ports=false on a discrete-time plant.

(2) By default, setting the positions of a discrete-time plant in the Context will not have any effect on the dynamics-related output ports, e.g., the contact results will not change. If you need to see changes to outputs without running the plant in a Simulator, then you can either use a continuous-time plant, set the config option use_sampled_output_ports=false, or use ExecuteForcedEvents() to force a dynamics step and then the outputs (and positions) will change.

**** Actuation

In a MultibodyPlant model an actuator can be added as a JointActuator, see AddJointActuator(). The plant declares actuation input ports to provide feedforward actuation, both for the MultibodyPlant as a whole (see get_actuation_input_port()) and for each individual model_instances “model instance” in the MultibodyPlant (see get_actuation_input_port(ModelInstanceIndex)const “get_actuation_input_port(ModelInstanceIndex)”). Any actuation input ports not connected are assumed to be zero. Actuation values from the full MultibodyPlant model port (get_actuation_input_port()) and from the per model-instance ports ( get_actuation_input_port(ModelInstanceIndex)const “get_actuation_input_port(ModelInstanceIndex)”) are summed up.

Note

A JointActuator’s index into the vector data supplied to MultibodyPlant’s actuation input port for all actuators (get_actuation_input_port()) is given by JointActuator::input_start(), NOT by its JointActuatorIndex. That is, the vector element data for a JointActuator at index JointActuatorIndex(i) in the full input port vector is found at index: MultibodyPlant::get_joint_actuator(JointActuatorIndex(i)).input_start(). For the get_actuation_input_port(ModelInstanceIndex)const “get_actuation_input_port(ModelInstanceIndex)” specific to a model index, the vector data is ordered by monotonically increasing JointActuatorIndex for the actuators within that model instance: the 0ᵗʰ vector element corresponds to the lowest-numbered JointActuatorIndex of that instance, the 1ˢᵗ vector element corresponds to the second-lowest-numbered JointActuatorIndex of that instance, etc.

Note

The following snippet shows how per model instance actuation can be set:

Click to expand C++ code...

ModelInstanceIndex model_instance_index = ...;
VectorX<T> u_instance(plant.num_actuated_dofs(model_instance_index));
int offset = 0;
for (JointActuatorIndex joint_actuator_index :
plant.GetJointActuatorIndices(model_instance_index)) {
const JointActuator<T>& actuator = plant.get_joint_actuator(
joint_actuator_index);
const Joint<T>& joint = actuator.joint();
VectorX<T> u_joint = ... my_actuation_logic_for(joint) ...;
ASSERT(u_joint.size() == joint_actuator.num_inputs());
u_instance.segment(offset, u_joint.size()) = u_joint;
offset += u_joint.size();
}
plant.get_actuation_input_port(model_instance_index).FixValue(
plant_context, u_instance);

Note

To inter-operate between the whole plant actuation vector and sets of per-model instance actuation vectors, see SetActuationInArray() to gather the model instance vectors into a whole plant vector and GetActuationFromArray() to scatter the whole plant vector into per-model instance vectors.

Warning

Effort limits (JointActuator::effort_limit()) are not enforced, unless PD controllers are defined. See pd_controllers “Using PD controlled actuators”.

** Using PD controlled actuators

While PD controllers can be modeled externally and be connected to the MultibodyPlant model via the get_actuation_input_port(), simulation stability at discrete-time steps can be compromised for high controller gains. For such cases, simulation stability and robustness can be improved significantly by moving your PD controller into the plant where the discrete solver can strongly couple controller and model dynamics.

Warning

Currently, this feature is only supported for discrete models (is_discrete() is true) using the SAP solver (get_discrete_contact_solver() returns DiscreteContactSolver::kSap.)

PD controlled joint actuators can be defined by setting PD gains for each joint actuator, see JointActuator::set_controller_gains(). Unless these gains are specified, joint actuators will not be PD controlled and JointActuator::has_controller() will return False.

Warning

For PD controlled models, all joint actuators in a model instance are required to have PD controllers defined. That is, partially PD controlled model instances are not supported. An exception will be thrown when evaluating the actuation input ports if only a subset of the actuators in a model instance is PD controlled.

For models with PD controllers, the actuation torque per actuator is computed according to:

Click to expand C++ code...

ũ = -Kp⋅(q − qd) - Kd⋅(v − vd) + u_ff
u = max(−e, min(e, ũ))

where qd and vd are desired configuration and velocity (see get_desired_state_input_port()) for the actuated joint (see JointActuator::joint()), Kp and Kd are the proportional and derivative gains of the actuator (see JointActuator::get_controller_gains()), u_ff is the feed-forward actuation specified with get_actuation_input_port(), and e corresponds to effort limit (see JointActuator::effort_limit()).

Notice that actuation through get_actuation_input_port() and PD control are not mutually exclusive, and they can be used together. This is better explained through examples: 1. PD controlled gripper. In this case, only PD control is used to drive the opening and closing of the fingers. The feed-forward term is assumed to be zero and the actuation input port is not required to be connected. 2. Robot arm. A typical configuration consists on applying gravity compensation in the feed-forward term plus PD control to drive the robot to a given desired state.

** Actuation input ports requirements

The following table specifies whether actuation ports are required to be connected or not:

Port | without PD control | with PD control | |

——————————: :——————-: |
————-: | get_actuation_input_port() | yes | no¹ | |

get_desired_state_input_port() | no² | yes |

¹ Feed-forward actuation is not required for models with PD controlled actuators. This simplifies the diagram wiring for models that only rely on PD controllers.

² This port is always declared, though it will be zero sized for model instances with no PD controllers.

** Net actuation

The total joint actuation applied via the actuation input port (get_actuation_input_port()) and applied by the PD controllers is reported by the net actuation port (get_net_actuation_output_port()). That is, the net actuation port reports the total actuation applied by a given actuator.

Note

PD controllers are ignored when a joint is locked (see Joint::Lock()), and thus they have no effect on the actuation output.

**** Loading models from SDFormat files

Drake has the capability to load multibody models from SDFormat and URDF files. Consider the example below which loads an acrobot model:

Click to expand C++ code...

MultibodyPlant<T> acrobot;
SceneGraph<T> scene_graph;
Parser parser(&acrobot, &scene_graph);
const std::string url =
"package://drake/multibody/benchmarks/acrobot/acrobot.sdf";
parser.AddModelsFromUrl(url);

As in the example above, for models including visual geometry, collision geometry or both, the user must specify a SceneGraph for geometry handling. You can find a full example of the LQR controlled acrobot in examples/multibody/acrobot/run_lqr.cc.

AddModelFromFile() can be invoked multiple times on the same plant in order to load multiple model instances. Other methods are available on Parser such as AddModels() which allows creating model instances per each <model> tag found in the file. Please refer to each of these methods’ documentation for further details.

**** Working with SceneGraph

** Adding a MultibodyPlant connected to a SceneGraph to your Diagram

Probably the simplest way to add and wire up a MultibodyPlant with a SceneGraph in your Diagram is using AddMultibodyPlantSceneGraph().

Recommended usages:

Assign to a MultibodyPlant reference (ignoring the SceneGraph):

Click to expand C++ code...

MultibodyPlant<double>& plant =
AddMultibodyPlantSceneGraph(&builder, 0.0 /+ time_step +/);
plant.DoFoo(...);

This flavor is the simplest, when the SceneGraph is not explicitly needed. (It can always be retrieved later via GetSubsystemByName(“scene_graph”).)

Assign to auto, and use the named public fields:

Click to expand C++ code...

auto items = AddMultibodyPlantSceneGraph(&builder, 0.0 /+ time_step +/);
items.plant.DoFoo(...);
items.scene_graph.DoBar(...);

or taking advantage of C++’s structured binding:

Click to expand C++ code...

auto [plant, scene_graph] = AddMultibodyPlantSceneGraph(&builder, 0.0);
...
plant.DoFoo(...);
scene_graph.DoBar(...);

This is the easiest way to use both the plant and scene_graph.

Assign to already-declared pointer variables:

Click to expand C++ code...

MultibodyPlant<double>* plant{};
SceneGraph<double>* scene_graph{};
std::tie(plant, scene_graph) =
AddMultibodyPlantSceneGraph(&builder, 0.0 /+ time_step +/);
plant->DoFoo(...);
scene_graph->DoBar(...);

This flavor is most useful when the pointers are class member fields (and so perhaps cannot be references).

** Registering geometry with a SceneGraph

MultibodyPlant users can register geometry with a SceneGraph for essentially two purposes; a) visualization and, b) contact modeling.

Before any geometry registration takes place, a user must first make a call to RegisterAsSourceForSceneGraph() in order to register the MultibodyPlant as a client of a SceneGraph instance, point at which the plant will have assigned a valid geometry::SourceId. At Finalize(), MultibodyPlant will declare input/output ports as appropriate to communicate with the SceneGraph instance on which registrations took place. All geometry registration must be performed pre-finalize.

Multibodyplant declares an input port for geometric queries, see get_geometry_query_input_port(). If MultibodyPlant registers geometry with a SceneGraph via calls to RegisterCollisionGeometry(), users may use this port for geometric queries. The port must be connected to the same SceneGraph used for registration. The preferred mechanism is to use AddMultibodyPlantSceneGraph() as documented above.

In extraordinary circumstances, this can be done by hand and the setup process will include:

Call to RegisterAsSourceForSceneGraph().
Calls to RegisterCollisionGeometry(), as many as needed.
Call to Finalize(), user is done specifying the model.

4. Connect geometry::SceneGraph::get_query_output_port() to get_geometry_query_input_port(). 5. Connect get_geometry_pose_output_port() to geometry::SceneGraph::get_source_pose_port()

Refer to the documentation provided in each of the methods above for further details.

** Accessing point contact parameters MultibodyPlant’s point contact model looks for model parameters stored as geometry::ProximityProperties by geometry::SceneGraph. These properties can be obtained before or after context creation through geometry::SceneGraphInspector APIs as outlined below. MultibodyPlant expects the following properties for point contact modeling:

|Group name|Property Name|Required|Property Type|Property Description| |:--------:|:———–:|:------:|:—————-:|:-------------------| |material|coulomb_friction|yes¹|CoulombFriction<T>|Static and Dynamic friction.| |material|point_contact_stiffness|no²|T| Compliant point contact stiffness.| |material|hunt_crossley_dissipation |no²⁴|T| Compliant contact dissipation.| |material|relaxation_time|yes³⁴|T|Linear Kelvin–Voigt model parameter.|

¹ Collision geometry is required to be registered with a geometry::ProximityProperties object that contains the (“material”, “coulomb_friction”) property. If the property is missing, MultibodyPlant will throw an exception.

² If the property is missing, MultibodyPlant will use a heuristic value as the default. Refer to the section point_contact_defaults “Point Contact Default Parameters” for further details.

³ When using a linear Kelvin–Voigt model of dissipation (for instance when selecting the SAP solver), collision geometry is required to be registered with a geometry::ProximityProperties object that contains the (“material”, “relaxation_time”) property. If the property is missing, an exception will be thrown.

⁴ We allow to specify both hunt_crossley_dissipation and relaxation_time for a given geometry. However only one of these will get used, depending on the configuration of the MultibodyPlant. As an example, if the SAP contact approximation is specified (see set_discrete_contact_approximation()) only the relaxation_time is used while hunt_crossley_dissipation is ignored. Conversely, if the TAMSI, Similar or Lagged approximation is used (see set_discrete_contact_approximation()) only hunt_crossley_dissipation is used while relaxation_time is ignored. Currently, a continuous MultibodyPlant model will always use the Hunt & Crossley model and relaxation_time will be ignored.

Accessing and modifying contact properties requires interfacing with geometry::SceneGraph’s model inspector. Interfacing with a model inspector obtained from geometry::SceneGraph will provide the default registered values for a given parameter. These are the values that will initially appear in a systems::Context created by CreateDefaultContext(). Subsequently, true system parameters can be accessed and changed through a systems::Context once available. For both of the above cases, proximity properties are accessed through geometry::SceneGraphInspector APIs.

Before context creation an inspector can be retrieved directly from SceneGraph as:

Click to expand C++ code...

// For a SceneGraph<T> instance called scene_graph.
const geometry::SceneGraphInspector<T>& inspector =
scene_graph.model_inspector();

After context creation, an inspector can be retrieved from the state stored in the context:

Click to expand C++ code...

// For a MultibodyPlant<T> instance called mbp and a Context<T> called
// context.
const geometry::SceneGraphInspector<T>& inspector =
mbp.EvalSceneGraphInspector(context);

Once an inspector is available, proximity properties can be retrieved as:

Click to expand C++ code...

// For a body with GeometryId called geometry_id
const geometry::ProximityProperties* props =
inspector.GetProximityProperties(geometry_id);
const CoulombFriction<T>& geometry_friction =
props->GetProperty<CoulombFriction<T>>("material",
"coulomb_friction");

**** Working with MultibodyElement parameters Several MultibodyElements expose parameters, allowing the user flexible modification of some aspects of the plant’s model, post systems::Context creation. For details, refer to the documentation for the MultibodyElement whose parameters you are trying to modify/access (e.g. RigidBody, FixedOffsetFrame, etc.)

As an example, here is how to access and modify rigid body mass parameters:

Click to expand C++ code...

MultibodyPlant<double> plant;
// ... Code to add bodies, finalize plant, and to obtain a context.
const RigidBody<double>& body =
plant.GetRigidBodyByName("BodyName");
const SpatialInertia<double> M_BBo_B =
body.GetSpatialInertiaInBodyFrame(context);
// .. logic to determine a new SpatialInertia parameter for body.
const SpatialInertia<double>& M_BBo_B_new = ....

// Modify the body parameter for spatial inertia.
body.SetSpatialInertiaInBodyFrame(&context, M_BBo_B_new);

Another example, working with automatic differentiation in order to take derivatives with respect to one of the bodies’ masses:

Click to expand C++ code...

MultibodyPlant<double> plant;
// ... Code to add bodies, finalize plant, and to obtain a
// context and a body's spatial inertia M_BBo_B.

// Scalar convert the plant.
unique_ptr<MultibodyPlant<AutoDiffXd>> plant_autodiff =
systems::System<double>::ToAutoDiffXd(plant);
unique_ptr<Context<AutoDiffXd>> context_autodiff =
plant_autodiff->CreateDefaultContext();
context_autodiff->SetTimeStateAndParametersFrom(context);

const RigidBody<AutoDiffXd>& body =
plant_autodiff->GetRigidBodyByName("BodyName");

// Modify the body parameter for mass.
const AutoDiffXd mass_autodiff(mass, Vector1d(1));
body.SetMass(context_autodiff.get(), mass_autodiff);

// M_autodiff(i, j).derivatives()(0), contains the derivatives of
// M(i, j) with respect to the body's mass.
MatrixX<AutoDiffXd> M_autodiff(plant_autodiff->num_velocities(),
plant_autodiff->num_velocities());
plant_autodiff->CalcMassMatrix(*context_autodiff, &M_autodiff);

**** Adding modeling elements

Add multibody elements to a MultibodyPlant with methods like:

Bodies: AddRigidBody()
Joints: AddJoint()
see mbp_construction “Construction” for more.

All modeling elements must be added before Finalize() is called. See mbp_finalize_stage “Finalize stage” for a discussion.

**** Modeling contact

Please refer to drake_contacts “Contact Modeling in Drake” for details on the available approximations, setup, and considerations for a multibody simulation with frictional contact.

**** Energy and Power

MultibodyPlant implements the System energy and power methods, with some limitations. - Kinetic energy: fully implemented. - Potential energy and conservative power: currently include only gravity and contributions from ForceElement objects; potential energy from compliant contact and joint limits are not included. - Nonconservative power: currently includes only contributions from ForceElement objects; actuation and input port forces, joint damping, and dissipation from joint limits, friction, and contact dissipation are not included.

See Drake issue #12942 for more discussion.

**** Finalize() stage

Once the user is done adding modeling elements and registering geometry, a call to Finalize() must be performed. This call will: - Build the underlying tree structure of the multibody model, - declare the plant’s state, - declare the plant’s input and output ports, - declare collision filters to ignore collisions among rigid bodies: - between rigid bodies connected by a joint, - within subgraphs of welded rigid bodies. Note that MultibodyPlant will not introduce any collision filters on deformable bodies.

**** References

[Featherstone 2008] Featherstone, R., 2008.

Rigid body dynamics algorithms. Springer. - [Jain 2010] Jain, A., 2010. Robot and multibody dynamics: analysis and algorithms. Springer Science & Business Media. - [Seth 2010] Seth, A., Sherman, M., Eastman, P. and Delp, S., 2010. Minimal formulation of joint motion for biomechanisms. Nonlinear dynamics, 62(1), pp.291-303.

Note

This class is templated; see MultibodyPlant_ for the list of instantiations.

__init__(self: pydrake.multibody.plant.MultibodyPlant, time_step: float) → None

This constructor creates a plant with a single “world” body. Therefore, right after creation, num_bodies() returns one.

MultibodyPlant offers two different modalities to model mechanical systems in time. These are: 1. As a discrete system with periodic updates, time_step is strictly greater than zero. 2. As a continuous system, time_step equals exactly zero.

Currently the discrete model is preferred for simulation given its robustness and speed in problems with frictional contact. However this might change as we work towards developing better strategies to model contact. See multibody_simulation for further details.

Warning

Users should be aware of current limitations in either modeling modality. While the discrete model is often the preferred option for problems with frictional contact given its robustness and speed, it might become unstable when using large feedback gains, high damping or large external forcing. MultibodyPlant will throw an exception whenever the discrete solver is detected to fail. Conversely, the continuous modality has the potential to leverage the robustness and accuracy control provide by Drake’s integrators. However thus far this has proved difficult in practice and especially due to poor performance.

Parameter time_step:: Indicates whether this plant is modeled as a continuous system (time_step = 0) or as a discrete system with periodic updates of period time_step > 0. See multibody_simulation for further details.

Warning

Currently the continuous modality with time_step = 0 does not support joint limits for simulation, these are ignored. MultibodyPlant prints a warning to console if joint limits are provided. If your simulation requires joint limits currently you must use a discrete MultibodyPlant model.

Raises: RuntimeError if time_step is negative. –

AddBallConstraint(self: pydrake.multibody.plant.MultibodyPlant, body_A: pydrake.multibody.tree.RigidBody, p_AP: numpy.ndarray[numpy.float64[3, 1]], body_B: pydrake.multibody.tree.RigidBody, p_BQ: Optional[numpy.ndarray[numpy.float64[3, 1]]] = None) → pydrake.multibody.tree.MultibodyConstraintId

Defines a constraint such that point P affixed to body A is coincident at all times with point Q affixed to body B, effectively modeling a ball-and-socket joint.

Parameter body_A:: RigidBody to which point P is rigidly attached.
Parameter p_AP:: Position of point P in body A’s frame.
Parameter body_B:: RigidBody to which point Q is rigidly attached.
Parameter p_BQ:: (optional) Position of point Q in body B’s frame. If p_BQ is std::nullopt, then p_BQ will be computed so that the constraint is satisfied for the default configuration at Finalize() time; subsequent changes to the default configuration will not change the computed p_BQ.

Returns

the id of the newly added constraint.

