Drake
MultibodyPlant< T > Class Template Reference

## Detailed Description

### template<typename T> class drake::multibody::MultibodyPlant< T >

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 Kinematics and Dynamics for an overview of concepts/notation.

 applied_generalized_force→ applied_spatial_force→ model_instance_name[i]_actuation→ geometry_query→
MultibodyPlant
 → continuous_state → body_poses → body_spatial_velocities → body_spatial_accelerations → generalized_acceleration → reaction_forces → contact_results → model_instance_name[i]_continuous_state → model_instance_name[i]_generalized_acceleration → model_instance_name[i]_generalized_contact_forces → geometry_pose

The ports whose names begin with model_instance_name[i] represent groups of ports, one for each of the 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 SceneGraph system for dealing with geometry.

MultibodyPlant provides a user-facing API for:

### 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 SDF files (using the model tag) and are automatically created when SDF 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.

### 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()). As a Drake 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 the actuation forces. The governing equations for the dynamics of a multibody system modeled with MultibodyPlant are [Featherstone 2008, Jain 2010]:

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


where M(q) is the mass matrix of the multibody system, 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.

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

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

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 AddAllModelsFromFile() 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

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):

MultibodyPlant<double>& plant =
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:

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

or taking advantage of C++17's structured binding

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.

MultibodyPlant<double>* plant{};
SceneGraph<double>* scene_graph{};
std::tie(plant, scene_graph) =
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. Users must connect this input port to the output port for geometric queries of the SceneGraph used for registration, which can be obtained with SceneGraph::get_query_output_port(). In summary, if MultibodyPlant registers collision geometry, the setup process will include:

1. Call to RegisterAsSourceForSceneGraph().
2. Calls to RegisterCollisionGeometry(), as many as needed.
3. Call to Finalize(), user is done specifying the model.
4. Connect SceneGraph::get_query_output_port() to get_geometry_query_input_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 Penalty method stiffness.
material hunt_crossley_dissipation no² T Penalty method dissipation.

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 exeception.

² If the property is missing, MultibodyPlant will use a heuristic value as the default. Refer to the section Penalty method point contact for further details.

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:

// 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 by the plant's geometry query input port:

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

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

// 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 docmentation 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:

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:

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 =
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);

Add multibody elements to a MultibodyPlant with methods like:

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

### Modeling contact

Please refer to 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 MultibodyTree topology, see MultibodyTree::Finalize() for details,
• declare the plant's state,
• declare the plant's input and output ports,
• declare input and output ports for communication with a SceneGraph.

### 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.
Template Parameters
 T The scalar type, which must be one of the default scalars.

#include <drake/multibody/tree/multibody_element.h>

## Public Member Functions

Does not allow copy, move, or assignment
MultibodyPlant (const MultibodyPlant &)=delete

MultibodyPlantoperator= (const MultibodyPlant &)=delete

MultibodyPlant (MultibodyPlant &&)=delete

MultibodyPlantoperator= (MultibodyPlant &&)=delete

Input and output ports

These methods provide access to the Drake System input and output ports as depicted in the MultibodyPlant class documentation.

Actuation values can be provided through a single input port which describes the entire plant (in the case where only a single model instance has actuated dofs), or through multiple input ports which each provide the actuation values for a specific model instance. See AddJointActuator() and num_actuators().

Output ports provide information about the entire MultibodyPlant or its individual model instances.

const systems::OutputPort< T > & get_body_poses_output_port () const
Returns the output port of all body poses in the world frame. More...

const systems::OutputPort< T > & get_body_spatial_velocities_output_port () const
Returns the output port of all body spatial velocities in the world frame. More...

const systems::OutputPort< T > & get_body_spatial_accelerations_output_port () const
Returns the output port of all body spatial accelerations in the world frame. More...

const systems::InputPort< T > & get_actuation_input_port (ModelInstanceIndex model_instance) const
Returns a constant reference to the input port for external actuation for a specific model instance. More...

const systems::InputPort< T > & get_actuation_input_port () const
Returns a constant reference to the input port for external actuation for the case where only one model instance has actuated dofs. More...

const systems::InputPort< T > & get_applied_generalized_force_input_port () const
Returns a constant reference to the vector-valued input port for applied generalized forces, and the vector will be added directly into tau (see System dynamics). More...

const systems::InputPort< T > & get_applied_spatial_force_input_port () const
Returns a constant reference to the input port for applying spatial forces to bodies in the plant. More...

const systems::InputPort< T > & get_geometry_query_input_port () const
Returns a constant reference to the input port used to perform geometric queries on a SceneGraph. More...

const systems::OutputPort< T > & get_state_output_port () const
Returns a constant reference to the output port for the multibody state x = [q, v] of the model. More...

const systems::OutputPort< T > & get_state_output_port (ModelInstanceIndex model_instance) const
Returns a constant reference to the output port for the state xᵢ = [qᵢ vᵢ] of model instance i. More...

const systems::OutputPort< T > & get_generalized_acceleration_output_port () const
Returns a constant reference to the output port for generalized accelerations v̇ of the model. More...

const systems::OutputPort< T > & get_generalized_acceleration_output_port (ModelInstanceIndex model_instance) const
Returns a constant reference to the output port for the generalized accelerations v̇ᵢ ⊆ v̇ for model instance i. More...

const systems::OutputPort< T > & get_generalized_contact_forces_output_port (ModelInstanceIndex model_instance) const
Returns a constant reference to the output port of generalized contact forces for a specific model instance. More...

const systems::OutputPort< T > & get_reaction_forces_output_port () const
Returns the port for joint reaction forces. More...

const systems::OutputPort< T > & get_contact_results_output_port () const
Returns a constant reference to the port that outputs ContactResults. More...

const systems::OutputPort< T > & get_geometry_poses_output_port () const
Returns the output port of frames' poses to communicate with a SceneGraph. More...

Construction

To add modeling elements like bodies, joints, force elements, constraints, etc. to a MultibodyPlant, use one of the following construction methods. Once all modeling elements have been added, the Finalize() method must be called. A call to any construction method after a call to Finalize() causes an exception to be thrown. After calling Finalize(), you may invoke MultibodyPlant methods that perform computations. See Finalize() for details.

MultibodyPlant (double time_step)
This constructor creates a plant with a single "world" body. More...

template<typename U >
MultibodyPlant (const MultibodyPlant< U > &other)
Scalar-converting copy constructor. See System Scalar Conversion. More...

const RigidBody< T > & AddRigidBody (const std::string &name, ModelInstanceIndex model_instance, const SpatialInertia< double > &M_BBo_B)
Creates a rigid body with the provided name and spatial inertia. More...

const RigidBody< T > & AddRigidBody (const std::string &name, const SpatialInertia< double > &M_BBo_B)
Creates a rigid body with the provided name and spatial inertia. More...

template<template< typename > class FrameType>
const FrameType< T > & AddFrame (std::unique_ptr< FrameType< T >> frame)
This method adds a Frame of type FrameType<T>. More...

template<template< typename Scalar > class JointType>
const JointType< T > & AddJoint (std::unique_ptr< JointType< T >> joint)
This method adds a Joint of type JointType between two bodies. More...

template<template< typename > class JointType, typename... Args>
const JointType< T > & AddJoint (const std::string &name, const Body< T > &parent, const std::optional< math::RigidTransform< double >> &X_PF, const Body< T > &child, const std::optional< math::RigidTransform< double >> &X_BM, Args &&... args)
This method adds a Joint of type JointType between two bodies. More...

const WeldJoint< T > & WeldFrames (const Frame< T > &A, const Frame< T > &B, const math::RigidTransform< double > &X_AB=math::RigidTransform< double >::Identity())
Welds frames A and B with relative pose X_AB. More...

template<template< typename Scalar > class ForceElementType, typename... Args>
const ForceElementType< T > & AddForceElement (Args &&... args)
Adds a new force element model of type ForceElementType to this MultibodyPlant. More...

const JointActuator< T > & AddJointActuator (const std::string &name, const Joint< T > &joint, double effort_limit=std::numeric_limits< double >::infinity())
Creates and adds a JointActuator model for an actuator acting on a given joint. More...