Raises

RuntimeError if bodies A and B are the same body. –
RuntimeError if the MultibodyPlant has already been finalized. –
RuntimeError if this MultibodyPlant is not a discrete model –
(is_discrete() == false) –
RuntimeError if this MultibodyPlant's underlying contact –
solver is not SAP. (i.e. get_discrete_contact_solver() != –
DiscreteContactSolver::kSap) –

AddCouplerConstraint(self: pydrake.multibody.plant.MultibodyPlant, joint0: pydrake.multibody.tree.Joint, joint1: pydrake.multibody.tree.Joint, gear_ratio: float, offset: float = 0.0) → pydrake.multibody.tree.MultibodyConstraintId

Defines a holonomic constraint between two single-dof joints joint0 and joint1 with positions q₀ and q₁, respectively, such that q₀ = ρ⋅q₁ + Δq, where ρ is the gear ratio and Δq is a fixed offset. The gear ratio can have units if the units of q₀ and q₁ are different. For instance, between a prismatic and a revolute joint the gear ratio will specify the “pitch” of the resulting mechanism. As defined, offset has units of q₀.

Note

joint0 and/or joint1 can still be actuated, regardless of whether we have coupler constraint among them. That is, one or both of these joints can have external actuation applied to them.

Note

Generally, to couple (q0, q1, q2), the user would define a coupler between (q0, q1) and a second coupler between (q1, q2), or any combination therein.

Raises

if joint0 and joint1 are not both single-dof joints. –
RuntimeError if the MultibodyPlant has already been finalized. –
RuntimeError if this MultibodyPlant is not a discrete model –
(is_discrete() == false) –
RuntimeError if this MultibodyPlant's underlying contact –
solver is not SAP. (i.e. get_discrete_contact_solver() != –
DiscreteContactSolver::kSap) –

AddDistanceConstraint(self: pydrake.multibody.plant.MultibodyPlant, body_A: pydrake.multibody.tree.RigidBody, p_AP: numpy.ndarray[numpy.float64[3, 1]], body_B: pydrake.multibody.tree.RigidBody, p_BQ: numpy.ndarray[numpy.float64[3, 1]], distance: float, stiffness: float = inf, damping: float = 0.0) → pydrake.multibody.tree.MultibodyConstraintId

Defines a distance constraint between a point P on a body A and a point Q on a body B.

This constraint can be compliant, modeling a spring with free length distance and given stiffness and damping parameters between points P and Q. For d = ‖p_PQ‖, then a compliant distance constraint models a spring with force along p_PQ given by:

f = −stiffness ⋅ d − damping ⋅ ḋ

Parameter body_A:: RigidBody to which point P is rigidly attached.
Parameter p_AP:: Position of point P in body A’s frame.
Parameter body_B:: RigidBody to which point Q is rigidly attached.
Parameter p_BQ:: Position of point Q in body B’s frame.
Parameter distance:: Fixed length of the distance constraint, in meters. It must be strictly positive.
Parameter stiffness:: For modeling a spring with free length equal to distance, the stiffness parameter in N/m. Optional, with its default value being infinite to model a rigid massless rod of length distance connecting points A and B.
Parameter damping:: For modeling a spring with free length equal to distance, damping parameter in N⋅s/m. Optional, with its default value being zero for a non-dissipative constraint.

Returns: the id of the newly added constraint.

Warning

Currently, it is the user’s responsibility to initialize the model’s context in a configuration compatible with the newly added constraint.

Warning

A distance constraint is the wrong modeling choice if the distance needs to go through zero. To constrain two points to be coincident we need a 3-dof ball constraint, the 1-dof distance constraint is singular in this case. Therefore we require the distance parameter to be strictly positive.

Raises

RuntimeError if bodies A and B are the same body. –
RuntimeError if distance is not strictly positive. –
RuntimeError if stiffness is not positive or zero. –
RuntimeError if damping is not positive or zero. –
RuntimeError if the MultibodyPlant has already been finalized. –
RuntimeError if this MultibodyPlant is not a discrete model –
(is_discrete() == false) –
RuntimeError if this MultibodyPlant's underlying contact –
solver is not SAP. (i.e. get_discrete_contact_solver() != –
DiscreteContactSolver::kSap) –

AddForceElement(self: pydrake.multibody.plant.MultibodyPlant, force_element: pydrake.multibody.tree.ForceElement) → pydrake.multibody.tree.ForceElement

Adds a new force element model of type ForceElementType to this MultibodyPlant. The arguments to this method args are forwarded to ``ForceElementType`’s constructor.

Parameter args:: Zero or more parameters provided to the constructor of the new force element. It must be the case that ForceElementType<T>(args)` is a valid constructor.
Template parameter ForceElementType:: The type of the ForceElement to add. As there is always a UniformGravityFieldElement present (accessible through gravity_field()), an exception will be thrown if this function is called to add another UniformGravityFieldElement.

Returns: A constant reference to the new ForceElement just added, of type ForceElementType<T> specialized on the scalar type T of this MultibodyPlant. It will remain valid for the lifetime of this MultibodyPlant.

See also

The ForceElement class’s documentation for further details on how a force element is defined.

AddFrame(self: pydrake.multibody.plant.MultibodyPlant, frame: pydrake.multibody.tree.Frame) → pydrake.multibody.tree.Frame

This method adds a Frame of type FrameType<T>. For more information, please see the corresponding constructor of FrameType.

Template parameter FrameType:: Template which will be instantiated on T.
Parameter frame:: Unique pointer frame instance.

Returns: A constant reference to the new Frame just added, which will remain valid for the lifetime of this MultibodyPlant.

AddJoint(self: pydrake.multibody.plant.MultibodyPlant, joint: pydrake.multibody.tree.Joint) → pydrake.multibody.tree.Joint: This method adds a Joint of type JointType between two bodies. For more information, see the below overload of AddJoint<>.

AddJointActuator(self: pydrake.multibody.plant.MultibodyPlant, name: str, joint: pydrake.multibody.tree.Joint, effort_limit: float = inf) → pydrake.multibody.tree.JointActuator

Creates and adds a JointActuator model for an actuator acting on a given joint. This method returns a constant reference to the actuator just added, which will remain valid for the lifetime of this plant.

Parameter name:: A string that uniquely identifies the new actuator to be added to this model. A RuntimeError is thrown if an actuator with the same name already exists in the model. See HasJointActuatorNamed().
Parameter joint:: The Joint to be actuated by the new JointActuator.
Parameter effort_limit:: The maximum effort for the actuator. It must be strictly positive, otherwise an RuntimeError is thrown. If +∞, the actuator has no limit, which is the default. The effort limit has physical units in accordance to the joint type it actuates. For instance, it will have units of N⋅m (torque) for revolute joints while it will have units of N (force) for prismatic joints.

Note

The effort limit is unused by MultibodyPlant and is simply provided here for bookkeeping purposes. It will not, for instance, saturate external actuation inputs based on this value. If, for example, a user intends to saturate the force/torque that is applied to the MultibodyPlant via this actuator, the user-level code (e.g., a controller) should query this effort limit and impose the saturation there.

Returns

A constant reference to the new JointActuator just added, which will remain valid for the lifetime of this plant or until the JointActuator has been removed from the plant with RemoveJointActuator().

Raises

RuntimeError if joint.num_velocities() > 1 since for now we –
only support actuators for single dof joints. –

See also

RemoveJointActuator()

AddModelInstance(self: pydrake.multibody.plant.MultibodyPlant, name: str) → pydrake.multibody.tree.ModelInstanceIndex

Creates a new model instance. Returns the index for the model instance.

Parameter name:: A string that uniquely identifies the new instance to be added to this model. An exception is thrown if an instance with the same name already exists in the model. See HasModelInstanceNamed().

AddRigidBody(*args, **kwargs)

Overloaded function.

AddRigidBody(self: pydrake.multibody.plant.MultibodyPlant, name: str, M_BBo_B: pydrake.multibody.tree.SpatialInertia = SpatialInertia.Zero()) -> pydrake.multibody.tree.RigidBody

Creates a rigid body with the provided name and spatial inertia. This method returns a constant reference to the body just added, which will remain valid for the lifetime of this MultibodyPlant. The body will use the default model instance (model_instance “more on model instances”).

Example of usage:

Click to expand C++ code...

MultibodyPlant<T> plant;
  // ... Code to define spatial_inertia, a SpatialInertia<T> object ...
  const RigidBody<T>& body =
    plant.AddRigidBody("BodyName", spatial_inertia);

Parameter name:: A string that identifies the new body to be added to this model. A RuntimeError is thrown if a body named name already is part of the model in the default model instance. See HasBodyNamed(), RigidBody::name().
Parameter M_BBo_B:: The SpatialInertia of the new rigid body to be added to this MultibodyPlant, computed about the body frame origin Bo and expressed in the body frame B. When not provided, defaults to zero.

Returns

A constant reference to the new RigidBody just added, which will remain valid for the lifetime of this MultibodyPlant.

Raises

RuntimeError if additional model instances have been created –
beyond the world and default instances. –

AddRigidBody(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex, M_BBo_B: pydrake.multibody.tree.SpatialInertia = SpatialInertia.Zero()) -> pydrake.multibody.tree.RigidBody

Creates a rigid body with the provided name and spatial inertia. This method returns a constant reference to the body just added, which will remain valid for the lifetime of this MultibodyPlant.

Example of usage:

Click to expand C++ code...

MultibodyPlant<T> plant;
  // ... Code to define spatial_inertia, a SpatialInertia<T> object ...
  ModelInstanceIndex model_instance = plant.AddModelInstance("instance");
  const RigidBody<T>& body =
    plant.AddRigidBody("BodyName", model_instance, spatial_inertia);

Parameter name:: A string that identifies the new body to be added to this model. A RuntimeError is thrown if a body named name already is part of model_instance. See HasBodyNamed(), RigidBody::name().
Parameter model_instance:: A model instance index which this body is part of.
Parameter M_BBo_B:: The SpatialInertia of the new rigid body to be added to this MultibodyPlant, computed about the body frame origin Bo and expressed in the body frame B. When not provided, defaults to zero.

Returns: A constant reference to the new RigidBody just added, which will remain valid for the lifetime of this MultibodyPlant.

AddWeldConstraint(self: pydrake.multibody.plant.MultibodyPlant, body_A: pydrake.multibody.tree.RigidBody, X_AP: pydrake.math.RigidTransform, body_B: pydrake.multibody.tree.RigidBody, X_BQ: pydrake.math.RigidTransform) → pydrake.multibody.tree.MultibodyConstraintId

Defines a constraint such that frame P affixed to body A is coincident at all times with frame Q affixed to body B, effectively modeling a weld joint.

Parameter body_A:: RigidBody to which frame P is rigidly attached.
Parameter X_AP:: Pose of frame P in body A’s frame.
Parameter body_B:: RigidBody to which frame Q is rigidly attached.
Parameter X_BQ:: Pose of frame Q in body B’s frame.

Returns

the id of the newly added constraint.

Raises

RuntimeError if bodies A and B are the same body. –
RuntimeError if the MultibodyPlant has already been finalized. –
RuntimeError if this MultibodyPlant is not a discrete model –
(is_discrete() == false) –
RuntimeError if this MultibodyPlant's underlying contact –
solver is not SAP. (i.e. get_discrete_contact_solver() != –
DiscreteContactSolver::kSap) –

CalcBiasCenterOfMassTranslationalAcceleration(*args, **kwargs)

Overloaded function.

CalcBiasCenterOfMassTranslationalAcceleration(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) -> numpy.ndarray[numpy.float64[3, 1]]

For the system S of all bodies other than the world body, calculates a𝑠Bias_AScm_E, Scm’s translational acceleration bias in frame A with respect to “speeds” 𝑠, expressed in frame E, where Scm is the center of mass of S and speeds 𝑠 is either q̇ or v.

Parameter context:: Contains the state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the accceleration bias is with respect to 𝑠 = q̇ or 𝑠 = v. Currently, an exception is thrown if with_respect_to is JacobianWrtVariable::kQDot.
Parameter frame_A:: The frame in which a𝑠Bias_AScm is measured.
Parameter frame_E:: The frame in which a𝑠Bias_AScm is expressed on output.

Returns

a𝑠Bias_AScm_E Point Scm’s translational acceleration bias in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E.

Raises

RuntimeError if this has no body except world_body() –
RuntimeError if mₛ ≤ 0, where mₛ is the mass of system S. –
RuntimeError if with_respect_to is JacobianWrtVariable::kQDot. –

See also

CalcJacobianCenterOfMassTranslationalVelocity() to compute J𝑠_v_Scm, point Scm’s translational velocity Jacobian in frame A with respect to 𝑠.

Note

The world_body() is ignored. asBias_AScm_E = ∑ (mᵢ aᵢ) / mₛ, where mₛ = ∑ mᵢ is the mass of system S, mᵢ is the mass of the iᵗʰ body, and aᵢ is the translational bias acceleration of Bᵢcm in frame A expressed in frame E for speeds 𝑠 (Bᵢcm is the center of mass of the iᵗʰ body).

Note

See bias_acceleration_functions “Bias acceleration functions” for theory and details.

CalcBiasCenterOfMassTranslationalAcceleration(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex], with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) -> numpy.ndarray[numpy.float64[3, 1]]

For the system S containing the selected model instances, calculates a𝑠Bias_AScm_E, Scm’s translational acceleration bias in frame A with respect to “speeds” 𝑠, expressed in frame E, where Scm is the center of mass of S and speeds 𝑠 is either q̇ or v.

Parameter context:: Contains the state of the multibody system.
Parameter model_instances:: Vector of selected model instances. If a model instance is repeated in the vector (unusual), it is only counted once.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the accceleration bias is with respect to 𝑠 = q̇ or 𝑠 = v. Currently, an exception is thrown if with_respect_to is JacobianWrtVariable::kQDot.
Parameter frame_A:: The frame in which a𝑠Bias_AScm is measured.
Parameter frame_E:: The frame in which a𝑠Bias_AScm is expressed on output.

Returns

a𝑠Bias_AScm_E Point Scm’s translational acceleration bias in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E.

Raises

RuntimeError if this has no body except world_body() –
RuntimeError if mₛ ≤ 0, where mₛ is the mass of system S. –
RuntimeError if with_respect_to is JacobianWrtVariable::kQDot. –

See also

CalcJacobianCenterOfMassTranslationalVelocity() to compute J𝑠_v_Scm, point Scm’s translational velocity Jacobian in frame A with respect to 𝑠.

Note

The world_body() is ignored. asBias_AScm_E = ∑ (mᵢ aᵢ) / mₛ, where mₛ = ∑ mᵢ is the mass of system S, mᵢ is the mass of the iᵗʰ body, and aᵢ is the translational bias acceleration of Bᵢcm in frame A expressed in frame E for speeds 𝑠 (Bᵢcm is the center of mass of the iᵗʰ body).

Note

See bias_acceleration_functions “Bias acceleration functions” for theory and details.

CalcBiasSpatialAcceleration(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_B: pydrake.multibody.tree.Frame, p_BoBp_B: numpy.ndarray[numpy.float64[3, 1]], frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → pydrake.multibody.math.SpatialAcceleration

For one point Bp affixed/welded to a frame B, calculates A𝑠Bias_ABp, Bp’s spatial acceleration bias in frame A with respect to “speeds” 𝑠, expressed in frame E, where speeds 𝑠 is either q̇ or v.

Parameter context:: Contains the state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the spatial accceleration bias is with respect to 𝑠 = q̇ or 𝑠 = v. Currently, an exception is thrown if with_respect_to is JacobianWrtVariable::kQDot.
Parameter frame_B:: The frame on which point Bp is affixed/welded.
Parameter p_BoBp_B:: Position vector from Bo (frame_B’s origin) to point Bp (regarded as affixed/welded to B), expressed in frame_B.
Parameter frame_A:: The frame in which A𝑠Bias_ABp is measured.
Parameter frame_E:: The frame in which A𝑠Bias_ABp is expressed on output.

Returns: A𝑠Bias_ABp_E Point Bp’s spatial acceleration bias in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E.

See also

CalcJacobianSpatialVelocity() to compute J𝑠_V_ABp, point Bp’s spatial velocity Jacobian in frame A with respect to 𝑠.

Raises: RuntimeError if with_respect_to is JacobianWrtVariable::kQDot. –

Note

Use CalcBiasTranslationalAcceleration() to efficiently calculate bias translational accelerations for a list of points (each fixed to frame B). This function returns only one bias spatial acceleration, which contains both frame B’s bias angular acceleration and point Bp’s bias translational acceleration.

Note

See bias_acceleration_functions “Bias acceleration functions” for theory and details.

CalcBiasTerm(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → numpy.ndarray[numpy.float64[m, 1]]

Computes the bias term C(q, v) v containing Coriolis, centripetal, and gyroscopic effects in the multibody equations of motion:

Click to expand C++ code...

M(q) v̇ + C(q, v) v = tau_app + ∑ (Jv_V_WBᵀ(q) ⋅ Fapp_Bo_W)

where M(q) is the multibody model’s mass matrix (including rigid body mass properties and reflected_inertia “reflected inertias”) and tau_app is a vector of applied generalized forces. The last term is a summation over all bodies of the dot-product of Fapp_Bo_W (applied spatial force on body B at Bo) with Jv_V_WB(q) (B’s spatial Jacobian in world W with respect to generalized velocities v). Note: B’s spatial velocity in W can be written V_WB = Jv_V_WB * v.

Parameter context:: Contains the state of the multibody system, including the generalized positions q and the generalized velocities v.
Parameter Cv:: On output, Cv will contain the product C(q, v)v. It must be a valid (non-null) pointer to a column vector in ℛⁿ with n the number of generalized velocities (num_velocities()) of the model. This method aborts if Cv is nullptr or if it does not have the proper size.

CalcBiasTranslationalAcceleration(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_B: pydrake.multibody.tree.Frame, p_BoBi_B: numpy.ndarray[numpy.float64[3, n], flags.f_contiguous], frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[3, n]]

For each point Bi affixed/welded to a frame B, calculates a𝑠Bias_ABi, Bi’s translational acceleration bias in frame A with respect to “speeds” 𝑠, expressed in frame E, where speeds 𝑠 is either q̇ or v.

Parameter context:: Contains the state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the translational acceleration bias is with respect to 𝑠 = q̇ or 𝑠 = v. Currently, an exception is thrown if with_respect_to is JacobianWrtVariable::kQDot.
Parameter frame_B:: The frame on which points Bi are affixed/welded.
Parameter p_BoBi_B:: A position vector or list of p position vectors from Bo (frame_B’s origin) to points Bi (regarded as affixed to B), where each position vector is expressed in frame_B. Each column in the 3 x p matrix p_BoBi_B corresponds to a position vector.
Parameter frame_A:: The frame in which a𝑠Bias_ABi is measured.
Parameter frame_E:: The frame in which a𝑠Bias_ABi is expressed on output.

Returns: a𝑠Bias_ABi_E Point Bi’s translational acceleration bias in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E. a𝑠Bias_ABi_E is a 3 x p matrix, where p is the number of points Bi.

See also

CalcJacobianTranslationalVelocity() to compute J𝑠_v_ABi, point Bi’s translational velocity Jacobian in frame A with respect to 𝑠.