Creates a new model instance. More...

void Finalize ()
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. More...

Geometry

The following geometry methods provide a convenient means for associating geometries with bodies. Ultimately, the geometries are owned by SceneGraph. These methods do the work of registering the requested geometries with SceneGraph and maintaining a mapping between the body and the registered data. Particularly, SceneGraph knows nothing about the concepts inherent in the MultibodyPlant. These methods account for those differences as documented below.

#### Geometry registration with roles

Geometries can be associated with bodies via the RegisterFooGeometry family of methods. In SceneGraph, geometries have roles. The RegisterCollisionGeometry() methods register geometry with SceneGraph and assign it the proximity role. The RegisterVisualGeometry() methods do the same, but assign the illustration role.

All geometry registration methods return a geometry::GeometryId GeometryId. This is how SceneGraph refers to the geometries. The properties of an individual geometry can be accessed with its id and geometry::SceneGraphInspector and geometry::QueryObject (for its state-dependent pose in world).

#### Body frames and SceneGraph frames

The first time a geometry registration method is called on a particular body, that body's frame B is registered with SceneGraph. As SceneGraph knows nothing about bodies, in the SceneGraph domain, the frame is simply notated as F; this is merely an alias for the body frame. Thus, the pose of the geometry G in the SceneGraph frame F is the same as the pose of the geometry in the body frame B; X_FG = X_BG.

The model instance index of the body is passed to the SceneGraph frame as its "frame group". This can be retrieved from the geometry::SceneGraphInspector::GetFrameGroup(FrameId) method.

Given a GeometryId, SceneGraph cannot report what body it is affixed to. It can only report the SceneGraph alias frame F. But the following idiom can report the body:

const MultibodyPlant<T>& plant = ...;
const SceneGraphInspector<T>& inspector = ...;
const GeometryId g_id = id_from_some_query;
const FrameId f_id = inspector.GetFrameId(g_id);
const Body<T>* body = plant.GetBodyFromFrameId(f_id);

See documentation of geometry::SceneGraphInspector on where to get an inspector.

In MultibodyPlant, frame names only have to be unique in a single model instance. However, SceneGraph knows nothing of model instances. So, to generate unique names for the corresponding frames in SceneGraph, when MultibodyPlant registers the corresponding SceneGraph frame, it is named with a "scoped name". This is a concatenation of [model instance name]::[body name]. Searching for a frame with just the name body name will fail. (See Body::name() and GetModelInstanceName() for those values.)

geometry::SourceId RegisterAsSourceForSceneGraph (geometry::SceneGraph< T > *scene_graph)
Registers this plant to serve as a source for an instance of SceneGraph. More...

geometry::GeometryId RegisterVisualGeometry (const Body< T > &body, const math::RigidTransform< double > &X_BG, const geometry::Shape &shape, const std::string &name, const geometry::IllustrationProperties &properties)
Registers geometry in a SceneGraph with a given geometry::Shape to be used for visualization of a given body. More...

geometry::GeometryId RegisterVisualGeometry (const Body< T > &body, const math::RigidTransform< double > &X_BG, const geometry::Shape &shape, const std::string &name, const Vector4< double > &diffuse_color)
Overload for visual geometry registration; it converts the diffuse_color (RGBA with values in the range [0, 1]) into a geometry::DrakeVisualizer-compatible set of geometry::IllustrationProperties. More...

geometry::GeometryId RegisterVisualGeometry (const Body< T > &body, const math::RigidTransform< double > &X_BG, const geometry::Shape &shape, const std::string &name)
Overload for visual geometry registration; it relies on the downstream geometry::IllustrationProperties consumer to provide default parameter values (see Geometry Queries and Roles for details). More...

const std::vector< geometry::GeometryId > & GetVisualGeometriesForBody (const Body< T > &body) const
Returns an array of GeometryId's identifying the different visual geometries for body previously registered with a SceneGraph. More...

geometry::GeometryId RegisterCollisionGeometry (const Body< T > &body, const math::RigidTransform< double > &X_BG, const geometry::Shape &shape, const std::string &name, geometry::ProximityProperties properties)
Registers geometry in a SceneGraph with a given geometry::Shape to be used for the contact modeling of a given body. More...

geometry::GeometryId RegisterCollisionGeometry (const Body< T > &body, const math::RigidTransform< double > &X_BG, const geometry::Shape &shape, const std::string &name, const CoulombFriction< double > &coulomb_friction)
Overload which specifies a single property: coulomb_friction. More...

const std::vector< geometry::GeometryId > & GetCollisionGeometriesForBody (const Body< T > &body) const
Returns an array of GeometryId's identifying the different contact geometries for body previously registered with a SceneGraph. More...

void ExcludeCollisionGeometriesWithCollisionFilterGroupPair (const std::pair< std::string, geometry::GeometrySet > &collision_filter_group_a, const std::pair< std::string, geometry::GeometrySet > &collision_filter_group_b)
Excludes the collision geometries between two given collision filter groups. More...

geometry::GeometrySet CollectRegisteredGeometries (const std::vector< const Body< T > * > &bodies) const
For each of the provided bodies, collects up all geometries that have been registered to that body. More...

const Body< T > * GetBodyFromFrameId (geometry::FrameId frame_id) const
Given a geometry frame identifier, returns a pointer to the body associated with that id (nullptr if there is no such body). More...

std::optional< geometry::FrameIdGetBodyFrameIdIfExists (BodyIndex body_index) const
If the body with body_index belongs to the called plant, it returns the geometry::FrameId associated with it. More...

geometry::FrameId GetBodyFrameIdOrThrow (BodyIndex body_index) const
If the body with body_index belongs to the called plant, it returns the geometry::FrameId associated with it. More...

Contact modeling

Use methods in this section to choose the contact model and to provide parameters for that model. Currently Drake supports an advanced compliant contact model we call Hydroelastic contact that is still experimental, and a penalty-based point contact model as a reliable fallback.

#### Hydroelastic contact

To understand how material properties enter into the modeling of contact traction in the hydroelastic model, the user is referred to [R. Elandt 2019] for details. For brevity, here we limit ourselves to state the relationship between the material properties and the computation of the normal traction or "pressure" p(x) at each point x in the contact patch. Given two bodies A and B, with elastic moduli Eᵃ and Eᵇ respectively and dissipation dᵃ and dᵇ respectively, we define the effective material properties of the pair according to:

  E = Eᵃ⋅Eᵇ/(Eᵃ + Eᵇ),
d = E/Eᵃ⋅dᵃ + E/Eᵇ⋅dᵇ = Eᵇ/(Eᵃ+Eᵇ)⋅dᵃ + Eᵃ/(Eᵃ+Eᵇ)⋅dᵇ


The effective modulus of elasticity is computed in accordance with the Hertz theory of contact. Dissipation is weighted in accordance with the fact that the softer material will deform more and faster and thus the softer material dissipation is given more importance. Elastic modulus has units of pressure, i.e. Pa (N/m²). The elastic modulus is often estimated based on the Young's modulus of the material though in the hydroelastic model it represents an effective elastic property. For instance, [R. Elandt 2019] chooses to use E = G, with G the P-wave elastic modulus G = (1-ν)/(1+ν)/(1-2ν)E, with ν the Poisson ratio, consistent with the theory of layered solids in which plane sections remain planar after compression. Another possibility is to specify E = E*, with E* the effective elastic modulus given by the Hertz theory of contact, E* = E/(1-ν²). In all of these cases a sound estimation of elastic_modulus starts with the Young's modulus of the material.