Precondition:: p_BoBi_B must have 3 rows.

Raises: RuntimeError if with_respect_to is JacobianWrtVariable::kQDot. –

Note

See bias_acceleration_functions “Bias acceleration functions” for theory and details.

CalcCenterOfMassPositionInWorld(*args, **kwargs)

Overloaded function.

CalcCenterOfMassPositionInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[3, 1]]

Calculates the position vector from the world origin Wo to the center of mass of all bodies in this MultibodyPlant, expressed in the world frame W.

Parameter context:: Contains the state of the model.
Returns p_WoScm_W:: position vector from Wo to Scm expressed in world frame W, where Scm is the center of mass of the system S stored by this plant.

Raises

RuntimeError if this has no body except world_body() –
RuntimeError if mₛ ≤ 0 (where mₛ is the mass of system S) –

Note

The world_body() is ignored. p_WoScm_W = ∑ (mᵢ pᵢ) / mₛ, where mₛ = ∑ mᵢ, mᵢ is the mass of the iᵗʰ body, and pᵢ is Bᵢcm’s position from Wo expressed in frame W (Bᵢcm is the center of mass of the iᵗʰ body).

CalcCenterOfMassPositionInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex]) -> numpy.ndarray[numpy.float64[3, 1]]

Calculates the position vector from the world origin Wo to the center of mass of all non-world bodies contained in model_instances, expressed in the world frame W.

Parameter context:: Contains the state of the model.
Parameter model_instances:: Vector of selected model instances. If a model instance is repeated in the vector (unusual), it is only counted once.
Returns p_WoScm_W:: position vector from world origin Wo to Scm expressed in the world frame W, where Scm is the center of mass of the system S of non-world bodies contained in model_instances.

Raises

RuntimeError if model_instances is empty or only has world body. –
RuntimeError if mₛ ≤ 0 (where mₛ is the mass of system S) –

Note

The world_body() is ignored. p_WoScm_W = ∑ (mᵢ pᵢ) / mₛ, where mₛ = ∑ mᵢ, mᵢ is the mass of the iᵗʰ body contained in model_instances, and pᵢ is Bᵢcm’s position vector from Wo expressed in frame W (Bᵢcm is the center of mass of the iᵗʰ body).

CalcCenterOfMassTranslationalAccelerationInWorld(*args, **kwargs)

Overloaded function.

CalcCenterOfMassTranslationalAccelerationInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[3, 1]]

For the system S contained in this MultibodyPlant, calculates Scm’s translational acceleration in the world frame W expressed in W, where Scm is the center of mass of S.

Parameter context:: The context contains the state of the model.
Returns a_WScm_W:: Scm’s translational acceleration in the world frame W expressed in the world frame W.

Raises

RuntimeError if this has no body except world_body() –
RuntimeError if mₛ ≤ 0, where mₛ is the mass of system S. –

Note

The world_body() is ignored. a_WScm_W = ∑ (mᵢ aᵢ) / mₛ, where mₛ = ∑ mᵢ is the mass of system S, mᵢ is the mass of the iᵗʰ body, and aᵢ is the translational acceleration of Bᵢcm in world W expressed in W (Bᵢcm is the center of mass of the iᵗʰ body).

Note

When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcCenterOfMassTranslationalAccelerationInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex]) -> numpy.ndarray[numpy.float64[3, 1]]

For the system S containing the selected model instances, calculates Scm’s translational acceleration in the world frame W expressed in W, where Scm is the center of mass of S.

Parameter context:: The context contains the state of the model.
Parameter model_instances:: Vector of selected model instances. If a model instance is repeated in the vector (unusual), it is only counted once.
Returns a_WScm_W:: Scm’s translational acceleration in the world frame W expressed in the world frame W.

Raises

RuntimeError if model_instances is empty or only has world body. –
RuntimeError if mₛ ≤ 0, where mₛ is the mass of system S. –

Note

The world_body() is ignored. a_WScm_W = ∑ (mᵢ aᵢ) / mₛ, where mₛ = ∑ mᵢ is the mass of system S, mᵢ is the mass of the iᵗʰ body in model_instances, and aᵢ is the translational acceleration of Bᵢcm in world W expressed in W (Bᵢcm is the center of mass of the iᵗʰ body).

Note

When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

CalcCenterOfMassTranslationalVelocityInWorld(*args, **kwargs)

Overloaded function.

CalcCenterOfMassTranslationalVelocityInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[3, 1]]

Calculates system center of mass translational velocity in world frame W.

Parameter context:: The context contains the state of the model.
Returns v_WScm_W:: Scm’s translational velocity in frame W, expressed in W, where Scm is the center of mass of the system S stored by this plant.

Raises

RuntimeError if this has no body except world_body() –
RuntimeError if mₛ ≤ 0 (where mₛ is the mass of system S) –

Note

The world_body() is ignored. v_WScm_W = ∑ (mᵢ vᵢ) / mₛ, where mₛ = ∑ mᵢ, mᵢ is the mass of the iᵗʰ body, and vᵢ is Bᵢcm’s velocity in world W (Bᵢcm is the center of mass of the iᵗʰ body).

CalcCenterOfMassTranslationalVelocityInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex]) -> numpy.ndarray[numpy.float64[3, 1]]

Calculates system center of mass translational velocity in world frame W.

Parameter context:: The context contains the state of the model.
Parameter model_instances:: Vector of selected model instances. If a model instance is repeated in the vector (unusual), it is only counted once.
Returns v_WScm_W:: Scm’s translational velocity in frame W, expressed in W, where Scm is the center of mass of the system S of non-world bodies contained in model_instances.

Raises

RuntimeError if model_instances is empty or only has world body. –
RuntimeError if mₛ ≤ 0 (where mₛ is the mass of system S) –

Note

The world_body() is ignored. v_WScm_W = ∑ (mᵢ vᵢ) / mₛ, where mₛ = ∑ mᵢ, mᵢ is the mass of the iᵗʰ body contained in model_instances, and vᵢ is Bᵢcm’s velocity in world W expressed in frame W (Bᵢcm is the center of mass of the iᵗʰ body).

CalcForceElementsContribution(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, forces: pydrake.multibody.tree.MultibodyForces) → None

Computes the combined force contribution of ForceElement objects in the model. A ForceElement can apply forces as a spatial force per body or as generalized forces, depending on the ForceElement model. ForceElement contributions are a function of the state and time only. The output from this method can immediately be used as input to CalcInverseDynamics() to include the effect of applied forces by force elements.

Parameter context:: The context containing the state of this model.
Parameter forces:: A pointer to a valid, non nullptr, multibody forces object. On output forces will store the forces exerted by all the ForceElement objects in the model.

Raises

RuntimeError if forces is null or not compatible with this –
model, per MultibodyForces::CheckInvariants() –

CalcGeneralizedForces(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, forces: pydrake.multibody.tree.MultibodyForces) → numpy.ndarray[numpy.float64[m, 1]]

Computes the generalized forces result of a set of MultibodyForces applied to this model.

MultibodyForces stores applied forces as both generalized forces τ and spatial forces F on each body, refer to documentation in MultibodyForces for details. Users of MultibodyForces will use MultibodyForces::mutable_generalized_forces() to mutate the stored generalized forces directly and will use RigidBody::AddInForceInWorld() to append spatial forces.

For a given set of forces stored as MultibodyForces, this method will compute the total generalized forces on this model. More precisely, if J_WBo is the Jacobian (with respect to velocities) for this model, including all bodies, then this method computes:

Click to expand C++ code...

τᵣₑₛᵤₗₜ = τ + J_WBo⋅F

Parameter context:: Context that stores the state of the model.
Parameter forces:: Set of multibody forces, including both generalized forces and per-body spatial forces.
Parameter generalized_forces:: The total generalized forces on the model that would result from applying forces. In other words, forces can be replaced by the equivalent generalized_forces. On output, generalized_forces is resized to num_velocities().

Raises

RuntimeError if forces is null or not compatible with this –
model. –
RuntimeError if generalized_forces is not a valid non-null –
pointer. –

CalcGravityGeneralizedForces(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → numpy.ndarray[numpy.float64[m, 1]]

Computes the generalized forces tau_g(q) due to gravity as a function of the generalized positions q stored in the input context. The vector of generalized forces due to gravity tau_g(q) is defined such that it appears on the right hand side of the equations of motion together with any other generalized forces, like so:

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Mv̇ + C(q, v)v = tau_g(q) + tau_app

where tau_app includes any other generalized forces applied on the system.

Parameter context:: The context storing the state of the model.

Returns: tau_g A vector containing the generalized forces due to gravity. The generalized forces are consistent with the vector of generalized velocities v for this so that the inner product v⋅tau_g corresponds to the power applied by the gravity forces on the mechanical system. That is, v⋅tau_g > 0 corresponds to potential energy going into the system, as either mechanical kinetic energy, some other potential energy, or heat, and therefore to a decrease of the gravitational potential energy.

CalcInverseDynamics(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, known_vdot: numpy.ndarray[numpy.float64[m, 1]], external_forces: pydrake.multibody.tree.MultibodyForces) → numpy.ndarray[numpy.float64[m, 1]]

Given the state of this model in context and a known vector of generalized accelerations vdot, this method computes the set of generalized forces tau that would need to be applied in order to attain the specified generalized accelerations. Mathematically, this method computes:

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tau = M(q)v̇ + C(q, v)v - tau_app - ∑ J_WBᵀ(q) Fapp_Bo_W

where M(q) is the model’s mass matrix (including rigid body mass properties and reflected_inertia “reflected inertias”), C(q, v)v is the bias term for Coriolis and gyroscopic effects and tau_app consists of a vector applied generalized forces. The last term is a summation over all bodies in the model where Fapp_Bo_W is an applied spatial force on body B at Bo which gets projected into the space of generalized forces with the transpose of Jv_V_WB(q) (where Jv_V_WB is B’s spatial velocity Jacobian in W with respect to generalized velocities v). Note: B’s spatial velocity in W can be written as V_WB = Jv_V_WB * v.

This method does not compute explicit expressions for the mass matrix nor for the bias term, which would be of at least O(n²) complexity, but it implements an O(n) Newton-Euler recursive algorithm, where n is the number of bodies in the model. The explicit formation of the mass matrix M(q) would require the calculation of O(n²) entries while explicitly forming the product C(q, v) * v could require up to O(n³) operations (see [Featherstone 1987, §4]), depending on the implementation. The recursive Newton-Euler algorithm is the most efficient currently known general method for solving inverse dynamics [Featherstone 2008].

Parameter context:: The context containing the state of the model.
Parameter known_vdot:: A vector with the known generalized accelerations vdot for the full model. Use the provided Joint APIs in order to access entries into this array.
Parameter external_forces:: A set of forces to be applied to the system either as body spatial forces Fapp_Bo_W or generalized forces tau_app, see MultibodyForces for details.

Returns: the vector of generalized forces that would need to be applied to the mechanical system in order to achieve the desired acceleration given by known_vdot.

CalcJacobianAngularVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_B: pydrake.multibody.tree.Frame, frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[3, n]]

Calculates J𝑠_w_AB, a frame B’s angular velocity Jacobian in a frame A with respect to “speeds” 𝑠.

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J𝑠_w_AB ≜ [ ∂(w_AB)/∂𝑠₁,  ...  ∂(w_AB)/∂𝑠ₙ ]    (n is j or k)
     w_AB = J𝑠_w_AB ⋅ 𝑠          w_AB is linear in 𝑠 ≜ [𝑠₁ ... 𝑠ₙ]ᵀ

w_AB is B’s angular velocity in frame A and “speeds” 𝑠 is either q̇ ≜ [q̇₁ … q̇ⱼ]ᵀ (time-derivatives of j generalized positions) or v ≜ [v₁ … vₖ]ᵀ (k generalized velocities).

Parameter context:: The state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian J𝑠_w_AB is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities).
Parameter frame_B:: The frame B in w_AB (B’s angular velocity in A).
Parameter frame_A:: The frame A in w_AB (B’s angular velocity in A).
Parameter frame_E:: The frame in which w_AB is expressed on input and the frame in which the Jacobian J𝑠_w_AB is expressed on output.
Parameter J𝑠_w_AB_E:: Frame B’s angular velocity Jacobian in frame A with respect to speeds 𝑠 (which is either q̇ or v), expressed in frame E. The Jacobian is a function of only generalized positions q (which are pulled from the context). The previous definition shows J𝑠_w_AB_E is a matrix of size 3 x n, where n is the number of elements in 𝑠.

See also

See Jacobian_functions “Jacobian functions” for related functions.

Raises: RuntimeError if J𝑠_w_AB_E is nullptr or not of size 3 x n. –

CalcJacobianCenterOfMassTranslationalVelocity(*args, **kwargs)

Overloaded function.

CalcJacobianCenterOfMassTranslationalVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) -> numpy.ndarray[numpy.float64[3, n]]

Calculates J𝑠_v_ACcm_E, point Ccm’s translational velocity Jacobian in frame A with respect to “speeds” 𝑠, expressed in frame E, where point CCm is the center of mass of the system of all non-world bodies contained in this MultibodyPlant.

Parameter context:: contains the state of the model.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian J𝑠_v_ACcm_E is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities).
Parameter frame_A:: The frame in which the translational velocity v_ACcm and its Jacobian J𝑠_v_ACcm are measured.
Parameter frame_E:: The frame in which the Jacobian J𝑠_v_ACcm is expressed on output.
Parameter J𝑠_v_ACcm_E:: Point Ccm’s translational velocity Jacobian in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E. J𝑠_v_ACcm_E is a 3 x n matrix, where n is the number of elements in 𝑠. The Jacobian is a function of only generalized positions q (which are pulled from the context).

Raises

RuntimeError if CCm does not exist, which occurs if there are no –
massive bodies in MultibodyPlant (except world_body()) –
RuntimeError if mₛ ≤ 0 (where mₛ is the mass of all non-world –
bodies contained in this MultibodyPlant) –

See also

See Jacobian_functions “Jacobian functions” for related functions.

CalcJacobianCenterOfMassTranslationalVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex], with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) -> numpy.ndarray[numpy.float64[3, n]]

Calculates J𝑠_v_ACcm_E, point Ccm’s translational velocity Jacobian in frame A with respect to “speeds” 𝑠, expressed in frame E, where point CCm is the center of mass of the system of all non-world bodies contained in model_instances.

Parameter context:: contains the state of the model.
Parameter model_instances:: Vector of selected model instances. If a model instance is repeated in the vector (unusual), it is only counted once.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian J𝑠_v_ACcm_E is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities).
Parameter frame_A:: The frame in which the translational velocity v_ACcm and its Jacobian J𝑠_v_ACcm are measured.
Parameter frame_E:: The frame in which the Jacobian J𝑠_v_ACcm is expressed on output.
Parameter J𝑠_v_ACcm_E:: Point Ccm’s translational velocity Jacobian in frame A with respect to speeds 𝑠 (𝑠 = q̇ or 𝑠 = v), expressed in frame E. J𝑠_v_ACcm_E is a 3 x n matrix, where n is the number of elements in 𝑠. The Jacobian is a function of only generalized positions q (which are pulled from the context).

Raises

RuntimeError if mₛ ≤ 0 (where mₛ is the mass of all non-world –
bodies contained in model_instances) –
RuntimeError if model_instances is empty or only has world body. –

Note

The world_body() is ignored. J𝑠_v_ACcm_ = ∑ (mᵢ Jᵢ) / mₛ, where mₛ = ∑ mᵢ, mᵢ is the mass of the iᵗʰ body contained in model_instances, and Jᵢ is Bᵢcm’s translational velocity Jacobian in frame A, expressed in frame E (Bᵢcm is the center of mass of the iᵗʰ body).

See also

See Jacobian_functions “Jacobian functions” for related functions.

CalcJacobianPositionVector(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, frame_B: pydrake.multibody.tree.Frame, p_BoBi_B: numpy.ndarray[numpy.float64[3, n], flags.f_contiguous], frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[m, n]]

For each point Bi affixed/welded to a frame B, calculates Jq_p_AoBi, Bi’s position vector Jacobian in frame A with respect to the generalized positions q ≜ [q₁ … qₙ]ᵀ as

Click to expand C++ code...

Jq_p_AoBi ≜ [ ᴬ∂(p_AoBi)/∂q₁,  ...  ᴬ∂(p_AoBi)/∂qₙ ]

where p_AoBi is Bi’s position vector from point Ao (frame A’s origin) and ᴬ∂(p_AoBi)/∂qᵣ denotes the partial derivative in frame A of p_AoBi with respect to the generalized position qᵣ, where qᵣ is one of q₁ … qₙ.

Parameter context:: The state of the multibody system.
Parameter frame_B:: The frame on which point Bi is affixed/welded.
Parameter p_BoBi_B:: A position vector or list of k position vectors from Bo (frame_B’s origin) to points Bi (Bi is regarded as affixed to B), where each position vector is expressed in frame_B.
Parameter frame_A:: The frame in which partial derivatives are calculated and the frame in which point Ao is affixed.
Parameter frame_E:: The frame in which the Jacobian Jq_p_AoBi is expressed on output.
Parameter Jq_p_AoBi_E:: Point Bi’s position vector Jacobian in frame A with generalized positions q, expressed in frame E. Jq_p_AoBi_E is a 3*k x n matrix, where k is the number of points Bi and n is the number of elements in q. The Jacobian is a function of only generalized positions q (which are pulled from the context).

Raises: RuntimeError if Jq_p_AoBi_E is nullptr or not sized 3*k x n. –

Note

Jq̇_v_ABi = Jq_p_AoBi. In other words, point Bi’s velocity Jacobian in frame A with respect to q̇ is equal to point Bi’s position vector Jacobian in frame A with respect to q.

Click to expand C++ code...

[∂(v_ABi)/∂q̇₁, ... ∂(v_ABi)/∂q̇ₙ] = [ᴬ∂(p_AoBi)/∂q₁, ... ᴬ∂(p_AoBi)/∂qₙ]

See also

CalcJacobianTranslationalVelocity() for details on Jq̇_v_ABi. Note: Jq_p_AaBi = Jq_p_AoBi, where point Aa is any point fixed/welded to frame A, i.e., this calculation’s result is the same if point Ao is replaced with any point fixed on frame A.

See also

See Jacobian_functions “Jacobian functions” for related functions.

CalcJacobianSpatialVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_B: pydrake.multibody.tree.Frame, p_BoBp_B: numpy.ndarray[numpy.float64[3, 1]], frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[m, n]]

For one point Bp fixed/welded to a frame B, calculates J𝑠_V_ABp, Bp’s spatial velocity Jacobian in frame A with respect to “speeds” 𝑠.

Click to expand C++ code...

J𝑠_V_ABp ≜ [ ∂(V_ABp)/∂𝑠₁,  ...  ∂(V_ABp)/∂𝑠ₙ ]    (n is j or k)
     V_ABp = J𝑠_V_ABp ⋅ 𝑠          V_ABp is linear in 𝑠 ≜ [𝑠₁ ... 𝑠ₙ]ᵀ

V_ABp is Bp’s spatial velocity in frame A and “speeds” 𝑠 is either q̇ ≜ [q̇₁ … q̇ⱼ]ᵀ (time-derivatives of j generalized positions) or v ≜ [v₁ … vₖ]ᵀ (k generalized velocities).