We use a dissipation model inspired by the model in [Hunt and Crossley, 1975], parameterized by a dissipation constant with units of inverse of velocity, i.e. s/m.

The elastic modulus and dissipation can be specified in one of two ways:

With the effective properties of the pair defined as above, the hydroelastic model pressure field is computed according to:

  p(x) = E⋅ε(x)⋅(1 - d⋅vₙ(x))₊


where we defined the effective strain:

  ε(x) = εᵃ(x) + εᵇ(x)


which relates to the quasi-static pressure field p₀(x) (i.e. when velocity is neglected) by:

  p₀(x) = E⋅ε(x) = Eᵃ⋅εᵃ(x) = Eᵇ⋅εᵇ(x)


that is, the hydroelastic model computes the contact patch assuming quasi-static equilibrium. The separation speed vₙ(x) is computed as the component in the direction of the contact surface's normal n̂(x) of the relative velocity between points Ax and Bx at point x instantaneously moving with body frames A and B respectively, i.e. vₙ(x) = ᴬˣvᴮˣ⋅n̂(x), where the normal n̂(x) points from body A into body B.

[Elandt 2019] R. Elandt, E. Drumwright, M. Sherman, and A. Ruina. A pressure field model for fast, robust approximation of net contact force and moment between nominally rigid objects. Proc. IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems (IROS), 2019. [Hunt and Crossley 1975] Hunt, KH and Crossley, FRE, 1975. Coefficient of restitution interpreted as damping in vibroimpact. Journal of Applied Mechanics, vol. 42, pp. 440–445.

#### Penalty method point contact

Currently MultibodyPlant uses a rigid contact model that is, bodies in the model are infinitely stiff or ideal rigid bodies. Therefore, the mathematical description of the rigid contact model needs to include non-penetration constraints among bodies in the formulation. There are several numerical methods to impose and solve these constraints. In a penalty method approach, we allow for a certain amount of interpenetration and we compute contact forces according to a simple law of the form:

  fₙ = k(1+dẋ)x


where the normal contact force fₙ is made a continuous function of the penetration distance x between the bodies (defined to be positive when the bodies are in contact) and the penetration distance rate ẋ (with ẋ > 0 meaning the penetration distance is increasing and therefore the interpenetration between the bodies is also increasing). k and d are the combined penalty method coefficients for stiffness and dissipation, given a pair of colliding geometries. For flexibility of parameterization, stiffness and dissipation are set on a per-geometry basis (accessing_contact_properties). Given two geometries with individual stiffness and dissipation parameters (k₁, d₁) and (k₂, d₂), we define the rule for combined stiffness (k) and dissipation (d) as:

    k = (k₁⋅k₂)/(k₁+k₂)
d = (k₂/(k₁+k₂))⋅d₁ + (k₁/(k₁+k₂))⋅d₂


These parameters are optional for each geometry. For any geometry not assigned these parameters by a user Pre-Finalize, MultibodyPlant will assign default values such that the combined parameters of two geometries with default values match those estimated using the user-supplied "penetration allowance", as described below.

These are ad-hoc parameters which need to be tuned as a trade-off between:

• The accuracy of the numerical approximation to rigid contact, which requires a stiffness that approaches infinity, and
• the computational cost of the numerical integration, which will require smaller time steps for stiffer systems.

There is no exact procedure for choosing these coefficients, and estimating them manually can be cumbersome since in general they will depend on the scale of the problem including masses, speeds and even body sizes. However, MultibodyPlant aids the estimation of these coefficients using a heuristic function based on a user-supplied "penetration allowance", see set_penetration_allowance(). The penetration allowance is a number in meters that specifies the order of magnitude of the average penetration between bodies in the system that the user is willing to accept as reasonable for the problem being solved. For instance, in the robotics manipulation of ordinary daily objects the user might set this number to 1 millimeter. However, the user might want to increase it for the simulation of heavy walking robots for which an allowance of 1 millimeter would result in a very stiff system.

As for the dissipation coefficient in the simple law above, MultibodyPlant chooses the dissipation coefficient d to model inelastic collisions and therefore sets it so that the penetration distance x behaves as a critically damped oscillator. That is, at the limit of ideal rigid contact (very stiff penalty coefficient k or equivalently the penetration allowance goes to zero), this method behaves as a unilateral constraint on the penetration distance, which models a perfect inelastic collision. For most applications, such as manipulation and walking, this is the desired behavior.

When set_penetration_allowance() is called, MultibodyPlant will estimate reasonable penalty method coefficients as a function of the input penetration allowance. Users will want to run their simulation a number of times and assess they are satisfied with the level of inter-penetration actually observed in the simulation; if the observed penetration is too large, the user will want to set a smaller penetration allowance. If the system is too stiff and the time integration requires very small time steps while at the same time the user can afford larger inter-penetrations, the user will want to increase the penetration allowance. Typically, the observed penetration will be proportional to the penetration allowance. Thus scaling the penetration allowance by say a factor of 0.5, would typically results in inter-penetrations being reduced by the same factor of 0.5. In summary, users should choose the largest penetration allowance that results in inter-penetration levels that are acceptable for the particular application (even when in theory this penetration should be zero for perfectly rigid bodies.)

For a given penetration allowance, the contact interaction that takes two bodies with a non-zero approaching velocity to zero approaching velocity, takes place in a finite amount of time (for ideal rigid contact this time is zero.) A good estimate of this time period is given by a call to get_contact_penalty_method_time_scale(). Users might want to query this value to either set the maximum time step in error-controlled time integration or to set the time step for fixed time step integration. As a guidance, typical fixed time step integrators will become unstable for time steps larger than about a tenth of this time scale.

For further details on contact modeling in Drake, please refer to the section Contact Modeling in Drake of our documentation.

void set_contact_model (ContactModel model)
Sets the contact model to be used by this MultibodyPlant, see ContactModel for available options. More...

void set_penetration_allowance (double penetration_allowance=0.001)
Sets the penetration allowance used to estimate the coefficients in the penalty method used to impose non-penetration among bodies. More...

double get_contact_penalty_method_time_scale () const
Returns a time-scale estimate tc based on the requested penetration allowance δ set with set_penetration_allowance(). More...

void set_stiction_tolerance (double v_stiction=0.001)

State accessors and mutators

The following state methods allow getting and setting the kinematic state variables [q; v], where q is the vector of generalized positions and v is the vector of generalized velocities. The state resides in a Context that is supplied as the first argument to every method.

There are also utilities for accessing and mutating portions of state or actuation arrays corresponding to just a single model instance.

Eigen::VectorBlock< const VectorX< T > > GetPositionsAndVelocities (const systems::Context< T > &context) const
Returns a const vector reference containing the vector [q; v] with q the vector of generalized positions and v the vector of generalized velocities. More...

VectorX< T > GetPositionsAndVelocities (const systems::Context< T > &context, ModelInstanceIndex model_instance) const
Returns the vector [q; v] of the model with q the vector of generalized positions and v the vector of generalized velocities for model instance model_instance. More...

Eigen::VectorBlock< VectorX< T > > GetMutablePositionsAndVelocities (systems::Context< T > *context) const
(Advanced) Returns a mutable vector containing the vector [q; v] of the model with q the vector of generalized positions and v the vector of generalized velocities (see warning). More...

void SetPositionsAndVelocities (systems::Context< T > *context, const VectorX< T > &q_v) const
Sets all generalized positions and velocities from the given vector [q; v]. More...

void SetPositionsAndVelocities (systems::Context< T > *context, ModelInstanceIndex model_instance, const VectorX< T > &q_v) const
Sets generalized positions and velocities from the given vector [q; v] for the specified model instance. More...

Eigen::VectorBlock< const VectorX< T > > GetPositions (const systems::Context< T > &context) const
Returns a const vector reference containing the vector of generalized positions. More...

VectorX< T > GetPositions (const systems::Context< T > &context, ModelInstanceIndex model_instance) const
Returns an vector containing the generalized positions (q) for the given model instance. More...

Eigen::VectorBlock< VectorX< T > > GetMutablePositions (systems::Context< T > *context) const
(Advanced) Returns a mutable vector reference containing the vector of generalized positions (see warning). More...

Eigen::VectorBlock< VectorX< T > > GetMutablePositions (const systems::Context< T > &context, systems::State< T > *state) const
(Advanced) Returns a mutable vector reference containing the vector of generalized positions (see warning). More...

void SetPositions (systems::Context< T > *context, const VectorX< T > &q) const
Sets all generalized positions from the given vector. More...

void SetPositions (systems::Context< T > *context, ModelInstanceIndex model_instance, const VectorX< T > &q_instance) const
Sets the positions for a particular model instance from the given vector. More...

void SetPositions (const systems::Context< T > &context, systems::State< T > *state, ModelInstanceIndex model_instance, const VectorX< T > &q_instance) const
Sets the positions for a particular model instance from the given vector. More...

Eigen::VectorBlock< const VectorX< T > > GetVelocities (const systems::Context< T > &context) const
Returns a const vector reference containing the generalized velocities. More...

VectorX< T > GetVelocities (const systems::Context< T > &context, ModelInstanceIndex model_instance) const
Returns a vector containing the generalized velocities (v) for the given model instance. More...

Eigen::VectorBlock< VectorX< T > > GetMutableVelocities (const systems::Context< T > &context, systems::State< T > *state) const
(Advanced) Returns a mutable vector reference containing the vector of generalized velocities (see warning). More...

Eigen::VectorBlock< VectorX< T > > GetMutableVelocities (systems::Context< T > *context) const
See GetMutableVelocities() method above. More...

void SetVelocities (systems::Context< T > *context, const VectorX< T > &v) const
Sets all generalized velocities from the given vector. More...

void SetVelocities (const systems::Context< T > &context, systems::State< T > *state, ModelInstanceIndex model_instance, const VectorX< T > &v_instance) const
Sets the generalized velocities for a particular model instance from the given vector. More...

void SetVelocities (systems::Context< T > *context, ModelInstanceIndex model_instance, const VectorX< T > &v_instance) const
Sets the generalized velocities for a particular model instance from the given vector. More...

void SetDefaultState (const systems::Context< T > &context, systems::State< T > *state) const override
Sets state according to defaults set by the user for joints (e.g. More...

void SetRandomState (const systems::Context< T > &context, systems::State< T > *state, RandomGenerator *generator) const override
Assigns random values to all elements of the state, by drawing samples independently for each joint/free body (coming soon: and then solving a mathematical program to "project" these samples onto the registered system constraints). More...

VectorX< T > GetActuationFromArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &u) const
Returns a vector of actuation values for model_instance from a vector u of actuation values for the entire model. More...

void SetActuationInArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &u_instance, EigenPtr< VectorX< T >> u) const
Given the actuation values u_instance for all actuators in model_instance, this method sets the actuation vector u for the entire model to which this actuator belongs to. More...

VectorX< T > GetPositionsFromArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &q) const
Returns a vector of generalized positions for model_instance from a vector q_array of generalized positions for the entire model model. More...

void SetPositionsInArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &q_instance, EigenPtr< VectorX< T >> q) const
Sets the vector of generalized positions for model_instance in q using q_instance, leaving all other elements in the array untouched. More...

VectorX< T > GetVelocitiesFromArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &v) const
Returns a vector of generalized velocities for model_instance from a vector v of generalized velocities for the entire MultibodyPlant model. More...

void SetVelocitiesInArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &v_instance, EigenPtr< VectorX< T >> v) const
Sets the vector of generalized velocities for model_instance in v using v_instance, leaving all other elements in the array untouched. More...

Working with free bodies

A MultibodyPlant user adds sets of Body and Joint objects to this plant to build a physical representation of a mechanical model. At Finalize(), MultibodyPlant builds a mathematical representation of such system, consisting of a tree representation. In this representation each body is assigned a Mobilizer, which grants a certain number of degrees of freedom in accordance to the physical specification. In this regard, the modeling representation can be seen as a forest of tree structures each of which contains a single body at the root of the tree. If the root body has six degrees of freedom with respect to the world, it is called a "free body" (sometimes called a "floating body"). A user can request the set of all free bodies with a call to GetFloatingBaseBodies(). Alternatively, a user can query whether a Body is free (floating) or not with Body::is_floating(). For many applications, a user might need to work with indexes in the multibody state vector. For such applications, Body::floating_positions_start() and Body::floating_velocities_start() offer the additional level of introspection needed.

std::unordered_set< BodyIndexGetFloatingBaseBodies () const
Returns the set of body indexes corresponding to the free (floating) bodies in the model, in no particular order. More...

math::RigidTransform< T > GetFreeBodyPose (const systems::Context< T > &context, const Body< T > &body) const
Gets the pose of a given body in the world frame W. More...

void SetFreeBodyPose (systems::Context< T > *context, const Body< T > &body, const math::RigidTransform< T > &X_WB) const
Sets context to store the pose X_WB of a given body B in the world frame W. More...

void SetFreeBodyPose (const systems::Context< T > &context, systems::State< T > *state, const Body< T > &body, const math::RigidTransform< T > &X_WB) const
Sets state to store the pose X_WB of a given body B in the world frame W, for a given context of this model. More...

void SetDefaultFreeBodyPose (const Body< T > &body, const math::RigidTransform< double > &X_WB)
Sets the default pose of body. More...

const math::RigidTransform< double > & GetDefaultFreeBodyPose (const Body< T > &body) const
Gets the default pose of body as set by SetDefaultFreeBodyPose(). More...

void SetFreeBodySpatialVelocity (systems::Context< T > *context, const Body< T > &body, const SpatialVelocity< T > &V_WB) const
Sets context to store the spatial velocity V_WB of a given body B in the world frame W. More...

void SetFreeBodySpatialVelocity (const systems::Context< T > &context, systems::State< T > *state, const Body< T > &body, const SpatialVelocity< T > &V_WB) const
Sets state to store the spatial velocity V_WB of a given body B in the world frame W, for a given context of this model. More...

void SetFreeBodyRandomPositionDistribution (const Body< T > &body, const Vector3< symbolic::Expression > &position)
Sets the distribution used by SetRandomState() to populate the free body's x-y-z position with respect to World. More...