Parameter context:: The state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian J𝑠_V_ABp is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities).
Parameter frame_B:: The frame on which point Bp is fixed/welded.
Parameter p_BoBp_B:: A position vector from Bo (frame_B’s origin) to point Bp (regarded as fixed/welded to B), expressed in frame_B.
Parameter frame_A:: The frame that measures v_ABp (Bp’s velocity in A). Note: It is natural to wonder why there is no parameter p_AoAp_A (similar to the parameter p_BoBp_B for frame_B). There is no need for p_AoAp_A because Bp’s velocity in A is defined as the derivative in frame A of Bp’s position vector from any point fixed to A.
Parameter frame_E:: The frame in which v_ABp is expressed on input and the frame in which the Jacobian J𝑠_V_ABp is expressed on output.
Parameter J𝑠_V_ABp_E:: Point Bp’s spatial velocity Jacobian in frame A with respect to speeds 𝑠 (which is either q̇ or v), expressed in frame E. J𝑠_V_ABp_E is a 6 x n matrix, where n is the number of elements in 𝑠. The Jacobian is a function of only generalized positions q (which are pulled from the context).

Note

The returned 6 x n matrix stores frame B’s angular velocity Jacobian in A in rows 1-3 and stores point Bp’s translational velocity Jacobian in A in rows 4-6, i.e.,

Click to expand C++ code...

J𝑠_w_AB_E = J𝑠_V_ABp_E.topRows<3>();
    J𝑠_v_ABp_E = J𝑠_V_ABp_E.bottomRows<3>();

Note

Consider CalcJacobianTranslationalVelocity() for multiple points fixed to frame B and consider CalcJacobianAngularVelocity() to calculate frame B’s angular velocity Jacobian.

See also

See Jacobian_functions “Jacobian functions” for related functions.

Raises: RuntimeError if J𝑠_V_ABp_E is nullptr or not sized 6 x n. –

CalcJacobianTranslationalVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, with_respect_to: pydrake.multibody.tree.JacobianWrtVariable, frame_B: pydrake.multibody.tree.Frame, p_BoBi_B: numpy.ndarray[numpy.float64[3, n], flags.f_contiguous], frame_A: pydrake.multibody.tree.Frame, frame_E: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[m, n]]

For each point Bi affixed/welded to a frame B, calculates J𝑠_v_ABi, Bi’s translational velocity Jacobian in frame A with respect to “speeds” 𝑠.

Click to expand C++ code...

J𝑠_v_ABi ≜ [ ∂(v_ABi)/∂𝑠₁,  ...  ∂(v_ABi)/∂𝑠ₙ ]    (n is j or k)
     v_ABi = J𝑠_v_ABi ⋅ 𝑠          v_ABi is linear in 𝑠 ≜ [𝑠₁ ... 𝑠ₙ]ᵀ

v_ABi is Bi’s translational velocity in frame A and “speeds” 𝑠 is either q̇ ≜ [q̇₁ … q̇ⱼ]ᵀ (time-derivatives of j generalized positions) or v ≜ [v₁ … vₖ]ᵀ (k generalized velocities).

Parameter context:: The state of the multibody system.
Parameter with_respect_to:: Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian J𝑠_v_ABi is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities).
Parameter frame_B:: The frame on which point Bi is affixed/welded.
Parameter p_BoBi_B:: A position vector or list of p position vectors from Bo (frame_B’s origin) to points Bi (regarded as affixed to B), where each position vector is expressed in frame_B.
Parameter frame_A:: The frame that measures v_ABi (Bi’s velocity in A). Note: It is natural to wonder why there is no parameter p_AoAi_A (similar to the parameter p_BoBi_B for frame_B). There is no need for p_AoAi_A because Bi’s velocity in A is defined as the derivative in frame A of Bi’s position vector from any point affixed to A.
Parameter frame_E:: The frame in which v_ABi is expressed on input and the frame in which the Jacobian J𝑠_v_ABi is expressed on output.
Parameter J𝑠_v_ABi_E:: Point Bi’s velocity Jacobian in frame A with respect to speeds 𝑠 (which is either q̇ or v), expressed in frame E. J𝑠_v_ABi_E is a 3*p x n matrix, where p is the number of points Bi and n is the number of elements in 𝑠. The Jacobian is a function of only generalized positions q (which are pulled from the context).

Raises

RuntimeError if J𝑠_v_ABi_E is nullptr or not sized ``3*p x –
n``. –

Note

When 𝑠 = q̇, Jq̇_v_ABi = Jq_p_AoBi. In other words, point Bi’s velocity Jacobian in frame A with respect to q̇ is equal to point Bi’s position Jacobian from Ao (A’s origin) in frame A with respect to q.

Click to expand C++ code...

[∂(v_ABi)/∂q̇₁,  ...  ∂(v_ABi)/∂q̇ⱼ] = [∂(p_AoBi)/∂q₁,  ...  ∂(p_AoBi)/∂qⱼ]

Note: Each partial derivative of p_AoBi is taken in frame A.

See also

CalcJacobianPositionVector() for details on Jq_p_AoBi.

See also

See Jacobian_functions “Jacobian functions” for related functions.

CalcMassMatrix(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → numpy.ndarray[numpy.float64[m, n]]

Efficiently computes the mass matrix M(q) of the model. The generalized positions q are taken from the given context. M includes the mass properties of rigid bodies and reflected_inertia “reflected inertias” as provided with JointActuator specifications.

This method employs the Composite Body Algorithm, which we believe to be the fastest O(n²) algorithm to compute the mass matrix of a multibody system.

Parameter context:: The Context containing the state of the model from which generalized coordinates q are extracted.
Parameter M:: A pointer to a square matrix in ℛⁿˣⁿ with n the number of generalized velocities (num_velocities()) of the model. Although symmetric, the matrix is filled in completely on return.
Precondition:: M is non-null and has the right size.

Warning

This is an O(n²) algorithm. Avoid the explicit computation of the mass matrix whenever possible.

See also

CalcMassMatrixViaInverseDynamics() (slower)

CalcMassMatrixViaInverseDynamics(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → numpy.ndarray[numpy.float64[m, n]]

Computes the mass matrix M(q) of the model using a slow method (inverse dynamics). The generalized positions q are taken from the given context. M includes the mass properties of rigid bodies and reflected_inertia “reflected inertias” as provided with JointActuator specifications.

Use CalcMassMatrix() for a faster implementation using the Composite Body Algorithm.

Parameter context:: The Context containing the state of the model from which generalized coordinates q are extracted.
Parameter M:: A pointer to a square matrix in ℛⁿˣⁿ with n the number of generalized velocities (num_velocities()) of the model. Although symmetric, the matrix is filled in completely on return.
Precondition:: M is non-null and has the right size.

The algorithm used to build M(q) consists in computing one column of M(q) at a time using inverse dynamics. The result from inverse dynamics, with no applied forces, is the vector of generalized forces:

Click to expand C++ code...

tau = M(q)v̇ + C(q, v)v

where q and v are the generalized positions and velocities, respectively. When v = 0 the Coriolis and gyroscopic forces term C(q, v)v is zero. Therefore the i-th column of M(q) can be obtained performing inverse dynamics with an acceleration vector v̇ = eᵢ, with eᵢ the standard (or natural) basis of ℛⁿ with n the number of generalized velocities. We write this as:

Click to expand C++ code...

M.ᵢ(q) = M(q) * e_i

where M.ᵢ(q) (notice the dot for the rows index) denotes the i-th column in M(q).

Warning

This is an O(n²) algorithm. Avoid the explicit computation of the mass matrix whenever possible.

See also

CalcMassMatrix(), CalcInverseDynamics()

CalcPointsPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, frame_B: pydrake.multibody.tree.Frame, p_BQi: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], frame_A: pydrake.multibody.tree.Frame) → numpy.ndarray[numpy.float64[m, n]]

Given the positions p_BQi for a set of points Qi measured and expressed in a frame B, this method computes the positions p_AQi(q) of each point Qi in the set as measured and expressed in another frame A, as a function of the generalized positions q of the model.

Parameter context:: The context containing the state of the model. It stores the generalized positions q of the model.
Parameter frame_B:: The frame B in which the positions p_BQi of a set of points Qi are given.
Parameter p_BQi:: The input positions of each point Qi in frame B. p_BQi ∈ ℝ³ˣⁿᵖ with np the number of points in the set. Each column of p_BQi corresponds to a vector in ℝ³ holding the position of one of the points in the set as measured and expressed in frame B.
Parameter frame_A:: The frame A in which it is desired to compute the positions p_AQi of each point Qi in the set.
Parameter p_AQi:: The output positions of each point Qi now computed as measured and expressed in frame A. The output p_AQi must have the same size as the input p_BQi or otherwise this method aborts. That is p_AQi must be in ℝ³ˣⁿᵖ.

Note

Both p_BQi and p_AQi must have three rows. Otherwise this method will throw a RuntimeError. This method also throws a RuntimeError if p_BQi and p_AQi differ in the number of columns.

CalcRelativeRotationMatrix(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, frame_A: pydrake.multibody.tree.Frame, frame_B: pydrake.multibody.tree.Frame) → pydrake.math.RotationMatrix

Calculates the rotation matrix R_AB relating frame A and frame B.

Parameter context:: The state of the multibody system, which includes the system’s generalized positions q. Note: R_AB is a function of q.
Parameter frame_A:: The frame A designated in the rigid transform R_AB.
Parameter frame_B:: The frame G designated in the rigid transform R_AB.
Returns R_AB:: The RigidTransform relating frame A and frame B.

CalcRelativeTransform(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, frame_A: pydrake.multibody.tree.Frame, frame_B: pydrake.multibody.tree.Frame) → pydrake.math.RigidTransform

Calculates the rigid transform (pose) X_AB relating frame A and frame B.

Parameter context:: The state of the multibody system, which includes the system’s generalized positions q. Note: X_AB is a function of q.
Parameter frame_A:: The frame A designated in the rigid transform X_AB.
Parameter frame_B:: The frame G designated in the rigid transform X_AB.
Returns X_AB:: The RigidTransform relating frame A and frame B.

CalcSpatialAccelerationsFromVdot(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, known_vdot: numpy.ndarray[numpy.float64[m, 1]]) → list[pydrake.multibody.math.SpatialAcceleration]

Given the state of this model in context and a known vector of generalized accelerations known_vdot, this method computes the spatial acceleration A_WB for each body as measured and expressed in the world frame W.

Parameter context:: The context containing the state of this model.
Parameter known_vdot:: A vector with the generalized accelerations for the full model.
Parameter A_WB_array:: A pointer to a valid, non nullptr, vector of spatial accelerations containing the spatial acceleration A_WB for each body. It must be of size equal to the number of bodies in the model. On output, entries will be ordered by BodyIndex.

Raises: RuntimeError if A_WB_array is not of size num_bodies() –

CalcSpatialInertia(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, frame_F: pydrake.multibody.tree.Frame, body_indexes: list[pydrake.multibody.tree.BodyIndex]) → pydrake.multibody.tree.SpatialInertia

Returns M_SFo_F, the spatial inertia of a set S of bodies about point Fo (the origin of a frame F), expressed in frame F. You may regard M_SFo_F as measuring spatial inertia as if the set S of bodies were welded into a single composite body at the configuration specified in the context.

Parameter context:: Contains the configuration of the set S of bodies.
Parameter frame_F:: specifies the about-point Fo (frame_F’s origin) and the expressed-in frame for the returned spatial inertia.
Parameter body_indexes:: Array of selected bodies. This method does not distinguish between welded bodies, joint-connected bodies, etc.

Raises

RuntimeError if body_indexes contains an invalid BodyIndex or if –
there is a repeated BodyIndex. –

Note

The mass and inertia of the world_body() does not contribute to the the returned spatial inertia.

CalcSpatialMomentumInWorldAboutPoint(*args, **kwargs)

Overloaded function.

CalcSpatialMomentumInWorldAboutPoint(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, p_WoP_W: numpy.ndarray[numpy.float64[3, 1]]) -> pydrake.multibody.math.SpatialMomentum

This method returns the spatial momentum of this MultibodyPlant in the world frame W, about a designated point P, expressed in the world frame W.

Parameter context:: Contains the state of the model.
Parameter p_WoP_W:: Position from Wo (origin of the world frame W) to an arbitrary point P, expressed in the world frame W.
Returns L_WSP_W:: , spatial momentum of the system S represented by this plant, measured in the world frame W, about point P, expressed in W.

Note

To calculate the spatial momentum of this system S in W about Scm (the system’s center of mass), use something like:

Click to expand C++ code...

MultibodyPlant<T> plant;
  // ... code to load a model ....
  const Vector3<T> p_WoScm_W =
    plant.CalcCenterOfMassPositionInWorld(context);
  const SpatialMomentum<T> L_WScm_W =
    plant.CalcSpatialMomentumInWorldAboutPoint(context, p_WoScm_W);

CalcSpatialMomentumInWorldAboutPoint(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex], p_WoP_W: numpy.ndarray[numpy.float64[3, 1]]) -> pydrake.multibody.math.SpatialMomentum

This method returns the spatial momentum of a set of model instances in the world frame W, about a designated point P, expressed in frame W.

Parameter context:: Contains the state of the model.
Parameter model_instances:: Set of selected model instances.
Parameter p_WoP_W:: Position from Wo (origin of the world frame W) to an arbitrary point P, expressed in the world frame W.
Returns L_WSP_W:: , spatial momentum of the system S represented by the model_instances, measured in world frame W, about point P, expressed in W.

Note

To calculate the spatial momentum of this system S in W about Scm (the system’s center of mass), use something like:

Click to expand C++ code...

MultibodyPlant<T> plant;
  // ... code to create a set of selected model instances, e.g., ...
  const ModelInstanceIndex gripper_model_instance =
    plant.GetModelInstanceByName("gripper");
  const ModelInstanceIndex robot_model_instance =
    plant.GetBodyByName("end_effector").model_instance();
  const std::vector<ModelInstanceIndex> model_instances{
    gripper_model_instance, robot_model_instance};
  const Vector3<T> p_WoScm_W =
    plant.CalcCenterOfMassPositionInWorld(context, model_instances);
  SpatialMomentum<T> L_WScm_W =
    plant.CalcSpatialMomentumInWorldAboutPoint(context, model_instances,
                                               p_WoScm_W);

Raises

RuntimeError if model_instances contains an invalid –
ModelInstanceIndex. –

CalcTotalMass(*args, **kwargs)

Overloaded function.

CalcTotalMass(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> float

Calculates the total mass of all bodies in this MultibodyPlant.

Parameter context:: Contains the state of the model.
Returns The:: total mass of all bodies or 0 if there are none.

Note

The mass of the world_body() does not contribute to the total mass.

CalcTotalMass(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instances: list[pydrake.multibody.tree.ModelInstanceIndex]) -> float

Calculates the total mass of all bodies contained in model_instances.

Parameter context:: Contains the state of the model.
Parameter model_instances:: Vector of selected model instances. This method does not distinguish between welded, joint connected, or floating bodies.
Returns The:: total mass of all bodies belonging to a model instance in model_instances or 0 if model_instances is empty.

Note

The mass of the world_body() does not contribute to the total mass and each body only contributes to the total mass once, even if the body has repeated occurrence (instance) in model_instances.

CollectRegisteredGeometries(self: pydrake.multibody.plant.MultibodyPlant, bodies: list[pydrake.multibody.tree.RigidBody]) → pydrake.geometry.GeometrySet

For each of the provided bodies, collects up all geometries that have been registered to that body. Intended to be used in conjunction with CollisionFilterDeclaration and CollisionFilterManager::Apply() to filter collisions between the geometries registered to the bodies.

For example:

Click to expand C++ code...

// Don't report on collisions between geometries affixed to `body1`,
// `body2`, or `body3`.
std::vector<const RigidBody<T>*> bodies{&body1, &body2, &body3};
geometry::GeometrySet set = plant.CollectRegisteredGeometries(bodies);
scene_graph.collision_filter_manager().Apply(
    CollisionFilterDeclaration().ExcludeWithin(set));

Note

There is a very specific order of operations:

Bodies and geometries must be added to the MultibodyPlant.
Create GeometrySet instances from bodies (via this method).
Invoke SceneGraph::ExcludeCollisions*() to filter collisions.
Allocate context.

Changing the order will cause exceptions to be thrown.

Raises

RuntimeError if this MultibodyPlant was not registered with a –
SceneGraph. –

deformable_model(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.plant.DeformableModel

Returns the DeformableModel owned by this plant.

Raises: RuntimeError if this plant doesn't own a DeformableModel. –

Warning

This feature is considered to be experimental and may change or be removed at any time, without any deprecation notice ahead of time.

EvalBodyPoseInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody) → pydrake.math.RigidTransform

Evaluate the pose X_WB of a body B in the world frame W.

Parameter context:: The context storing the state of the model.
Parameter body_B:: The body B for which the pose is requested.
Returns X_WB:: The pose of body frame B in the world frame W.

Raises

RuntimeError if Finalize() was not called on this model or if –
body_B` does not belong to this model –

EvalBodySpatialAccelerationInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody) → pydrake.multibody.math.SpatialAcceleration

Evaluates A_WB, body B’s spatial acceleration in the world frame W.

Parameter context:: The context storing the state of the model.
Parameter body_B:: The body for which spatial acceleration is requested.
Returns A_WB_W:: RigidBody B’s spatial acceleration in the world frame W, expressed in W (for point Bo, the body’s origin).

Raises

RuntimeError if Finalize() was not called on this model or if –
body_B` does not belong to this model –

Note

When cached values are out of sync with the state stored in context, this method performs an expensive forward dynamics computation, whereas once evaluated, successive calls to this method are inexpensive.

EvalBodySpatialVelocityInWorld(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody) → pydrake.multibody.math.SpatialVelocity

Evaluates V_WB, body B’s spatial velocity in the world frame W.

Parameter context:: The context storing the state of the model.
Parameter body_B:: The body B for which the spatial velocity is requested.
Returns V_WB_W:: RigidBody B’s spatial velocity in the world frame W, expressed in W (for point Bo, the body’s origin).

Raises

RuntimeError if Finalize() was not called on this model or if –
body_B` does not belong to this model –

EvalSceneGraphInspector(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → pydrake.geometry.SceneGraphInspector: Returns the inspector from the context for the SceneGraph associated with this plant, via this plant’s “geometry_query” input port. (In the future, the inspector might come from a different context source that is more efficient than the “geometry_query” input port.)

Finalize(self: pydrake.multibody.plant.MultibodyPlant) → None

This method must be called after all elements in the model (joints, bodies, force elements, constraints, etc.) are added and before any computations are performed. It essentially compiles all the necessary “topological information”, i.e. how bodies, joints and, any other elements connect with each other, and performs all the required pre-processing to enable computations at a later stage.

If the finalize stage is successful, the topology of this MultibodyPlant is valid, meaning that the topology is up-to-date after this call. No more multibody elements can be added after a call to Finalize().

At Finalize(), state and input/output ports for this plant are declared.