void SetFreeBodyRandomRotationDistribution (const Body< T > &body, const Eigen::Quaternion< symbolic::Expression > &rotation)
Sets the distribution used by SetRandomState() to populate the free body's rotation with respect to World. More...

void SetFreeBodyRandomRotationDistributionToUniform (const Body< T > &body)
Sets the distribution used by SetRandomState() to populate the free body's rotation with respect to World using uniformly random rotations. More...

void SetFreeBodyPoseInWorldFrame (systems::Context< T > *context, const Body< T > &body, const math::RigidTransform< T > &X_WB) const
Sets context to store the pose X_WB of a given body B in the world frame W. More...

void SetFreeBodyPoseInAnchoredFrame (systems::Context< T > *context, const Frame< T > &frame_F, const Body< T > &body, const math::RigidTransform< T > &X_FB) const
Updates context to store the pose X_FB of a given body B in a frame F. More...

const Body< T > & GetUniqueFreeBaseBodyOrThrow (ModelInstanceIndex model_instance) const
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. More...

bool HasUniqueFreeBaseBody (ModelInstanceIndex model_instance) const
Return true if there exists a unique base body in the model given by model_instance and that unique base body is free. More...

Kinematic and dynamic computations

These methods return kinematic results for the state supplied in the given Context. Methods whose names being with Eval return a reference into the Context's cache, performing computation first only if the relevant state has changed. Methods beginning with Calc perform computation unconditionally and return a result without updating the cache.

const math::RigidTransform< T > & EvalBodyPoseInWorld (const systems::Context< T > &context, const Body< T > &body_B) const
Evaluate the pose X_WB of a body B in the world frame W. More...

const SpatialVelocity< T > & EvalBodySpatialVelocityInWorld (const systems::Context< T > &context, const Body< T > &body_B) const
Evaluates V_WB, body B's spatial velocity in the world frame W. More...

const SpatialAcceleration< T > & EvalBodySpatialAccelerationInWorld (const systems::Context< T > &context, const Body< T > &body_B) const
Evaluates A_WB, body B's spatial acceleration in the world frame W. More...

const std::vector< geometry::PenetrationAsPointPair< T > > & EvalPointPairPenetrations (const systems::Context< T > &context) const
Evaluates all point pairs of contact for a given state of the model stored in context. More...

math::RigidTransform< T > CalcRelativeTransform (const systems::Context< T > &context, const Frame< T > &frame_F, const Frame< T > &frame_G) const
Calculates the rigid transform (pose) X_FG relating frame F and frame G. More...

math::RotationMatrix< T > CalcRelativeRotationMatrix (const systems::Context< T > &context, const Frame< T > &frame_F, const Frame< T > &frame_G) const
Calculates the rotation matrix R_FG relating frame F and frame G. More...

void CalcPointsPositions (const systems::Context< T > &context, const Frame< T > &frame_B, const Eigen::Ref< const MatrixX< T >> &p_BQi, const Frame< T > &frame_A, EigenPtr< MatrixX< T >> p_AQi) const
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. More...

Vector3< T > CalcCenterOfMassPositionInWorld (const systems::Context< T > &context) const
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. More...

Vector3< T > CalcCenterOfMassPosition (const systems::Context< T > &context) const
(Deprecated.) More...

Vector3< T > CalcCenterOfMassPositionInWorld (const systems::Context< T > &context, const std::vector< ModelInstanceIndex > &model_instances) const
Calculates the position vector from the world origin Wo to the center of mass of all bodies contained in model_instances, expressed in the world frame W. More...

Vector3< T > CalcCenterOfMassPosition (const systems::Context< T > &context, const std::vector< ModelInstanceIndex > &model_instances) const
(Deprecated.) More...

Vector3< T > CalcCenterOfMassTranslationalVelocityInWorld (const systems::Context< T > &context) const
Calculates system center of mass translational velocity in world frame W. More...

Vector3< T > CalcCenterOfMassTranslationalVelocityInWorld (const systems::Context< T > &context, const std::vector< ModelInstanceIndex > &model_instances) const
Calculates system center of mass translational velocity in world frame W. More...

SpatialMomentum< T > CalcSpatialMomentumInWorldAboutPoint (const systems::Context< T > &context, const Vector3< T > &p_WoP_W) const
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. More...

SpatialMomentum< T > CalcSpatialMomentumInWorldAboutPoint (const systems::Context< T > &context, const std::vector< ModelInstanceIndex > &model_instances, const Vector3< T > &p_WoP_W) const
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. More...

void CalcSpatialAccelerationsFromVdot (const systems::Context< T > &context, const VectorX< T > &known_vdot, std::vector< SpatialAcceleration< T >> *A_WB_array) const
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. More...

VectorX< T > CalcInverseDynamics (const systems::Context< T > &context, const VectorX< T > &known_vdot, const MultibodyForces< T > &external_forces) const
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. More...

void CalcForceElementsContribution (const systems::Context< T > &context, MultibodyForces< T > *forces) const
Computes the combined force contribution of ForceElement objects in the model. More...

VectorX< T > CalcGravityGeneralizedForces (const systems::Context< T > &context) const
Computes the generalized forces tau_g(q) due to gravity as a function of the generalized positions q stored in the input context. More...

void MapVelocityToQDot (const systems::Context< T > &context, const Eigen::Ref< const VectorX< T >> &v, EigenPtr< VectorX< T >> qdot) const
Transforms generalized velocities v to time derivatives qdot of the generalized positions vector q (stored in context). More...

void MapQDotToVelocity (const systems::Context< T > &context, const Eigen::Ref< const VectorX< T >> &qdot, EigenPtr< VectorX< T >> v) const
Transforms the time derivative qdot of the generalized positions vector q (stored in context) to generalized velocities v. More...

System matrix computations

Methods in this section compute and return various matrices that appear in the system equations of motion. For better performance, prefer to use direct computations where available rather than work with explicit matrices. See Kinematic and dynamics computations for available computations. For example, you can obtain the mass matrix, Coriolis, centripetal, and gyroscopic "bias" terms, and a variety of Jacobian and actuation matrices.

void CalcMassMatrixViaInverseDynamics (const systems::Context< T > &context, EigenPtr< MatrixX< T >> M) const
Performs the computation of the mass matrix M(q) of the model using inverse dynamics, where the generalized positions q are stored in context. More...

void CalcMassMatrix (const systems::Context< T > &context, EigenPtr< MatrixX< T >> M) const
Performs the computation of the mass matrix M(q) of the model, as a function of the generalized positions q stored in context. More...

void CalcBiasTerm (const systems::Context< T > &context, EigenPtr< VectorX< T >> Cv) const
Computes the bias term C(q, v)v containing Coriolis, centripetal, and gyroscopic effects in the multibody equations of motion: More...

Matrix3X< T > CalcBiasTranslationalAcceleration (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Eigen::Ref< const Matrix3X< T >> &p_BoBi_B, const Frame< T > &frame_A, const Frame< T > &frame_E) const
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, where 𝑠 is either q̇ (time-derivatives of generalized positions) or v (generalized velocities). More...

SpatialAcceleration< T > CalcBiasSpatialAcceleration (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Eigen::Ref< const Vector3< T >> &p_BoBp_B, const Frame< T > &frame_A, const Frame< T > &frame_E) const
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, where 𝑠 is either q̇ (time-derivatives of generalized positions) or v (generalized velocities). More...

void CalcJacobianSpatialVelocity (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Eigen::Ref< const Vector3< T >> &p_BoBp_B, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< MatrixX< T >> Js_V_ABp_E) const
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. More...

void CalcJacobianAngularVelocity (const systems::Context< T > &context, const JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< Matrix3X< T >> Js_w_AB_E) const
Calculates J𝑠_w_AB, a frame B's angular velocity Jacobian in a frame A with respect to "speeds" 𝑠. More...

void CalcJacobianTranslationalVelocity (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Eigen::Ref< const Matrix3X< T >> &p_BoBi_B, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< MatrixX< T >> Js_v_ABi_E) const
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. More...

void CalcJacobianCenterOfMassTranslationalVelocity (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< Matrix3X< T >> Js_v_ACcm_E) const
This method computes 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 composite center of mass of the system of all bodies in the MultibodyPlant (except world_body()). More...

Vector3< T > CalcBiasCenterOfMassTranslationalAcceleration (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_A, const Frame< T > &frame_E) const
Calculates abias_ACcm_E, point Ccm's translational "bias" acceleration term in frame A with respect to "speeds" 𝑠, expressed in frame E, where point Ccm is the composite center of mass of the system of all bodies (except world_body()) in the MultibodyPlant. More...

MatrixX< double > MakeStateSelectorMatrix (const std::vector< JointIndex > &user_to_joint_index_map) const
This method allows users to map the state of this model, x, into a vector of selected state xₛ with a given preferred ordering. More...

MatrixX< double > MakeActuatorSelectorMatrix (const std::vector< JointActuatorIndex > &user_to_actuator_index_map) const
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. More...

MatrixX< T > MakeActuationMatrix () const
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_actuators() and nv equal to num_velocities(). More...

MatrixX< double > MakeActuatorSelectorMatrix (const std::vector< JointIndex > &user_to_joint_index_map) const
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 (ordered by JointActuatorIndex) and uₛ is a vector of actuation values for the actuators acting on the joints listed by user_to_joint_index_map. More...

Introspection

These methods allow a user to query whether a given multibody element is part of this plant's model. These queries can be performed at any time during the lifetime of a MultibodyPlant model, i.e. there is no restriction on whether they must be called before or after Finalize(). These queries can be performed while new multibody elements are being added to the model. These methods allow a user to retrieve a reference to a multibody element by its name. An exception is thrown if there is no element with the requested name.

If the named element is present in more than one model instance and a model instance is not explicitly specified, std::logic_error is thrown.

double time_step () const
The time step (or period) used to model this plant as a discrete system with periodic updates. More...

bool is_finalized () const
Returns true if this MultibodyPlant was finalized with a call to Finalize(). More...

const RigidBody< T > & world_body () const
Returns a constant reference to the world body. More...

const BodyFrame< T > & world_frame () const
Returns a constant reference to the world frame. More...

int num_bodies () const
Returns the number of bodies in the model, including the "world" body, which is always part of the model. More...

const Body< T > & get_body (BodyIndex body_index) const
Returns a constant reference to the body with unique index body_index. More...

bool IsAnchored (const Body< T > &body) const
Returns true if body is anchored (i.e. More...

bool HasBodyNamed (const std::string &name) const

bool HasBodyNamed (const std::string &name, ModelInstanceIndex model_instance) const

const Body< T > & GetBodyByName (const std::string &name) const
Returns a constant reference to a body that is identified by the string name in this MultibodyPlant. More...

const Body< T > & GetBodyByName (const std::string &name, ModelInstanceIndex model_instance) const
Returns a constant reference to the body that is uniquely identified by the string name and model_instance in this MultibodyPlant. More...

std::vector< BodyIndexGetBodyIndices (ModelInstanceIndex model_instance) const
Returns a list of body indices associated with model_instance. More...

const RigidBody< T > & GetRigidBodyByName (const std::string &name) const
Returns a constant reference to a rigid body that is identified by the string name in this model. More...

const RigidBody< T > & GetRigidBodyByName (const std::string &name, ModelInstanceIndex model_instance) const
Returns a constant reference to the rigid body that is uniquely identified by the string name in model_instance. More...

std::vector< const Body< T > * > GetBodiesWeldedTo (const Body< T > &body) const
Returns all bodies that are transitively welded, or rigidly affixed, to body, per these two definitions: More...

int num_joints () const
Returns the number of joints in the model. More...

const Joint< T > & get_joint (JointIndex joint_index) const
Returns a constant reference to the joint with unique index joint_index. More...

bool HasJointNamed (const std::string &name) const

bool HasJointNamed (const std::string &name, ModelInstanceIndex model_instance) const

Joint< T > & get_mutable_joint (JointIndex joint_index)
Returns a mutable reference to the joint with unique index joint_index. More...

std::vector< JointIndexGetJointIndices (ModelInstanceIndex model_instance) const
Returns a list of joint indices associated with model_instance. More...

template<template< typename > class JointType = Joint>
const JointType< T > & GetJointByName (const std::string &name, std::optional< ModelInstanceIndex > model_instance=std::nullopt) const
Returns a constant reference to a joint that is identified by the string name in this MultibodyPlant. More...

template<template< typename > class JointType = Joint>
JointType< T > & GetMutableJointByName (const std::string &name, std::optional< ModelInstanceIndex > model_instance=std::nullopt)
A version of GetJointByName that returns a mutable reference. More...

int num_frames () const
Returns the number of Frame objects in this model. More...

const Frame< T > & get_frame (FrameIndex frame_index) const
Returns a constant reference to the frame with unique index frame_index. More...

bool HasFrameNamed (const std::string &name) const

bool HasFrameNamed (const std::string &name, ModelInstanceIndex model_instance) const

const Frame< T > & GetFrameByName (const std::string &name) const
Returns a constant reference to a frame that is identified by the string name in this model. More...

const Frame< T > & GetFrameByName (const std::string &name, ModelInstanceIndex model_instance) const
Returns a constant reference to the frame that is uniquely identified by the string name in model_instance. More...

int num_actuators () const
Returns the number of joint actuators in the model. More...

int num_actuated_dofs () const
Returns the total number of actuated degrees of freedom. More...

int num_actuated_dofs (ModelInstanceIndex model_instance) const
Returns the total number of actuated degrees of freedom for a specific model instance. More...

const JointActuator< T > & get_joint_actuator (JointActuatorIndex actuator_index) const
Returns a constant reference to the joint actuator with unique index actuator_index. More...

JointActuator< T > & get_mutable_joint_actuator (JointActuatorIndex actuator_index) const
Returns a mutable reference to the joint actuator with unique index actuator_index. More...

bool HasJointActuatorNamed (const std::string &name) const

bool HasJointActuatorNamed (const std::string &name, ModelInstanceIndex model_instance) const

const JointActuator< T > & GetJointActuatorByName (const std::string &name) const
Returns a constant reference to an actuator that is identified by the string name in this MultibodyPlant. More...

const JointActuator< T > & GetJointActuatorByName (const std::string &name, ModelInstanceIndex model_instance) const
Returns a constant reference to the actuator that is uniquely identified by the string name and model_instance in this MultibodyPlant. More...

int num_force_elements () const
Returns the number of ForceElement objects. More...

const ForceElement< T > & get_force_element (ForceElementIndex force_element_index) const
Returns a constant reference to the force element with unique index force_element_index. More...

template<template< typename > class ForceElementType = ForceElement>
const ForceElementType< T > & GetForceElement (ForceElementIndex force_element_index) const
Returns a constant reference to a force element identified by its unique index in this MultibodyPlant. More...

const UniformGravityFieldElement< T > & gravity_field () const
An accessor to the current gravity field. More...