For a full account of the effects of Finalize(), see mbp_finalize_stage “Finalize() stage”.

See also

is_finalized(), mbp_finalize_stage “Finalize() stage”.

Raises: RuntimeError if the MultibodyPlant has already been finalized. –

geometry_source_is_registered(self: pydrake.multibody.plant.MultibodyPlant) → bool: Returns True if this MultibodyPlant was registered with a SceneGraph. This method can be called at any time during the lifetime of this plant to query if this plant has been registered with a SceneGraph, either pre- or post-finalize, see Finalize().

get_actuation_input_port(*args, **kwargs)

Overloaded function.

get_actuation_input_port(self: pydrake.multibody.plant.MultibodyPlant) -> pydrake.systems.framework.InputPort

Returns a constant reference to the input port for external actuation for all actuated dofs. This input port is a vector valued port and can be set with JointActuator::set_actuation_vector(). The actuation value for a particular actuator can be found at offset JointActuator::input_start() in this vector. Refer to mbp_actuation “Actuation” for further details.

Precondition:: Finalize() was already called on this plant.

Raises: RuntimeError if called before Finalize() –

get_actuation_input_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.systems.framework.InputPort

Returns a constant reference to the input port for external actuation for a specific model instance. This is a vector valued port with entries ordered by monotonically increasing JointActuatorIndex within model_instance. Refer to mbp_actuation “Actuation” for further details.

Every model instance in this plant model has an actuation input port, even if zero sized (for model instance with no actuators).

See also

GetJointActuatorIndices(), GetActuatedJointIndices().

Precondition:: Finalize() was already called on this plant.

Raises

RuntimeError if called before Finalize() –
RuntimeError if the model instance does not exist. –

get_adjacent_bodies_collision_filters(self: pydrake.multibody.plant.MultibodyPlant) → bool: Returns whether to apply collision filters to topologically adjacent bodies at Finalize() time.

get_applied_generalized_force_input_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.InputPort

Returns a constant reference to the vector-valued input port for applied generalized forces, and the vector will be added directly into tau (see mbp_equations_of_motion “System dynamics”). This vector is ordered using the same convention as the plant velocities: you can set the generalized forces that will be applied to model instance i using, e.g., SetVelocitiesInArray(i, model_forces, &force_array).

Raises: RuntimeError if called before Finalize() –

get_applied_spatial_force_input_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.InputPort: Returns a constant reference to the input port for applying spatial forces to bodies in the plant. The data type for the port is an std::vector of ExternallyAppliedSpatialForce; any number of spatial forces can be applied to any number of bodies in the plant.

get_body(self: pydrake.multibody.plant.MultibodyPlant, body_index: pydrake.multibody.tree.BodyIndex) → pydrake.multibody.tree.RigidBody

Returns a constant reference to the body with unique index body_index.

Raises

RuntimeError if body_index does not correspond to a body in –
this model. –

get_body_poses_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort

Returns the output port of all body poses in the world frame. You can obtain the pose X_WB of a body B in the world frame W with:

Click to expand C++ code...

const auto& X_WB_all = plant.get_body_poses_output_port().
      .Eval<std::vector<math::RigidTransform<double>>>(plant_context);
  const BodyIndex arm_body_index = plant.GetBodyByName("arm").index();
  const math::RigidTransform<double>& X_WArm = X_WB_all[arm_body_index];

As shown in the example above, the resulting std::vector of body poses is indexed by BodyIndex, and it has size num_bodies(). BodyIndex “zero” (0) always corresponds to the world body, with pose equal to the identity at all times.

Raises: RuntimeError if called pre-finalize. –

get_body_spatial_accelerations_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort

Returns the output port of all body spatial accelerations in the world frame. You can obtain the spatial acceleration A_WB of a body B (for point Bo, the body’s origin) in the world frame W with:

Click to expand C++ code...

const auto& A_WB_all =
  plant.get_body_spatial_accelerations_output_port().
      .Eval<std::vector<SpatialAcceleration<double>>>(plant_context);
  const BodyIndex arm_body_index = plant.GetBodyByName("arm").index();
  const SpatialVelocity<double>& A_WArm = A_WB_all[arm_body_index];

As shown in the example above, the resulting std::vector of body spatial accelerations is indexed by BodyIndex, and it has size num_bodies(). BodyIndex “zero” (0) always corresponds to the world body, with zero spatial acceleration at all times.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Raises: RuntimeError if called pre-finalize. –

get_body_spatial_velocities_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort

Returns the output port of all body spatial velocities in the world frame. You can obtain the spatial velocity V_WB of a body B in the world frame W with:

Click to expand C++ code...

const auto& V_WB_all = plant.get_body_spatial_velocities_output_port().
      .Eval<std::vector<SpatialVelocity<double>>>(plant_context);
  const BodyIndex arm_body_index = plant.GetBodyByName("arm").index();
  const SpatialVelocity<double>& V_WArm = V_WB_all[arm_body_index];

As shown in the example above, the resulting std::vector of body spatial velocities is indexed by BodyIndex, and it has size num_bodies(). BodyIndex “zero” (0) always corresponds to the world body, with zero spatial velocity at all times.

Raises: RuntimeError if called pre-finalize. –

get_contact_model(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.plant.ContactModel: Returns the model used for contact. See documentation for ContactModel.

get_contact_penalty_method_time_scale(self: pydrake.multibody.plant.MultibodyPlant) → float: Returns a time-scale estimate tc based on the requested penetration allowance δ set with set_penetration_allowance(). For the compliant contact model to enforce non-penetration, this time scale relates to the time it takes the relative normal velocity between two bodies to go to zero. This time scale tc is a global estimate of the dynamics introduced by the compliant contact model and goes to zero in the limit to ideal rigid contact. Since numerical integration methods for continuum systems must be able to resolve a system’s dynamics, the time step used by an integrator must in general be much smaller than the time scale tc. How much smaller will depend on the details of the problem and the convergence characteristics of the integrator and should be tuned appropriately. Another factor to take into account for setting up the simulation’s time step is the speed of the objects in your simulation. If vn represents a reference velocity scale for the normal relative velocity between bodies, the new time scale tn = δ / vn represents the time it would take for the distance between two bodies approaching with relative normal velocity vn to decrease by the penetration_allowance δ. In this case a user should choose a time step for simulation that can resolve the smallest of the two time scales tc and tn.

get_contact_results_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort

Returns a constant reference to the port that outputs ContactResults.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be empty (no contacts).

Raises: RuntimeError if called pre-finalize, see Finalize() –

get_contact_surface_representation(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.geometry.HydroelasticContactRepresentation: Gets the current representation of contact surfaces used by this MultibodyPlant.

get_deformable_body_configuration_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort: Returns the output port for vertex positions (configurations), measured and expressed in the World frame, of the deformable bodies in this plant as a GeometryConfigurationVector.

get_desired_state_input_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → pydrake.systems.framework.InputPort

For models with PD controlled joint actuators, returns the port to provide the desired state for the full model_instance. Refer to mbp_actuation “Actuation” for further details.

For consistency with get_actuation_input_port(), each model instance in this plant model has a desired states input port, even if zero sized (for model instance with no actuators.)

Note

This is a vector valued port of size 2*num_actuators(model_instance), where we assumed 1-DOF actuated joints. This is true even for unactuated models, for which this port is zero sized. This port must provide one desired position and one desired velocity per joint actuator. Desired state is assumed to be packed as xd = [qd, vd] that is, configurations first followed by velocities. The actuation value for a particular actuator can be found at offset JointActuator::input_start() in both qd and vd. For example:

Click to expand C++ code...

const double qd_actuator = xd[actuator.input_start()];
const double vd_actuator =
   xd[actuator.input_start() + plant.num_actuated_dofs()];

Warning

If a user specifies a PD controller for an actuator from a given model instance, then all actuators of that model instance are required to be PD controlled.

Warning

It is required to connect this port for PD controlled model instances.

get_discrete_contact_approximation(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.plant.DiscreteContactApproximation

Returns: the discrete contact solver approximation.

get_discrete_contact_solver(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.plant.DiscreteContactSolver: Returns the contact solver type used for discrete MultibodyPlant models.

get_force_element(self: pydrake.multibody.plant.MultibodyPlant, force_element_index: pydrake.multibody.tree.ForceElementIndex) → pydrake.multibody.tree.ForceElement

Returns a constant reference to the force element with unique index force_element_index.

Raises

RuntimeError when force_element_index does not correspond to a –
force element in this model. –

get_frame(self: pydrake.multibody.plant.MultibodyPlant, frame_index: pydrake.multibody.tree.FrameIndex) → pydrake.multibody.tree.Frame

Returns a constant reference to the frame with unique index frame_index.

Raises

RuntimeError if frame_index does not correspond to a frame in –
this plant. –

get_generalized_acceleration_output_port(*args, **kwargs)

Overloaded function.

get_generalized_acceleration_output_port(self: pydrake.multibody.plant.MultibodyPlant) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port for generalized accelerations v̇ of the model.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Precondition:: Finalize() was already called on this plant.

Raises: RuntimeError if called before Finalize() –

get_generalized_acceleration_output_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port for the generalized accelerations v̇ᵢ ⊆ v̇ for model instance i.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Precondition:: Finalize() was already called on this plant.

Raises

RuntimeError if called before Finalize() –
RuntimeError if the model instance does not exist. –

get_generalized_contact_forces_output_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → pydrake.systems.framework.OutputPort

Returns a constant reference to the output port of generalized contact forces for a specific model instance.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Precondition:: Finalize() was already called on this plant.

Raises

RuntimeError if called before Finalize() –
RuntimeError if the model instance does not exist. –

get_geometry_pose_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort: Returns the output port of frames’ poses to communicate with a SceneGraph.

get_geometry_query_input_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.InputPort: Returns a constant reference to the input port used to perform geometric queries on a SceneGraph. See SceneGraph::get_query_output_port(). Refer to section mbp_geometry “Geometry” of this class’s documentation for further details on collision geometry registration and connection with a SceneGraph.

get_joint(self: pydrake.multibody.plant.MultibodyPlant, joint_index: pydrake.multibody.tree.JointIndex) → pydrake.multibody.tree.Joint

Returns a constant reference to the joint with unique index joint_index.

Raises

RuntimeError when joint_index does not correspond to a joint –
in this model. –

get_joint_actuator(self: pydrake.multibody.plant.MultibodyPlant, actuator_index: pydrake.multibody.tree.JointActuatorIndex) → pydrake.multibody.tree.JointActuator

Returns a constant reference to the joint actuator with unique index actuator_index.

Raises

RuntimeError if actuator_index does not correspond to a joint –
actuator in this tree. –

get_mutable_joint(self: pydrake.multibody.plant.MultibodyPlant, joint_index: pydrake.multibody.tree.JointIndex) → pydrake.multibody.tree.Joint

Returns a mutable reference to the joint with unique index joint_index.

Raises

RuntimeError when joint_index does not correspond to a joint –
in this model. –

get_mutable_joint_actuator(self: pydrake.multibody.plant.MultibodyPlant, actuator_index: pydrake.multibody.tree.JointActuatorIndex) → pydrake.multibody.tree.JointActuator

Returns a mutable reference to the joint actuator with unique index actuator_index.

Raises

RuntimeError if actuator_index does not correspond to a joint –
actuator in this tree. –

get_net_actuation_output_port(*args, **kwargs)

Overloaded function.

get_net_actuation_output_port(self: pydrake.multibody.plant.MultibodyPlant) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port that reports actuation values applied through joint actuators. This output port is a vector valued port. The actuation value for a particular actuator can be found at offset JointActuator::input_start() in this vector. Models that include PD controllers will include their contribution in this port, refer to mbp_actuation “Actuation” for further details.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Note

PD controllers are not considered for actuators on locked joints, see Joint::Lock(). Therefore they do not contribute to this port.

Precondition:: Finalize() was already called on this plant.

Raises: RuntimeError if called before Finalize() –

get_net_actuation_output_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port that reports actuation values applied through joint actuators, for a specific model instance. Models that include PD controllers will include their contribution in this port, refer to mbp_actuation “Actuation” for further details. This is a vector valued port with entries ordered by monotonically increasing JointActuatorIndex within model_instance.

Every model instance in this plant model has a net actuation output port, even if zero sized (for model instance with no actuators).

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Note

PD controllers are not considered for actuators on locked joints, see Joint::Lock(). Therefore they do not contribute to this port.

Precondition:: Finalize() was already called on this plant.

Raises: RuntimeError if called before Finalize() –

get_reaction_forces_output_port(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.systems.framework.OutputPort

Returns the port for joint reaction forces. A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. In Drake, a joint connects a frame Jp on parent body P with a frame Jc on a child body C. This usage of the terms parent and child is just a convention and implies nothing about the inboard-outboard relationship between the bodies. Since a Joint imposes a kinematical relationship which characterizes the possible relative motion between frames Jp and Jc, reaction forces on each body are established. That is, we could cut the model at the joint and replace it with equivalent forces equal to these reaction forces in order to attain the same motions of the mechanical system.

This output port allows to evaluate the reaction force F_CJc_Jc on the child body C, at Jc, and expressed in Jc for all joints in the model. This port evaluates to a vector of type std::vector<SpatialForce<T>> and size num_joints() indexed by JointIndex, see Joint::index(). Each entry corresponds to the spatial force F_CJc_Jc applied on the joint’s child body C (Joint::child_body()), at the joint’s child frame Jc (Joint::frame_on_child()) and expressed in frame Jc.

In a discrete-time plant, the use_sampled_output_ports setting affects the output of this port. See output_port_sampling “Output port sampling” for details. When sampling is enabled and the plant has not yet taken a step, the output value will be all zeros.

Raises: RuntimeError if called pre-finalize. –

get_sap_near_rigid_threshold(self: pydrake.multibody.plant.MultibodyPlant) → float

Returns: the SAP near rigid regime threshold.

See also

See set_sap_near_rigid_threshold().

get_source_id(self: pydrake.multibody.plant.MultibodyPlant) → Optional[pydrake.geometry.SourceId]: Returns the unique id identifying this plant as a source for a SceneGraph. Returns nullopt if this plant did not register any geometry. This method can be called at any time during the lifetime of this plant to query if this plant has been registered with a SceneGraph, either pre- or post-finalize, see Finalize(). However, a geometry::SourceId is only assigned once at the first call of any of this plant’s geometry registration methods, and it does not change after that. Post-finalize calls will always return the same value.

get_state_output_port(*args, **kwargs)

Overloaded function.

get_state_output_port(self: pydrake.multibody.plant.MultibodyPlant) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port for the multibody state x = [q, v] of the model.

Precondition:: Finalize() was already called on this plant.

Raises: RuntimeError if called before Finalize() –

get_state_output_port(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.systems.framework.OutputPort

Returns a constant reference to the output port for the state xᵢ = [qᵢ vᵢ] of model instance i. (Here qᵢ ⊆ q and vᵢ ⊆ v.)

Precondition:: Finalize() was already called on this plant.

Raises

RuntimeError if called before Finalize() –
RuntimeError if the model instance does not exist. –

GetAccelerationLowerLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]

Returns a vector of size num_velocities() containing the lower acceleration limits for every generalized velocity coordinate. These include joint and free body coordinates. Any unbounded or unspecified limits will be -infinity.

Raises: RuntimeError if called pre-finalize. –

GetAccelerationUpperLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]: Upper limit analog of GetAccelerationsLowerLimits(), where any unbounded or unspecified limits will be +infinity.

See also

GetAccelerationLowerLimits() for more information.

GetActuatedJointIndices(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → list[pydrake.multibody.tree.JointIndex]

Returns a list of actuated joint indices associated with model_instance.

Raises: RuntimeError if called pre-finalize. –

GetActuatorNames(*args, **kwargs)

Overloaded function.

GetActuatorNames(self: pydrake.multibody.plant.MultibodyPlant, add_model_instance_prefix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the actuation vector. These strings take the form {model_instance_name}_{joint_actuator_name}, but the prefix may optionally be withheld using add_model_instance_prefix.

The returned names are guaranteed to be unique if add_model_instance_prefix is True (the default).

Raises: RuntimeError if the plant is not finalized. –

GetActuatorNames(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, add_model_instance_prefix: bool = False) -> list[str]

Returns a list of string names corresponding to each element of the actuation vector. These strings take the form {model_instance_name}_{joint_actuator_name}, but the prefix may optionally be withheld using add_model_instance_prefix.

The returned names are guaranteed to be unique.

Raises

RuntimeError if the plant is not finalized or if the –
model_instance` is invalid –

GetBodiesKinematicallyAffectedBy(self: pydrake.multibody.plant.MultibodyPlant, joint_indexes: list[pydrake.multibody.tree.JointIndex]) → list[pydrake.multibody.tree.BodyIndex]

Returns all bodies whose kinematics are transitively affected by the given vector of Joints. The affected bodies are returned in increasing order of body indexes. Note that this is a kinematic relationship rather than a dynamic one. For example, if one of the inboard joints is a free (6dof) joint, the kinematic influence is still felt even though dynamically there would be no influence on the outboard body. This function can be only be called post-finalize, see Finalize().

Raises

RuntimeError if any of the given joint has an invalid index, –
doesn't correspond to a mobilizer, or is welded. –

GetBodiesWeldedTo(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody) → list[pydrake.multibody.tree.RigidBody]

Returns all bodies that are transitively welded, or rigidly affixed, to body, per these two definitions:

A body is always considered welded to itself.

2. Two unique bodies are considered welded together exclusively by the presence of a weld joint, not by other constructs that prevent mobility (e.g. constraints).

This method can be called at any time during the lifetime of this plant, either pre- or post-finalize, see Finalize().

Meant to be used with CollectRegisteredGeometries.

The following example demonstrates filtering collisions between all bodies rigidly affixed to a door (which could be moving) and all bodies rigidly affixed to the world:

Click to expand C++ code...

GeometrySet g_world = plant.CollectRegisteredGeometries(
    plant.GetBodiesWeldedTo(plant.world_body()));
GeometrySet g_door = plant.CollectRegisteredGeometries(
    plant.GetBodiesWeldedTo(plant.GetBodyByName("door")));
scene_graph.ExcludeCollisionsBetweeen(g_world, g_door);

Note

Usages akin to this example may introduce redundant collision filtering; this will not have a functional impact, but may have a minor performance impact.

Returns: all bodies rigidly fixed to body. This does not return the bodies in any prescribed order.
Raises: RuntimeError if body is not part of this plant. –

GetBodyByName(*args, **kwargs)

Overloaded function.

GetBodyByName(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> pydrake.multibody.tree.RigidBody

Returns a constant reference to a body that is identified by the string name in this MultibodyPlant.

Raises

RuntimeError if there is no body with the requested name. –
RuntimeError if the body name occurs in multiple model instances. –

See also

HasBodyNamed() to query if there exists a body in this MultibodyPlant with a given specified name.

GetBodyByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.multibody.tree.RigidBody

Returns a constant reference to the body that is uniquely identified by the string name and model_instance in this MultibodyPlant.

Raises: RuntimeError if there is no body with the requested name. –

See also

HasBodyNamed() to query if there exists a body in this MultibodyPlant with a given specified name.