UniformGravityFieldElement< T > & mutable_gravity_field ()
A mutable accessor to the current gravity field. More...

int num_model_instances () const
Returns the number of model instances in the model. More...

const std::string & GetModelInstanceName (ModelInstanceIndex model_instance) const
Returns the name of a model_instance. More...

bool HasModelInstanceNamed (const std::string &name) const

ModelInstanceIndex GetModelInstanceByName (const std::string &name) const
Returns the index to the model instance that is uniquely identified by the string name in this MultibodyPlant. More...

std::string GetTopologyGraphvizString () const
Returns a Graphviz string describing the topology of this plant. More...

int num_positions () const
Returns the size of the generalized position vector q for this model. More...

int num_positions (ModelInstanceIndex model_instance) const
Returns the size of the generalized position vector qᵢ for model instance i. More...

int num_velocities () const
Returns the size of the generalized velocity vector v for this model. More...

int num_velocities (ModelInstanceIndex model_instance) const
Returns the size of the generalized velocity vector vᵢ for model instance i. More...

int num_multibody_states () const
Returns the size of the multibody system state vector x = [q v]. More...

int num_multibody_states (ModelInstanceIndex model_instance) const
Returns the size of the multibody system state vector xᵢ = [qᵢ vᵢ] for model instance i. More...

VectorX< double > GetPositionLowerLimits () const
Returns a vector of size num_positions() containing the lower position limits for every generalized position coordinate. More...

VectorX< double > GetPositionUpperLimits () const
Upper limit analog of GetPositionsLowerLimits(), where any unbounded or unspecified limits will be +infinity. More...

VectorX< double > GetVelocityLowerLimits () const
Returns a vector of size num_velocities() containing the lower velocity limits for every generalized velocity coordinate. More...

VectorX< double > GetVelocityUpperLimits () const
Upper limit analog of GetVelocitysLowerLimits(), where any unbounded or unspecified limits will be +infinity. More...

VectorX< double > GetAccelerationLowerLimits () const
Returns a vector of size num_velocities() containing the lower acceleration limits for every generalized velocity coordinate. More...

VectorX< double > GetAccelerationUpperLimits () const
Upper limit analog of GetAccelerationsLowerLimits(), where any unbounded or unspecified limits will be +infinity. More...

ContactModel get_contact_model () const
Returns the model used for contact. See documentation for ContactModel. More...

int num_visual_geometries () const
Returns the number of geometries registered for visualization. More...

int num_collision_geometries () const
Returns the number of geometries registered for contact modeling. More...

std::optional< geometry::SourceIdget_source_id () const
Returns the unique id identifying this plant as a source for a SceneGraph. More...

bool geometry_source_is_registered () const
Returns true if this MultibodyPlant was registered with a SceneGraph. More...

## Friends

template<typename U >
class MultibodyPlant

class MultibodyPlantTester

## Related Functions

(Note that these are not member functions.)

template<typename T >
AddMultibodyPlantSceneGraphResult< T > AddMultibodyPlantSceneGraph (systems::DiagramBuilder< T > *builder, double time_step, std::unique_ptr< geometry::SceneGraph< T >> scene_graph=nullptr)
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. More...

template<typename T >
AddMultibodyPlantSceneGraphResult< T > AddMultibodyPlantSceneGraph (systems::DiagramBuilder< T > *builder, std::unique_ptr< MultibodyPlant< T >> plant, std::unique_ptr< geometry::SceneGraph< T >> scene_graph=nullptr)
Adds a MultibodyPlant and a SceneGraph instance to a diagram builder, connecting the geometry ports. More...

## ◆ MultibodyPlant() [1/4]

 MultibodyPlant ( const MultibodyPlant< T > & )
delete

## ◆ MultibodyPlant() [2/4]

 MultibodyPlant ( MultibodyPlant< T > && )
delete

## ◆ MultibodyPlant() [3/4]

 MultibodyPlant ( double time_step )
explicit

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 Choice of Time Advancement Strategy 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.
Parameters
 [in] 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 Choice of Time Advancement Strategy 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.
Exceptions
 std::exception if time_step is negative.

## ◆ MultibodyPlant() [4/4]

 MultibodyPlant ( const MultibodyPlant< U > & other )
explicit

Scalar-converting copy constructor. See System Scalar Conversion.

## Member Function Documentation

 const ForceElementType& AddForceElement ( Args &&... args )

Adds a new force element model of type ForceElementType to this MultibodyPlant.

The arguments to this method args are forwarded to ForceElementType's constructor.

Parameters
 [in] args Zero or more parameters provided to the constructor of the new force element. It must be the case that ForceElementType(args) is a valid constructor.
Template Parameters
 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.
The ForceElement class's documentation for further details on how a force element is defined.

 const FrameType& AddFrame ( std::unique_ptr< FrameType< T >> frame )

This method adds a Frame of type FrameType<T>.

For more information, please see the corresponding constructor of FrameType.

Template Parameters
 FrameType Template which will be instantiated on T.
Parameters
 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.

 const JointType& AddJoint ( std::unique_ptr< JointType< T >> joint )

This method adds a Joint of type JointType between two bodies.

For more information, see the below overload of AddJoint<>.

 const JointType& AddJoint ( const std::string & name, const Body< T > & parent, const std::optional< math::RigidTransform< double >> & X_PF, const Body< T > & child, const std::optional< math::RigidTransform< double >> & X_BM, Args &&... args )

This method adds a Joint of type JointType between two bodies.

The two bodies connected by this Joint object are referred to as parent and child bodies. The parent/child ordering defines the sign conventions for the generalized coordinates and the coordinate ordering for multi-DOF joints.

Note: The previous figure also shows Pcm which is body P's center of mass and point Bcm which is body B's center of mass.

As explained in the Joint class's documentation, in Drake we define a frame F attached to the parent body P with pose X_PF and a frame M attached to the child body B with pose X_BM. This method helps creating a joint between two bodies with fixed poses X_PF and X_BM. Refer to the Joint class's documentation for more details.

Parameters
 name A string that uniquely identifies the new joint to be added to this model. A std::runtime_error is thrown if a joint named name already is part of the model. See HasJointNamed(), Joint::name(). [in] parent The parent body connected by the new joint. [in] X_PF The fixed pose of frame F attached to the parent body, measured in the frame P of that body. X_PF is an optional parameter; empty curly braces {} imply that frame F is the same body frame P. If instead your intention is to make a frame F with pose X_PF equal to the identity pose, provide RigidTransform::Identity() as your input. [in] child The child body connected by the new joint. [in] X_BM The fixed pose of frame M attached to the child body, measured in the frame B of that body. X_BM is an optional parameter; empty curly braces {} imply that frame M is the same body frame B. If instead your intention is to make a frame M with pose X_BM equal to the identity pose, provide RigidTransform::Identity() as your input. [in] args Zero or more parameters provided to the constructor of the new joint. It must be the case that JointType( const std::string&, const Frame&, const Frame&, args) is a valid constructor.
Template Parameters
 JointType The type of the Joint to add.
Returns
A constant reference to the new joint just added, of type JointType<T> specialized on the scalar type T of this MultibodyPlant. It will remain valid for the lifetime of this MultibodyPlant.