GetBodyFrameIdIfExists(self: pydrake.multibody.plant.MultibodyPlant, body_index: pydrake.multibody.tree.BodyIndex) → Optional[pydrake.geometry.FrameId]: If the body with body_index belongs to the called plant, it returns the geometry::FrameId associated with it. Otherwise, it returns nullopt.

GetBodyFrameIdOrThrow(self: pydrake.multibody.plant.MultibodyPlant, body_index: pydrake.multibody.tree.BodyIndex) → pydrake.geometry.FrameId

If the body with body_index belongs to the called plant, it returns the geometry::FrameId associated with it. Otherwise this method throws an exception.

Raises

RuntimeError if the called plant does not have the body indicated –
by body_index. –

GetBodyFromFrameId(self: pydrake.multibody.plant.MultibodyPlant, arg0: pydrake.geometry.FrameId) → pydrake.multibody.tree.RigidBody: Given a geometry frame identifier, returns a pointer to the body associated with that id (nullptr if there is no such body).

GetBodyIndices(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → list[pydrake.multibody.tree.BodyIndex]: Returns a list of body indices associated with model_instance.

GetCollisionGeometriesForBody(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody) → list[pydrake.geometry.GeometryId]: Returns an array of GeometryId’s identifying the different contact geometries for body previously registered with a SceneGraph.

Note

This method can be called at any time during the lifetime of this plant, either pre- or post-finalize, see Finalize(). Post-finalize calls will always return the same value.

See also

RegisterCollisionGeometry(), Finalize()

GetConstraintActiveStatus(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, id: pydrake.multibody.tree.MultibodyConstraintId) → bool

Returns the active status of the constraint given by id in context.

Raises

RuntimeError if the MultibodyPlant has not been finalized. –
RuntimeError if id does not belong to any multibody constraint –
in context. –

GetConstraintIds(self: pydrake.multibody.plant.MultibodyPlant) → list[pydrake.multibody.tree.MultibodyConstraintId]: Returns a list of all constraint identifiers. The returned vector becomes invalid after any calls to Add*Constraint() or RemoveConstraint().

static GetDefaultContactSurfaceRepresentation(time_step: float) → pydrake.geometry.HydroelasticContactRepresentation: Return the default value for contact representation, given the desired time step. Discrete systems default to use polygons; continuous systems default to use triangles.

GetDefaultFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody) → pydrake.math.RigidTransform

Gets the default pose of body as set by SetDefaultFreeBodyPose(). If no pose is specified for the body, returns the identity pose.

Parameter body:: RigidBody whose default pose will be retrieved.
Returns X_PB:: The pose of the free body relative to its parent frame.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

GetDefaultPositions(*args, **kwargs)

Overloaded function.

GetDefaultPositions(self: pydrake.multibody.plant.MultibodyPlant) -> numpy.ndarray[numpy.float64[m, 1]]

Gets the default positions for the plant, which can be changed via SetDefaultPositions().

Raises: RuntimeError if the plant is not finalized. –

GetDefaultPositions(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Gets the default positions for the plant for a given model instance, which can be changed via SetDefaultPositions().

Raises

RuntimeError if the plant is not finalized, or if the –
model_instance is invalid, –

GetEffortLowerLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]

Returns a vector of size num_actuated_dofs() containing the lower effort limits for every actuator. Any unbounded or unspecified limits will be -∞. The returned vector is indexed by JointActuatorIndex, see JointActuator::index().

See also

GetEffortUpperLimits()

Raises: RuntimeError if called pre-finalize. –

GetEffortUpperLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]

Returns a vector of size num_actuated_dofs() containing the upper effort limits for every actuator. Any unbounded or unspecified limits will be +∞. The returned vector is indexed by JointActuatorIndex, see JointActuator::index().

See also

GetEffortLowerLimits()

Raises: RuntimeError if called pre-finalize. –

GetFloatingBaseBodies(self: pydrake.multibody.plant.MultibodyPlant) → set[pydrake.multibody.tree.BodyIndex]

Returns the set of body indices corresponding to the floating base bodies in the model, in no particular order.

Raises: RuntimeError if called pre-finalize, see Finalize() –

GetFrameByName(*args, **kwargs)

Overloaded function.

GetFrameByName(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> pydrake.multibody.tree.Frame

Returns a constant reference to a frame that is identified by the string name in this model.

Raises

RuntimeError if there is no frame with the requested name. –
RuntimeError if the frame name occurs in multiple model instances. –

See also

HasFrameNamed() to query if there exists a frame in this model with a given specified name.

GetFrameByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.multibody.tree.Frame

Returns a constant reference to the frame that is uniquely identified by the string name in model_instance.

Raises

RuntimeError if there is no frame with the requested name. –
RuntimeError if model_instance is not valid for this model. –

See also

HasFrameNamed() to query if there exists a frame in this model with a given specified name.

GetFrameIndices(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → list[pydrake.multibody.tree.FrameIndex]: Returns a list of frame indices associated with model_instance.

GetFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody) → pydrake.math.RigidTransform

Gets the pose of a given body in the parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”. To acquire X_WB, regardless of what P is, kinematics need to be evaluated by calling EvalBodyPoseInWorld().

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

GetJointActuatorByName(*args, **kwargs)

Overloaded function.

GetJointActuatorByName(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> pydrake.multibody.tree.JointActuator

Returns a constant reference to an actuator that is identified by the string name in this MultibodyPlant.

Raises

RuntimeError if there is no actuator with the requested name. –
RuntimeError if the actuator name occurs in multiple model –
instances. –

See also

HasJointActuatorNamed() to query if there exists an actuator in this MultibodyPlant with a given specified name.

GetJointActuatorByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.multibody.tree.JointActuator

Returns a constant reference to the actuator that is uniquely identified by the string name and model_instance in this MultibodyPlant.

Raises

RuntimeError if there is no actuator with the requested name. –
RuntimeError if model_instance is not valid for this model. –

See also

HasJointActuatorNamed() to query if there exists an actuator in this MultibodyPlant with a given specified name.

GetJointActuatorIndices(*args, **kwargs)

Overloaded function.

GetJointActuatorIndices(self: pydrake.multibody.plant.MultibodyPlant) -> list[pydrake.multibody.tree.JointActuatorIndex]

Returns a list of all joint actuator indices. The vector is ordered by monotonically increasing JointActuatorIndex, but the indices will in general not be consecutive due to actuators that were removed.

GetJointActuatorIndices(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> list[pydrake.multibody.tree.JointActuatorIndex]

Returns a list of joint actuator indices associated with model_instance. The vector is ordered by monotonically increasing JointActuatorIndex.

Raises: RuntimeError if called pre-finalize. –

GetJointByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) → pydrake.multibody.tree.Joint

Returns a constant reference to a joint that is identified by the string name in this MultibodyPlant. If the optional template argument is supplied, then the returned value is downcast to the specified JointType.

Template parameter JointType:: The specific type of the Joint to be retrieved. It must be a subclass of Joint.

Raises

RuntimeError if the named joint is not of type JointType or if –
there is no Joint with that name. –
RuntimeError if model_instance is not valid for this model. –

See also

HasJointNamed() to query if there exists a joint in this MultibodyPlant with a given specified name.

GetJointIndices(*args, **kwargs)

Overloaded function.

GetJointIndices(self: pydrake.multibody.plant.MultibodyPlant) -> list[pydrake.multibody.tree.JointIndex]

Returns a list of all joint indices. The vector is ordered by monotonically increasing JointIndex, but the indices will in general not be consecutive due to joints that were removed.

GetJointIndices(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> list[pydrake.multibody.tree.JointIndex]

Returns a list of joint indices associated with model_instance.

GetModelInstanceByName(self: pydrake.multibody.plant.MultibodyPlant, name: str) → pydrake.multibody.tree.ModelInstanceIndex

Returns the index to the model instance that is uniquely identified by the string name in this MultibodyPlant.

Raises: RuntimeError if there is no instance with the requested name. –

See also

HasModelInstanceNamed() to query if there exists an instance in this MultibodyPlant with a given specified name.

GetModelInstanceName(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → str

Returns the name of a model_instance.

Raises

RuntimeError when model_instance does not correspond to a –
model in this model. –

GetMutableJointByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: Optional[pydrake.multibody.tree.ModelInstanceIndex] = None) → pydrake.multibody.tree.Joint

Returns a constant reference to a joint that is identified by the string name in this MultibodyPlant. If the optional template argument is supplied, then the returned value is downcast to the specified JointType.

Template parameter JointType:: The specific type of the Joint to be retrieved. It must be a subclass of Joint.

Raises

RuntimeError if the named joint is not of type JointType or if –
there is no Joint with that name. –
RuntimeError if model_instance is not valid for this model. –

See also

HasJointNamed() to query if there exists a joint in this MultibodyPlant with a given specified name.

GetPositionLowerLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]

Returns a vector of size num_positions() containing the lower position limits for every generalized position coordinate. These include joint and free body coordinates. Any unbounded or unspecified limits will be -infinity.

Raises: RuntimeError if called pre-finalize. –

GetPositionNames(*args, **kwargs)

Overloaded function.

GetPositionNames(self: pydrake.multibody.plant.MultibodyPlant, add_model_instance_prefix: bool = True, always_add_suffix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the position vector. These strings take the form {model_instance_name}_{joint_name}_{joint_position_suffix}, but the prefix and suffix may optionally be withheld using add_model_instance_prefix and always_add_suffix.

Parameter always_add_suffix:: (optional). If true, then the suffix is always added. If false, then the suffix is only added for joints that have more than one position (in this case, not adding would lead to ambiguity).

The returned names are guaranteed to be unique if add_model_instance_prefix is True (the default).

Raises: RuntimeError if the plant is not finalized. –

GetPositionNames(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, add_model_instance_prefix: bool = False, always_add_suffix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the position vector. These strings take the form {model_instance_name}_{joint_name}_{joint_position_suffix}, but the prefix and suffix may optionally be withheld using add_model_instance_prefix and always_add_suffix.

Parameter always_add_suffix:: (optional). If true, then the suffix is always added. If false, then the suffix is only added for joints that have more than one position (in this case, not adding would lead to ambiguity).

The returned names are guaranteed to be unique.

Raises

RuntimeError if the plant is not finalized or if the –
model_instance` is invalid –

GetPositions(*args, **kwargs)

Overloaded function.

GetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a const vector reference to the vector of generalized positions q in a given Context.

Note

This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model. –

GetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a vector containing the generalized positions q of a specified model instance in a given Context.

Note

Returns a dense vector of dimension num_positions(model_instance) associated with model_instance by copying from context.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model or model_instance is invalid. –

GetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a const vector reference to the vector of generalized positions q in a given Context.

Note

This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model. –

GetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a vector containing the generalized positions q of a specified model instance in a given Context.

Note

Returns a dense vector of dimension num_positions(model_instance) associated with model_instance by copying from context.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model or model_instance is invalid. –

GetPositionsAndVelocities(*args, **kwargs)

Overloaded function.

GetPositionsAndVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a const vector reference [q; v] to the generalized positions q and generalized velocities v in a given Context.

Note

This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model. –

GetPositionsAndVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a vector [q; v] containing the generalized positions q and generalized velocities v of a specified model instance in a given Context.

Note

Returns a dense vector of dimension num_positions(model_instance) + num_velocities(model_instance) associated with model_instance by copying from context.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model or model_instance is invalid. –

GetPositionsFromArray(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, q: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]: Returns a vector of generalized positions for model_instance from a vector q_array of generalized positions for the entire model model. This method throws an exception if q is not of size MultibodyPlant::num_positions().

GetPositionUpperLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]: Upper limit analog of GetPositionLowerLimits(), where any unbounded or unspecified limits will be +infinity.

See also

GetPositionLowerLimits() for more information.

GetRigidBodyByName(*args, **kwargs)

Overloaded function.

GetRigidBodyByName(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> pydrake.multibody.tree.RigidBody

Returns a constant reference to a rigid body that is identified by the string name in this model.

Raises

RuntimeError if there is no body with the requested name. –
RuntimeError if the body name occurs in multiple model instances. –
RuntimeError if the requested body is not a RigidBody. –

See also

HasBodyNamed() to query if there exists a body in this model with a given specified name.

GetRigidBodyByName(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> pydrake.multibody.tree.RigidBody

Returns a constant reference to the rigid body that is uniquely identified by the string name in model_instance.

Raises

RuntimeError if there is no body with the requested name. –
RuntimeError if the requested body is not a RigidBody. –
RuntimeError if model_instance is not valid for this model. –

See also

HasBodyNamed() to query if there exists a body in this model with a given specified name.

GetStateNames(*args, **kwargs)

Overloaded function.

GetStateNames(self: pydrake.multibody.plant.MultibodyPlant, add_model_instance_prefix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the multibody state vector. These strings take the form {model_instance_name}_{joint_name}_{joint_position_suffix | joint_velocity_suffix}, but the prefix may optionally be withheld using add_model_instance_prefix.

The returned names are guaranteed to be unique if add_model_instance_prefix is True (the default).

Raises: RuntimeError if the plant is not finalized. –

GetStateNames(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, add_model_instance_prefix: bool = False) -> list[str]

Returns a list of string names corresponding to each element of the multibody state vector. These strings take the form {model_instance_name}_{joint_name}_{joint_position_suffix | joint_velocity_suffix}, but the prefix may optionally be withheld using add_model_instance_prefix.

The returned names are guaranteed to be unique.

Raises

RuntimeError if the plant is not finalized or if the –
model_instance` is invalid –

GetTopologyGraphvizString(self: pydrake.multibody.plant.MultibodyPlant) → str

Returns a Graphviz string describing the topology of this plant. To render the string, use the Graphviz tool, dot. http://www.graphviz.org/

Note: this method can be called either before or after Finalize().

GetUniqueFreeBaseBodyOrThrow(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → pydrake.multibody.tree.RigidBody

If there exists a unique base body that belongs to the model given by model_instance and that unique base body is free (see HasUniqueBaseBody()), return that free body. Throw an exception otherwise.

Raises

RuntimeError if called pre-finalize. –
RuntimeError if model_instance is not valid. –
RuntimeError if HasUniqueFreeBaseBody(model_instance) == false. –

GetVelocities(*args, **kwargs)

Overloaded function.

GetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a const vector reference to the generalized velocities v in a given Context.

Note

This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model. –

GetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a vector containing the generalized velocities v of a specified model instance in a given Context.

Note

returns a dense vector of dimension num_velocities(model_instance) associated with model_instance by copying from context.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model or model_instance is invalid. –

GetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a const vector reference to the generalized velocities v in a given Context.

Note

This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model. –

GetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> numpy.ndarray[numpy.float64[m, 1]]

Returns a vector containing the generalized velocities v of a specified model instance in a given Context.

Note

returns a dense vector of dimension num_velocities(model_instance) associated with model_instance by copying from context.

Raises

RuntimeError if context does not correspond to the Context for –
a multibody model or model_instance is invalid. –

GetVelocitiesFromArray(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, v: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]: Returns a vector of generalized velocities for model_instance from a vector v of generalized velocities for the entire MultibodyPlant model. This method throws an exception if the input array is not of size MultibodyPlant::num_velocities().

GetVelocityLowerLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]

Returns a vector of size num_velocities() containing the lower velocity limits for every generalized velocity coordinate. These include joint and free body coordinates. Any unbounded or unspecified limits will be -infinity.

Raises: RuntimeError if called pre-finalize. –

GetVelocityNames(*args, **kwargs)

Overloaded function.

GetVelocityNames(self: pydrake.multibody.plant.MultibodyPlant, add_model_instance_prefix: bool = True, always_add_suffix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the velocity vector. These strings take the form {model_instance_name}_{joint_name}_{joint_velocity_suffix}, but the prefix and suffix may optionally be withheld using add_model_instance_prefix and always_add_suffix.

Parameter always_add_suffix:: (optional). If true, then the suffix is always added. If false, then the suffix is only added for joints that have more than one position (in this case, not adding would lead to ambiguity).

The returned names are guaranteed to be unique if add_model_instance_prefix is True (the default).

Raises: RuntimeError if the plant is not finalized. –

GetVelocityNames(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, add_model_instance_prefix: bool = False, always_add_suffix: bool = True) -> list[str]

Returns a list of string names corresponding to each element of the velocity vector. These strings take the form {model_instance_name}_{joint_name}_{joint_velocity_suffix}, but the prefix and suffix may optionally be withheld using add_model_instance_prefix and always_add_suffix.

Parameter always_add_suffix:: (optional). If true, then the suffix is always added. If false, then the suffix is only added for joints that have more than one position (in this case, not adding would lead to ambiguity).

The returned names are guaranteed to be unique.

Raises

RuntimeError if the plant is not finalized or if the –
model_instance` is invalid –

GetVelocityUpperLimits(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, 1]]: Upper limit analog of GetVelocitysLowerLimits(), where any unbounded or unspecified limits will be +infinity.

See also

GetVelocityLowerLimits() for more information.

GetVisualGeometriesForBody(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody) → list[pydrake.geometry.GeometryId]: Returns an array of GeometryId’s identifying the different visual geometries for body previously registered with a SceneGraph.

Note

This method can be called at any time during the lifetime of this plant, either pre- or post-finalize, see Finalize(). Post-finalize calls will always return the same value.

See also

RegisterVisualGeometry(), Finalize()

gravity_field(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.tree.UniformGravityFieldElement: An accessor to the current gravity field.

has_joint(self: pydrake.multibody.plant.MultibodyPlant, joint_index: pydrake.multibody.tree.JointIndex) → bool: Returns true if plant has a joint with unique index joint_index. The value could be false if the joint was removed using RemoveJoint().

has_joint_actuator(self: pydrake.multibody.plant.MultibodyPlant, actuator_index: pydrake.multibody.tree.JointActuatorIndex) → bool: Returns true if plant has a joint actuator with unique index actuator_index. The value could be false if the actuator was removed using RemoveJointActuator().

has_sampled_output_ports(self: pydrake.multibody.plant.MultibodyPlant) → bool: (Advanced) If this plant is continuous (i.e., is_discrete() is False), returns false. If this plant is discrete, returns whether or not the output ports are sampled (change only at a time step boundary) or live (instantaneously reflect changes to the input ports). See output_port_sampling “Output port sampling” for details.

HasBodyNamed(*args, **kwargs)

Overloaded function.

HasBodyNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> bool

Returns: True if a body named name was added to the MultibodyPlant.

See also

AddRigidBody().

Raises: RuntimeError if the body name occurs in multiple model instances. –

HasBodyNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> bool

Returns: True if a body named name was added to the MultibodyPlant in model_instance.

See also

AddRigidBody().

Raises: RuntimeError if model_instance is not valid for this model. –

HasFrameNamed(*args, **kwargs)

Overloaded function.

HasFrameNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> bool

Returns: True if a frame named name was added to the model.

See also

AddFrame().

Raises: RuntimeError if the frame name occurs in multiple model instances. –

HasFrameNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> bool

Returns: True if a frame named name was added to model_instance.

See also

AddFrame().

Raises: RuntimeError if model_instance is not valid for this model. –

HasJointActuatorNamed(*args, **kwargs)

Overloaded function.

HasJointActuatorNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> bool

Returns: True if an actuator named name was added to this model.

See also

AddJointActuator().

Raises

RuntimeError if the actuator name occurs in multiple model –
instances. –

HasJointActuatorNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> bool

Returns: True if an actuator named name was added to model_instance.

See also

AddJointActuator().

Raises: RuntimeError if model_instance is not valid for this model. –

HasJointNamed(*args, **kwargs)

Overloaded function.

HasJointNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str) -> bool

Returns: True if a joint named name was added to this model.

See also

AddJoint().

Raises: RuntimeError if the joint name occurs in multiple model instances. –

HasJointNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> bool

Returns: True if a joint named name was added to model_instance.

See also

AddJoint().

Raises: RuntimeError if model_instance is not valid for this model. –

HasModelInstanceNamed(self: pydrake.multibody.plant.MultibodyPlant, name: str) → bool

Returns: True if a model instance named name was added to this model.

See also

AddModelInstance().

HasUniqueFreeBaseBody(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → bool

Return true if there exists a unique base body in the model given by model_instance and that unique base body is free.

Raises

RuntimeError if called pre-finalize. –
RuntimeError if model_instance is not valid. –

is_finalized(self: pydrake.multibody.plant.MultibodyPlant) → bool: Returns True if this MultibodyPlant was finalized with a call to Finalize().

See also

Finalize().

is_gravity_enabled(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) → bool

Returns: True iff gravity is enabled for model_instance.

See also

set_gravity_enabled().

Raises: RuntimeError if the model instance is invalid. –

IsAnchored(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody) → bool

Returns True if body is anchored (i.e. the kinematic path between body and the world only contains weld joints.)

Raises: RuntimeError if called pre-finalize. –

IsVelocityEqualToQDot(self: pydrake.multibody.plant.MultibodyPlant) → bool: Returns true iff the generalized velocity v is exactly the time derivative q̇ of the generalized coordinates q. In this case MapQDotToVelocity() and MapVelocityToQDot() implement the identity map. This method is, in the worst case, O(n), where n is the number of joints.

MakeActuationMatrix(self: pydrake.multibody.plant.MultibodyPlant) → numpy.ndarray[numpy.float64[m, n]]: This method creates an actuation matrix B mapping a vector of actuation values u into generalized forces tau_u = B * u, where B is a matrix of size nv x nu with nu equal to num_actuated_dofs() and nv equal to num_velocities(). The vector u of actuation values is of size num_actuated_dofs(). For a given JointActuator, u[JointActuator::input_start()] stores the value for the external actuation corresponding to that actuator. tau_u on the other hand is indexed by generalized velocity indices according to Joint::velocity_start().

Warning

B is a permutation matrix. While making a permutation has O(n) complexity, making a full B matrix has O(n²) complexity. For most applications this cost can be neglected but it could become significant for very large systems.

MakeActuationMatrixPseudoinverse(self: pydrake.multibody.plant.MultibodyPlant) → scipy.sparse.csc_matrix[numpy.float64]

Creates the pseudoinverse of the actuation matrix B directly (without requiring an explicit inverse calculation). See MakeActuationMatrix().

Notably, when B is full row rank (the system is fully actuated), then the pseudoinverse is a true inverse.

MakeActuatorSelectorMatrix(*args, **kwargs)

Overloaded function.

MakeActuatorSelectorMatrix(self: pydrake.multibody.plant.MultibodyPlant, user_to_actuator_index_map: list[pydrake.multibody.tree.JointActuatorIndex]) -> numpy.ndarray[numpy.float64[m, n]]

This method allows user to map a vector uₛ containing the actuation for a set of selected actuators into the vector u containing the actuation values for this full model. The mapping, or selection, is returned in the form of a selector matrix Su such that u = Su⋅uₛ. The size nₛ of uₛ is always smaller or equal than the size of the full vector of actuation values u. That is, a user might be interested in only a given subset of actuators in the model.

This selection matrix is particularly useful when adding PID control on a portion of the state, see systems::controllers::PidController.

A user specifies the preferred order in uₛ via user_to_actuator_index_map. The actuation values in uₛ are a concatenation of the values for each actuator in the order they appear in user_to_actuator_index_map. The actuation value in the full vector of actuation values u for a particular actuator can be found at offset JointActuator::input_start().

MakeActuatorSelectorMatrix(self: pydrake.multibody.plant.MultibodyPlant, user_to_joint_index_map: list[pydrake.multibody.tree.JointIndex]) -> numpy.ndarray[numpy.float64[m, n]]

Alternative signature to build an actuation selector matrix Su such that u = Su⋅uₛ, where u is the vector of actuation values for the full model (see get_actuation_input_port()) and uₛ is a vector of actuation values for the actuators acting on the joints listed by user_to_joint_index_map. It is assumed that all joints referenced by user_to_joint_index_map are actuated. See MakeActuatorSelectorMatrix(const std::vector<JointActuatorIndex>&) for details.

Raises

RuntimeError if any of the joints in user_to_joint_index_map –
does not have an actuator. –

MakeQDotToVelocityMap(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → scipy.sparse.csc_matrix[numpy.float64]

Returns the matrix N⁺(q), which maps v = N⁺(q)⋅q̇, as described in MapQDotToVelocity(). Prefer calling MapQDotToVelocity() directly; this entry point is provided to support callers that require the explicit linear form (once q is given) of the relationship. This method is, in the worst case, O(n), where n is the number of joints.

Parameter context:: The context containing the state of the model.

See also

MapVelocityToQDot()

MakeStateSelectorMatrix(self: pydrake.multibody.plant.MultibodyPlant, user_to_joint_index_map: list[pydrake.multibody.tree.JointIndex]) → numpy.ndarray[numpy.float64[m, n]]

This method allows users to map the state of this model, x, into a vector of selected state xₛ with a given preferred ordering. The mapping, or selection, is returned in the form of a selector matrix Sx such that xₛ = Sx⋅x. The size nₛ of xₛ is always smaller or equal than the size of the full state x. That is, a user might be interested in only a given portion of the full state x.

This selection matrix is particularly useful when adding PID control on a portion of the state, see systems::controllers::PidController.

A user specifies the preferred order in xₛ via user_to_joint_index_map. The selected state is built such that selected positions are followed by selected velocities, as in xₛ = [qₛ, vₛ]. The positions in qₛ are a concatenation of the positions for each joint in the order they appear in user_to_joint_index_map. That is, the positions for user_to_joint_index_map[0] are first, followed by the positions for user_to_joint_index_map[1], etc. Similarly for the selected velocities vₛ.

Raises

RuntimeError if there are repeated indices in –
user_to_joint_index_map` –

MakeVelocityToQDotMap(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context) → scipy.sparse.csc_matrix[numpy.float64]

Returns the matrix N(q), which maps q̇ = N(q)⋅v, as described in MapVelocityToQDot(). Prefer calling MapVelocityToQDot() directly; this entry point is provided to support callers that require the explicit linear form (once q is given) of the relationship. Do not take the (pseudo-)inverse of N(q); call MakeQDotToVelocityMap instead. This method is, in the worst case, O(n), where n is the number of joints.

Parameter context:: The context containing the state of the model.

See also

MapVelocityToQDot()

MapQDotToVelocity(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, qdot: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]

Transforms the time derivative qdot of the generalized positions vector q (stored in context) to generalized velocities v. v and q̇ are related linearly by q̇ = N(q)⋅v. Although N(q) is not necessarily square, its left pseudo-inverse N⁺(q) can be used to invert that relationship without residual error, provided that qdot is in the range space of N(q) (that is, if it could have been produced as q̇ = N(q)⋅v for some v). Using the configuration q stored in the given context this method calculates v = N⁺(q)⋅q̇.

Parameter context:: The context containing the state of the model.
Parameter qdot:: A vector containing the time derivatives of the generalized positions. This method aborts if qdot is not of size num_positions().
Parameter v:: A valid (non-null) pointer to a vector in ℛⁿ with n the number of generalized velocities. This method aborts if v is nullptr or if it is not of size num_velocities().

See also

MapVelocityToQDot()

See also

Mobilizer::MapQDotToVelocity()

MapVelocityToQDot(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, v: numpy.ndarray[numpy.float64[m, 1]]) → numpy.ndarray[numpy.float64[m, 1]]

Transforms generalized velocities v to time derivatives qdot of the generalized positions vector q (stored in context). v and qdot are related linearly by q̇ = N(q)⋅v. Using the configuration q stored in the given context this method calculates q̇ = N(q)⋅v.

Parameter context:: The context containing the state of the model.
Parameter v:: A vector of generalized velocities for this model. This method aborts if v is not of size num_velocities().
Parameter qdot:: A valid (non-null) pointer to a vector in ℝⁿ with n being the number of generalized positions in this model, given by num_positions(). This method aborts if qdot is nullptr or if it is not of size num_positions().

See also

MapQDotToVelocity()

See also

Mobilizer::MapVelocityToQDot()

mutable_deformable_model(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.plant.DeformableModel

Returns a mutable reference to the DeformableModel owned by this plant.

Raises: RuntimeError if the plant is finalized. –

Warning

This feature is considered to be experimental and may change or be removed at any time, without any deprecation notice ahead of time.

mutable_gravity_field(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.tree.UniformGravityFieldElement: A mutable accessor to the current gravity field.

num_actuated_dofs(*args, **kwargs)

Overloaded function.

num_actuated_dofs(self: pydrake.multibody.plant.MultibodyPlant) -> int

Returns the total number of actuated degrees of freedom. That is, the vector of actuation values u has this size. See AddJointActuator().

num_actuated_dofs(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> int

Returns the total number of actuated degrees of freedom for a specific model instance. That is, the vector of actuation values u has this size. See AddJointActuator().

Raises: RuntimeError if called pre-finalize. –

num_actuators(*args, **kwargs)

Overloaded function.

num_actuators(self: pydrake.multibody.plant.MultibodyPlant) -> int

Returns the number of joint actuators in the model.

See also

AddJointActuator().

num_actuators(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> int

Returns the number of actuators for a specific model instance.

Raises: RuntimeError if called pre-finalize. –

num_bodies(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of RigidBody elements in the model, including the “world” RigidBody, which is always part of the model.

See also

AddRigidBody().

num_collision_geometries(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of geometries registered for contact modeling. This method can be called at any time during the lifetime of this plant, either pre- or post-finalize, see Finalize(). Post-finalize calls will always return the same value.

num_constraints(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the total number of constraints specified by the user.

num_force_elements(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of ForceElement objects.

See also

AddForceElement().

num_frames(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of Frame objects in this model. Frames include body frames associated with each of the bodies, including the world body. This means the minimum number of frames is one.

num_joints(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of joints in the model.

See also

AddJoint().

num_model_instances(self: pydrake.multibody.plant.MultibodyPlant) → int: Returns the number of model instances in the model.

See also

AddModelInstance().

num_multibody_states(*args, **kwargs)

Overloaded function.

num_multibody_states(self: pydrake.multibody.plant.MultibodyPlant) -> int

Returns the size of the multibody system state vector x = [q v]. This will be num_positions() plus num_velocities().

Raises: RuntimeError if called pre-finalize. –

num_multibody_states(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> int

Returns the size of the multibody system state vector xᵢ = [qᵢ vᵢ] for model instance i. (Here qᵢ ⊆ q and vᵢ ⊆ v.) will be num_positions(model_instance) plus num_velocities(model_instance).

Raises: RuntimeError if called pre-finalize. –

num_positions(*args, **kwargs)

Overloaded function.

num_positions(self: pydrake.multibody.plant.MultibodyPlant) -> int

Returns the size of the generalized position vector q for this model.

Raises: RuntimeError if called pre-finalize. –

num_positions(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> int

Returns the size of the generalized position vector qᵢ for model instance i.

Raises: RuntimeError if called pre-finalize. –

num_velocities(*args, **kwargs)

Overloaded function.

num_velocities(self: pydrake.multibody.plant.MultibodyPlant) -> int

Returns the size of the generalized velocity vector v for this model.

Raises: RuntimeError if called pre-finalize. –

num_velocities(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex) -> int

Returns the size of the generalized velocity vector vᵢ for model instance i.

Raises: RuntimeError if called pre-finalize. –

NumBodiesWithName(self: pydrake.multibody.plant.MultibodyPlant, name: str) → int

Returns: The total number of bodies (across all model instances) with the given name.

RegisterAsSourceForSceneGraph(self: pydrake.multibody.plant.MultibodyPlant, scene_graph: pydrake.geometry.SceneGraph) → pydrake.geometry.SourceId

Registers this plant to serve as a source for an instance of SceneGraph. This registration allows MultibodyPlant to register geometry with scene_graph for visualization and/or collision queries. The string returned by this->get_name() is passed to SceneGraph’s RegisterSource, so it is highly recommended that you give the plant a recognizable name before calling this. Successive registration calls with SceneGraph must be performed on the same instance to which the pointer argument scene_graph points to. Failure to do so will result in runtime exceptions.

Parameter scene_graph:: A valid non nullptr to the SceneGraph instance for which this plant will sever as a source, see SceneGraph documentation for further details.

Returns

the SourceId of this plant in scene_graph. It can also later on be retrieved with get_source_id().

Raises

RuntimeError if called post-finalize. –
RuntimeError if scene_graph is the nullptr. –
RuntimeError if called more than once. –

RegisterCollisionGeometry(*args, **kwargs)

Overloaded function.

RegisterCollisionGeometry(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, X_BG: pydrake.math.RigidTransform, shape: pydrake.geometry.Shape, name: str, properties: pydrake.geometry.ProximityProperties) -> pydrake.geometry.GeometryId

Registers geometry in a SceneGraph with a given geometry::Shape to be used for the contact modeling of a given body. More than one geometry can be registered with a body, in which case the body’s contact geometry is the union of all geometries registered to that body.

Parameter body:: The body for which geometry is being registered.
Parameter X_BG:: The fixed pose of the geometry frame G in the body frame B.
Parameter shape:: The geometry::Shape used for visualization. E.g.: geometry::Sphere, geometry::Cylinder, etc.
Parameter properties:: The proximity properties associated with the collision geometry. They must include the (material, coulomb_friction) property of type CoulombFriction<double>.

Raises

RuntimeError if called post-finalize or if the properties are –
missing the coulomb friction property (or if it is of the wrong –
type) –

RegisterCollisionGeometry(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, X_BG: pydrake.math.RigidTransform, shape: pydrake.geometry.Shape, name: str, coulomb_friction: pydrake.multibody.plant.CoulombFriction) -> pydrake.geometry.GeometryId

Overload which specifies a single property: coulomb_friction.

RegisterVisualGeometry(*args, **kwargs)

Overloaded function.

RegisterVisualGeometry(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, X_BG: pydrake.math.RigidTransform, shape: pydrake.geometry.Shape, name: str, diffuse_color: numpy.ndarray[numpy.float64[4, 1]]) -> pydrake.geometry.GeometryId

Overload for visual geometry registration. The following properties are set: - (“phong”, “diffuse”) = diffuse_color in both sets of properties. - (“label”, “id”) in perception properties as documented above.

See mbp_geometry “the overview” for more details.

RegisterVisualGeometry(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, geometry_instance: pydrake.geometry.GeometryInstance) -> pydrake.geometry.GeometryId

Registers the given geometry_instance in a SceneGraph to be used for visualization of a given body.

The roles that geometry_instance gets assigned (illustration/perception) in SceneGraph depend solely on the properties that have already been assigned to geometry_instance. If any visual roles have been assigned, those will be the only roles used. If no visual roles have been assigned, then both roles will be assigned using the default set of property values.

If the registered geometry has the perception role, it will have the (“label”, “id”) property. Possibly assigned as documented above.

See mbp_geometry “the overview” for more details.

Parameter body:: The body for which geometry is being registered.
Parameter geometry_instance:: The geometry to associate with the visual appearance of body.

Raises

RuntimeError if geometry_instance is null. –
RuntimeError if called post-finalize. –

Returns

the id for the registered geometry.

RemoveConstraint(self: pydrake.multibody.plant.MultibodyPlant, id: pydrake.multibody.tree.MultibodyConstraintId) → None

Removes the constraint id from the plant. Note that this will not remove constraints registered directly with DeformableModel.

Raises

RuntimeError if the MultibodyPlant has already been finalized. –
RuntimeError if id does not identify any multibody constraint –
in this plant. –

RemoveJoint(self: pydrake.multibody.plant.MultibodyPlant, joint: pydrake.multibody.tree.Joint) → None

Removes and deletes joint from this MultibodyPlant. Any existing references to joint will become invalid, and future calls to get_joint(joint_index) will throw an exception. Other elements of the plant may depend on joint at the time of removal and should be removed first. For example, a JointActuator that depends on joint should be removed with RemoveJointActuator(). Currently, we do not provide joint dependency tracking for force elements or constraints, so this function will throw an exception if there are any user-added force elements or constraints in the plant.

Raises

RuntimeError if the plant is already finalized. –
RuntimeError if the plant contains a non-zero number of user-added –
force elements or user-added constraints. –
RuntimeError if joint has a dependent JointActuator. –

See also

AddJoint()

Note

It is important to note that the JointIndex assigned to a joint is immutable. New joint indices are assigned in increasing order, even if a joint with a lower index has been removed. This has the consequence that when a joint is removed from the plant, the sequence [0, num_joints()) is not necessarily the correct set of un-removed joint indices in the plant. Thus, it is important NOT to loop over joint indices sequentially from 0 to num_joints() - 1. Instead users should use the provided GetJointIndices() and GetJointIndices(ModelIndex) functions:

Click to expand C++ code...

for (JointIndex index : plant.GetJointIndices()) {
  const Joint<double>& joint = plant.get_joint(index);
  ...
 }

RemoveJointActuator(self: pydrake.multibody.plant.MultibodyPlant, actuator: pydrake.multibody.tree.JointActuator) → None

Removes and deletes actuator from this MultibodyPlant. Any existing references to actuator will become invalid, and future calls to get_joint_actuator(actuator_index) will throw an exception.

Raises: RuntimeError if the plant is already finalized. –

See also

AddJointActuator()

RenameModelInstance(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, name: str) → None

Renames an existing model instance.

Parameter model_instance:: The instance to rename.
Parameter name:: A string that uniquely identifies the instance within this model.

Raises

RuntimeError if called after Finalize() –
RuntimeError if model_instance is not a valid index. –
RuntimeError if HasModelInstanceNamed(name) is true. –

set_adjacent_bodies_collision_filters(self: pydrake.multibody.plant.MultibodyPlant, value: bool) → None

Sets whether to apply collision filters to topologically adjacent bodies at Finalize() time. Filters are applied when there exists a joint between bodies, except in the case of 6-dof joints or joints in which the parent body is world.

Raises: RuntimeError iff called post-finalize. –

set_contact_model(self: pydrake.multibody.plant.MultibodyPlant, model: pydrake.multibody.plant.ContactModel) → None

Sets the contact model to be used by this MultibodyPlant, see ContactModel for available options. The default contact model is ContactModel::kHydroelasticWithFallback.

Raises: RuntimeError iff called post-finalize. –

set_contact_surface_representation(self: pydrake.multibody.plant.MultibodyPlant, surface_representation: pydrake.geometry.HydroelasticContactRepresentation) → None

Sets the representation of contact surfaces to be used by this MultibodyPlant. See geometry::HydroelasticContactRepresentation for available options. See GetDefaultContactSurfaceRepresentation() for explanation of default values.

Raises: RuntimeError if called post-finalize. –

set_discrete_contact_approximation(self: pydrake.multibody.plant.MultibodyPlant, approximation: pydrake.multibody.plant.DiscreteContactApproximation) → None

Sets the discrete contact model approximation.

Note

Calling this method also sets the contact solver type (see set_discrete_contact_solver()) according to: - DiscreteContactApproximation::kTamsi sets the solver to DiscreteContactSolver::kTamsi. - DiscreteContactApproximation::kSap, DiscreteContactApproximation::kSimilar and DiscreteContactApproximation::kLagged set the solver to DiscreteContactSolver::kSap.

Raises

iff this plant is continuous (i.e. is_discrete() is –
False`. –
RuntimeError iff called post-finalize. –

set_discrete_contact_solver(self: pydrake.multibody.plant.MultibodyPlant, contact_solver: pydrake.multibody.plant.DiscreteContactSolver) → None

Sets the contact solver type used for discrete MultibodyPlant models.

Note

Calling this method also sets a default discrete approximation of contact (see set_discrete_contact_approximation()) according to: - DiscreteContactSolver::kTamsi sets the approximation to DiscreteContactApproximation::kTamsi. - DiscreteContactSolver::kSap sets the approximation to DiscreteContactApproximation::kSap.

Warning

This function is a no-op for continuous models (when is_discrete() is false.)

Raises: RuntimeError iff called post-finalize. (Deprecated.) –

Deprecated:: Use set_discrete_contact_approximation() to set the contact model approximation. The underlying solver will be inferred automatically. This will be removed from Drake on or after 2024-04-01.

set_gravity_enabled(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, is_enabled: bool) → None

Sets is_gravity_enabled() for model_instance to is_enabled. The effect of is_enabled = false is effectively equivalent to disabling (or making zero) gravity for all bodies in the specified model instance. By default is_gravity_enabled() equals True for all model instances.

Raises

RuntimeError if called post-finalize. –
RuntimeError if the model instance is invalid. –

set_penetration_allowance(self: pydrake.multibody.plant.MultibodyPlant, penetration_allowance: float = 0.001) → None

Sets the penetration allowance used to estimate the coefficients in the penalty method used to impose non-penetration among bodies. Refer to the section point_contact_defaults “Point Contact Default Parameters” for further details.

Raises: RuntimeError if penetration_allowance is not positive. –

set_sap_near_rigid_threshold(self: pydrake.multibody.plant.MultibodyPlant, near_rigid_threshold: float = 1.0) → None

Non-negative dimensionless number typically in the range [0.0, 1.0], though larger values are allowed even if uncommon. This parameter controls the “near rigid” regime of the SAP solver, β in section V.B of [Castro et al., 2021]. It essentially controls a threshold value for the maximum amount of stiffness SAP can handle robustly. Beyond this value, stiffness saturates as explained in [Castro et al., 2021]. A value of 1.0 is a conservative choice to avoid ill-conditioning that might lead to softer than expected contact. If this is your case, consider turning off this approximation by setting this parameter to zero. For difficult cases where ill-conditioning is a problem, a small but non-zero number can be used, e.g. 1.0e-3.

Raises

RuntimeError if near_rigid_threshold is negative. –
RuntimeError if called post-finalize. –

set_stiction_tolerance(self: pydrake.multibody.plant.MultibodyPlant, v_stiction: float = 0.001) → None

**** Stribeck model of friction

Currently MultibodyPlant uses the Stribeck approximation to model dry friction. The Stribeck model of friction is an approximation to Coulomb’s law of friction that allows using continuous time integration without the need to specify complementarity constraints. While this results in a simpler model immediately tractable with standard numerical methods for integration of ODE’s, it often leads to stiff dynamics that require an explicit integrator to take very small time steps. It is therefore recommended to use error controlled integrators when using this model or the discrete time stepping (see multibody_simulation). See stribeck_approximation for a detailed discussion of the Stribeck model.

Sets the stiction tolerance v_stiction for the Stribeck model, where v_stiction must be specified in m/s (meters per second.) v_stiction defaults to a value of 1 millimeter per second. In selecting a value for v_stiction, you must ask yourself the question, “When two objects are ostensibly in stiction, how much slip am I willing to allow?” There are two opposing design issues in picking a value for vₛ. On the one hand, small values of vₛ make the problem numerically stiff during stiction, potentially increasing the integration cost. On the other hand, it should be picked to be appropriate for the scale of the problem. For example, a car simulation could allow a “large” value for vₛ of 1 cm/s (1×10⁻² m/s), but reasonable stiction for grasping a 10 cm box might require limiting residual slip to 1×10⁻³ m/s or less. Ultimately, picking the largest viable value will allow your simulation to run faster and more robustly. Note that v_stiction is the slip velocity that we’d have when we are at edge of the friction cone. For cases when the friction force is well within the friction cone the slip velocity will always be smaller than this value. See also stribeck_approximation.

Raises: RuntimeError if v_stiction is non-positive. –

SetActuationInArray(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, u_instance: numpy.ndarray[numpy.float64[m, 1]], u: Optional[numpy.ndarray[numpy.float64[m, 1], flags.writeable]]) → None

Given actuation values u_instance for the actuators in model_instance, this function updates the actuation vector u for the entire plant model to which this actuator belongs to. Refer to mbp_actuation “Actuation” for further details.

Parameter u_instance:: Actuation values for the model instance. Values are ordered by monotonically increasing JointActuatorIndex within the model instance.
Parameter u:: Actuation values for the entire plant model. The actuation value in u for a particular actuator must be found at offset JointActuator::input_start(). Only values corresponding to model_instance are changed.

Raises

RuntimeError if the size of u_instance is not equal to the –
number of actuation inputs for the joints of model_instance. –

SetConstraintActiveStatus(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, id: pydrake.multibody.tree.MultibodyConstraintId, status: bool) → None

Sets the active status of the constraint given by id in context.

Raises

RuntimeError if the MultibodyPlant has not been finalized. –
RuntimeError if context == nullptr –
RuntimeError if id does not belong to any multibody constraint –
in context. –

SetDefaultFreeBodyPose(*args, **kwargs)

Overloaded function.

SetDefaultFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, X_PB: pydrake.math.RigidTransform) -> None

Sets the default pose of body. If body.is_floating() is true, this will affect subsequent calls to SetDefaultState(); otherwise, the only effect of the call is that the value will be echoed back in GetDefaultFreeBodyPose().

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Parameter body:: RigidBody whose default pose will be set.
Parameter X_PB:: Default pose of the body.

SetDefaultFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, X_WB: pydrake.math.RigidTransform) -> None

Sets context to store the pose X_PB of a given body B in the parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

SetDefaultPositions(*args, **kwargs)

Overloaded function.

SetDefaultPositions(self: pydrake.multibody.plant.MultibodyPlant, q: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the default positions for the plant. Calls to CreateDefaultContext or SetDefaultContext/SetDefaultState will return a Context populated with these position values. They have no other effects on the dynamics of the system.

Raises

RuntimeError if the plant is not finalized or if q is not of size –
num_positions() –

SetDefaultPositions(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, q_instance: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the default positions for the model instance. Calls to CreateDefaultContext or SetDefaultContext/SetDefaultState will return a Context populated with these position values. They have no other effects on the dynamics of the system.

Raises

RuntimeError if the plant is not finalized, if the model_instance –
is invalid, or if the length of q_instance is not equal to –
num_positions(model_instance)` –

SetDefaultState(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, state: pydrake.systems.framework.State) → None

Sets state according to defaults set by the user for joints (e.g. RevoluteJoint::set_default_angle()) and free bodies (SetDefaultFreeBodyPose()). If the user does not specify defaults, the state corresponds to zero generalized positions and velocities.

Raises: RuntimeError if called pre-finalize. See Finalize() –

SetFreeBodyPose(*args, **kwargs)

Overloaded function.

SetFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody, X_PB: pydrake.math.RigidTransform) -> None

Sets context to store the pose X_PB of a given body B in the parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

SetFreeBodyPose(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, body: pydrake.multibody.tree.RigidBody, X_WB: pydrake.math.RigidTransform) -> None

Sets context to store the pose X_PB of a given body B in the parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

SetFreeBodySpatialVelocity(*args, **kwargs)

Overloaded function.

SetFreeBodySpatialVelocity(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, V_PB: pydrake.multibody.math.SpatialVelocity, context: pydrake.systems.framework.Context) -> None

Sets context to store the spatial velocity V_PB of a given body B in its parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

SetFreeBodySpatialVelocity(self: pydrake.multibody.plant.MultibodyPlant, body: pydrake.multibody.tree.RigidBody, V_WB: pydrake.multibody.math.SpatialVelocity, context: pydrake.systems.framework.Context) -> None

Sets context to store the spatial velocity V_PB of a given body B in its parent frame P.

Note

The parent frame is not necessarily the world frame. See mbp_working_with_free_bodies “above for details”.

Raises

RuntimeError if body is not a free body in the model. –
RuntimeError if called pre-finalize. –

SetPositions(*args, **kwargs)

Overloaded function.

SetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, q: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the generalized positions q in a given Context from a given vector. Prefer this method over GetMutablePositions().

Raises

RuntimeError if context is nullptr, if context does not –
correspond to the Context for a multibody model, or if the length –
of q is not equal to num_positions() –

SetPositions(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex, q: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the generalized positions q in a given Context from a given vector. Prefer this method over GetMutablePositions().

Raises

RuntimeError if context is nullptr, if context does not –
correspond to the Context for a multibody model, or if the length –
of q is not equal to num_positions() –

SetPositionsAndVelocities(*args, **kwargs)

Overloaded function.

SetPositionsAndVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, q_v: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets generalized positions q and generalized velocities v in a given Context from a given vector [q; v]. Prefer this method over GetMutablePositionsAndVelocities().

Raises

RuntimeError if context is nullptr, if context does not –
correspond to the context for a multibody model, or if the length –
of q_v is not equal to num_positions() + num_velocities() –

SetPositionsAndVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex, q_v: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets generalized positions q and generalized velocities v from a given vector [q; v] for a specified model instance in a given Context.

Raises

RuntimeError if context is nullptr, if context does not –
correspond to the Context for a multibody model, if the model –
instance index is invalid, or if the length of q_v is not –
equal to ``num_positions(model_instance) + –
num_velocities(model_instance)``. –

SetPositionsInArray(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, q_instance: numpy.ndarray[numpy.float64[m, 1]], q: Optional[numpy.ndarray[numpy.float64[m, 1], flags.writeable]]) → None: Sets the vector of generalized positions for model_instance in q using q_instance, leaving all other elements in the array untouched. This method throws an exception if q is not of size MultibodyPlant::num_positions() or q_instance is not of size MultibodyPlant::num_positions(model_instance).

SetUseSampledOutputPorts(self: pydrake.multibody.plant.MultibodyPlant, use_sampled_output_ports: bool) → None

(Advanced) For a discrete-time plant, configures whether the output ports are sampled (the default) or live (opt-in). See output_port_sampling “Output port sampling” for details.

Raises

RuntimeError if the plant is already finalized. –
RuntimeError if use_sampled_output_ports is True but –
this` MultibodyPlant is not a discrete model (is_discrete() = –
false) –

SetVelocities(*args, **kwargs)

Overloaded function.

SetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, v: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the generalized velocities v in a given Context from a given vector. Prefer this method over GetMutableVelocities().

Raises

RuntimeError if the context is nullptr, if the context does –
not correspond to the context for a multibody model, or if the –
length of v is not equal to num_velocities() –

SetVelocities(self: pydrake.multibody.plant.MultibodyPlant, context: pydrake.systems.framework.Context, model_instance: pydrake.multibody.tree.ModelInstanceIndex, v: numpy.ndarray[numpy.float64[m, 1]]) -> None

Sets the generalized velocities v for a particular model instance in a given Context from a given vector.

Raises

RuntimeError if the context is nullptr, if context does –
not correspond to the Context for a multibody model, if the model –
instance index is invalid, or if the length of v_instance is –
not equal to num_velocities(model_instance) –

SetVelocitiesInArray(self: pydrake.multibody.plant.MultibodyPlant, model_instance: pydrake.multibody.tree.ModelInstanceIndex, v_instance: numpy.ndarray[numpy.float64[m, 1]], v: Optional[numpy.ndarray[numpy.float64[m, 1], flags.writeable]]) → None: Sets the vector of generalized velocities for model_instance in v using v_instance, leaving all other elements in the array untouched. This method throws an exception if v is not of size MultibodyPlant::num_velocities() or v_instance is not of size MultibodyPlant::num_positions(model_instance).

time_step(self: pydrake.multibody.plant.MultibodyPlant) → float: The time step (or period) used to model this plant as a discrete system with periodic updates. Returns 0 (zero) if the plant is modeled as a continuous system. This property of the plant is specified at construction and therefore this query can be performed either pre- or post-finalize, see Finalize().

See also

MultibodyPlant::MultibodyPlant(double)

WeldFrames(self: pydrake.multibody.plant.MultibodyPlant, frame_on_parent_F: pydrake.multibody.tree.Frame, frame_on_child_M: pydrake.multibody.tree.Frame, X_FM: pydrake.math.RigidTransform = RigidTransform(R=RotationMatrix([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]), p=[0.0, 0.0, 0.0])) → pydrake.multibody.tree.WeldJoint

Welds frame_on_parent_F and frame_on_child_M with relative pose X_FM. That is, the pose of frame M in frame F is fixed, with value X_FM. If X_FM is omitted, the identity transform will be used. The call to this method creates and adds a new WeldJoint to the model. The new WeldJoint is named as: frame_on_parent_F.name() + “_welds_to_” + frame_on_child_M.name().

Returns: a constant reference to the WeldJoint welding frames F and M.
Raises: RuntimeError if the weld produces a duplicate joint name. –

world_body(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.tree.RigidBody: Returns a constant reference to the world body.

world_frame(self: pydrake.multibody.plant.MultibodyPlant) → pydrake.multibody.tree.RigidBodyFrame: Returns a constant reference to the world frame.

template pydrake.multibody.plant.MultibodyPlant_: Instantiations: MultibodyPlant_[float], MultibodyPlant_[AutoDiffXd], MultibodyPlant_[Expression]

class pydrake.multibody.plant.MultibodyPlant_[AutoDiffXd]

Bases: pydrake.systems.framework.LeafSystem_[AutoDiffXd]

MultibodyPlant is a Drake system framework representation (see systems::System) for the model of a physical system consisting of a collection of interconnected bodies. See multibody for an overview of concepts/notation.

actuation→

applied_generalized_force→

applied_spatial_force→

model_instance_name[i]_actuation→

model_instance_name[i]_desired_state→

geometry_query→

MultibodyPlant

→ state

→ body_poses

→ body_spatial_velocities

→ body_spatial_accelerations

→ generalized_acceleration

→ net_actuation

→ reaction_forces

→ contact_results

→ model_instance_name[i]_state

→ model_instance_name[i]_generalized_acceleration

→ model_instance_name[i]_generalized_contact_forces

→ model_instance_name[i]_net_actuation

→ geometry_pose

→ deformable_body_configuration

The ports whose names begin with model_instance_name[i] represent groups of ports, one for each of the model_instances “model instances”, with i ∈ {0, …, N-1} for the N model instances. If a model instance does not contain any data of the indicated type the port will still be present but its value will be a zero-length vector. (Model instances world_model_instance() and default_model_instance() always exist.)

The ports shown in green are for communication with Drake’s geometry::SceneGraph “SceneGraph” system for dealing with geometry.

MultibodyPlant provides a user-facing API for:

mbp_input_and_output_ports “Ports”:

Access input and output ports. - mbp_construction “Construction”: Add bodies, joints, frames, force elements, and actuators. - mbp_geometry “Geometry”: Register geometries to a provided SceneGraph instance. - mbp_contact_modeling “Contact modeling”: Select and parameterize contact models. - mbp_state_accessors_and_mutators “State access and modification”: Obtain and manipulate position and velocity state variables. - mbp_parameters “Parameters” Working with system parameters for various multibody elements. - mbp_working_with_free_bodies “Free bodies”: Work conveniently with free (floating) bodies. - mbp_kinematic_and_dynamic_computations “Kinematics and dynamics”: Perform systems::Context “Context”-dependent kinematic and dynamic queries. - mbp_system_matrix_computations “System matrices”: Explicitly form matrices that appear in the equations of motion. - mbp_introspection “Introspection”: Perform introspection to find out what’s in the MultibodyPlant.

**** Model Instances

A MultiBodyPlant may contain multiple model instances. Each model instance corresponds to a set of bodies and their connections (joints). Model instances provide methods to get or set the state of the set of bodies (e.g., through GetPositionsAndVelocities() and SetPositionsAndVelocities()), connecting controllers (through get_state_output_port() and get_actuation_input_port()), and organizing duplicate models (read through a parser). In fact, many MultibodyPlant methods are overloaded to allow operating on the entire plant or just the subset corresponding to the model instance; for example, one GetPositions() method obtains the generalized positions for the entire plant while another GetPositions() method obtains the generalized positions for model instance.

Model instances are frequently defined through SDFormat files (using the model tag) and are automatically created when SDFormat files are parsed (by Parser). There are two special multibody::ModelInstanceIndex values. The world body is always multibody::ModelInstanceIndex 0. multibody::ModelInstanceIndex 1 is reserved for all elements with no explicit model instance and is generally only relevant for elements created programmatically (and only when a model instance is not explicitly specified). Note that Parser creates model instances (resulting in a multibody::ModelInstanceIndex ≥ 2) as needed.

See num_model_instances(), num_positions(), num_velocities(), num_actuated_dofs(), AddModelInstance() GetPositionsAndVelocities(), GetPositions(), GetVelocities(), SetPositionsAndVelocities(), SetPositions(), SetVelocities(), GetPositionsFromArray(), GetVelocitiesFromArray(), SetPositionsInArray(), SetVelocitiesInArray(), SetActuationInArray(), HasModelInstanceNamed(), GetModelInstanceName(), get_state_output_port(), get_actuation_input_port().

**** System dynamics

The state of a multibody system x = [q; v] is given by its generalized positions vector q, of size nq (see num_positions()), and by its generalized velocities vector v, of size nv (see num_velocities()).

A MultibodyPlant can be constructed to be either continuous or discrete. The choice is indicated by the time_step passed to the constructor – a non-zero time_step indicates a discrete plant, while a zero time_step indicates continuous. A systems::Simulator “Simulator” will step a discrete plant using the indicated time_step, but will allow a numerical integrator to choose how to advance time for a continuous MultibodyPlant.

We’ll discuss continuous plant dynamics in this section. Discrete dynamics is more complicated and gets its own section below.

As a Drake systems::System “System”, MultibodyPlant implements the governing equations for a multibody dynamical system in the form ẋ = f(t, x, u) with t being time and u external inputs such as actuation forces. The governing equations for the dynamics of a multibody system modeled with MultibodyPlant are [Featherstone 2008, Jain 2010]:

Click to expand C++ code...

q̇ = N(q)v
(1)    M(q)v̇ + C(q, v)v = τ