Example of usage:

MultibodyPlant<T> plant;
// Code to define bodies serving as the joint's parent and child bodies.
const RigidBody<double>& body_1 =
const RigidBody<double>& body_2 =
// Body 1 serves as parent, Body 2 serves as child.
// Define the pose X_BM of a frame M rigidly attached to child body B.
const RevoluteJoint<double>& elbow =
"Elbow", /* joint name */
body_1, /* parent body */
{}, /* frame F IS the parent body frame P */
body_2, /* child body, the pendulum */
X_BM, /* pose of frame M in the body frame B */
Vector3d::UnitZ()); /* revolute axis in this case */
Exceptions
 std::exception if this MultibodyPlant already contains a joint with the given name. See HasJointNamed(), Joint::name().
The Joint class's documentation for further details on how a Joint is defined.

 const JointActuator& AddJointActuator ( const std::string & name, const Joint< T > & joint, double effort_limit = std::numeric_limits::infinity() )

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.

Parameters
 [in] name A string that uniquely identifies the new actuator to be added to this model. A std::runtime_error is thrown if an actuator with the same name already exists in the model. See HasJointActuatorNamed(). [in] joint The Joint to be actuated by the new JointActuator. [in] effort_limit The maximum effort for the actuator. It must be strictly positive, otherwise an std::exception 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.
Returns
A constant reference to the new JointActuator just added, which will remain valid for the lifetime of this plant.
Exceptions
 std::exception if joint.num_velocities() > 1 since for now we only support actuators for single dof joints.

 ModelInstanceIndex AddModelInstance ( const std::string & name )

Creates a new model instance.

Returns the index for the model instance.

Parameters
 [in] 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().

 const RigidBody& AddRigidBody ( const std::string & name, ModelInstanceIndex model_instance, const SpatialInertia< double > & M_BBo_B )

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:

MultibodyPlant<T> plant;
// ... Code to define spatial_inertia, a SpatialInertia<T> object ...
const RigidBody<T>& body =
Parameters
 [in] name A string that identifies the new body to be added to this model. A std::runtime_error is thrown if a body named name already is part of model_instance. See HasBodyNamed(), Body::name(). [in] model_instance A model instance index which this body is part of. [in] 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.
Returns
A constant reference to the new RigidBody just added, which will remain valid for the lifetime of this MultibodyPlant.

 const RigidBody& AddRigidBody ( const std::string & name, const SpatialInertia< double > & M_BBo_B )

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 (more on model instances).

Example of usage:

MultibodyPlant<T> plant;
// ... Code to define spatial_inertia, a SpatialInertia<T> object ...
const RigidBody<T>& body =
Parameters
 [in] name A string that identifies the new body to be added to this model. A std::runtime_error is thrown if a body named name already is part of the model in the default model instance. See HasBodyNamed(), Body::name(). [in] 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.
Returns
A constant reference to the new RigidBody just added, which will remain valid for the lifetime of this MultibodyPlant.
Exceptions
 std::logic_error if additional model instances have been created beyond the world and default instances.

## ◆ CalcBiasCenterOfMassTranslationalAcceleration()

 Vector3 CalcBiasCenterOfMassTranslationalAcceleration ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_A, const Frame< T > & frame_E ) const

Calculates abias_ACcm_E, point Ccm's translational "bias" acceleration term in frame A with respect to "speeds" 𝑠, expressed in frame E, where point Ccm is the composite center of mass of the system of all bodies (except world_body()) in the MultibodyPlant.

abias_ACcm is the part of a_ACcm (Ccm's translational acceleration) that does not multiply ṡ, equal to abias_ACcm = J̇𝑠_v_ACcm ⋅ s. This allows a_ACcm to be written as a_ACcm = J𝑠_v_ACcm ⋅ ṡ + abias_ACcm.

Parameters
 [in] context The state of the multibody system. [in] with_respect_to Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the Jacobian abias_ACcm is partial derivatives with respect to 𝑠 = q̇ (time-derivatives of generalized positions) or with respect to 𝑠 = v (generalized velocities). [in] frame_A The frame in which abias_ACcm is measured. [in] frame_E The frame in which abias_ACcm is expressed on output.
Return values
 abias_ACcm_E Point Ccm's translational "bias" acceleration term in frame A with respect to "speeds" 𝑠, expressed in frame E.
Exceptions
 std::runtime_error if Ccm does not exist, which occurs if there are no massive bodies in MultibodyPlant (except world_body()). std::exception if composite_mass <= 0, where composite_mass is the total mass of all bodies except world_body() in MultibodyPlant. std::exception if frame_A is not the world frame.

## ◆ CalcBiasSpatialAcceleration()

 SpatialAcceleration CalcBiasSpatialAcceleration ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_B, const Eigen::Ref< const Vector3< T >> & p_BoBp_B, const Frame< T > & frame_A, const Frame< T > & frame_E ) const

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, where 𝑠 is either q̇ (time-derivatives of generalized positions) or v (generalized velocities).

A𝑠Bias_ABp is the term in A_ABp (Bp's spatial acceleration in A) that does not include 𝑠̇, i.e., A𝑠Bias_ABp is Bi's translational acceleration in A when 𝑠̇ = 0.

  A_ABp =  J𝑠_V_ABp ⋅ 𝑠̇  +  J̇𝑠_V_ABp ⋅ 𝑠   (𝑠 = q̇ or 𝑠 = v), hence
A𝑠Bias_ABp = J̇𝑠_V_ABp ⋅ 𝑠


where J𝑠_V_ABp is Bp's spatial velocity Jacobian in frame A for speeds s (see CalcJacobianSpatialVelocity() for details on J𝑠_V_ABp).

Parameters
 [in] context The state of the multibody system. [in] 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. [in] frame_B The frame on which point Bp is affixed/welded. [in] p_BoBp_B Position vector from Bo (frame_B's origin) to point Bp (regarded as affixed/welded to B), expressed in frame_B. [in] frame_A The frame that measures A𝑠Bias_ABp. Currently, an exception is thrown if frame_A is not the World frame. [in] 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.
Note
Shown below, A𝑠Bias_ABp_E = J̇𝑠_V_ABp ⋅ 𝑠 is quadratic in 𝑠.
 V_ABp =  J𝑠_V_ABp ⋅ 𝑠        which upon vector differentiation in A gives
A_ABp =  J𝑠_V_ABp ⋅ 𝑠̇  +  J̇𝑠_V_ABp ⋅ 𝑠   Since J̇𝑠_V_ABp is linear in 𝑠,
A𝑠Bias_ABp = J̇𝑠_V_ABp ⋅ 𝑠                             is quadratic in 𝑠.

CalcJacobianSpatialVelocity() to compute J𝑠_V_ABp, point Bp's translational velocity Jacobian in frame A with respect to 𝑠.
Exceptions
 std::exception if with_respect_to is not JacobianWrtVariable::kV std::exception if frame_A is not the world frame.

## ◆ CalcBiasTerm()

 void CalcBiasTerm ( const systems::Context< T > & context, EigenPtr< VectorX< T >> Cv ) const

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

  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 and tau_app is a vector of 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.

Parameters
 [in] context The context containing the state of the model. It stores the generalized positions q and the generalized velocities v. [out] 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()

 Matrix3X CalcBiasTranslationalAcceleration ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_B, const Eigen::Ref< const Matrix3X< T >> & p_BoBi_B, const Frame< T > & frame_A, const Frame< T > & frame_E ) const

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, where 𝑠 is either q̇ (time-derivatives of generalized positions) or v (generalized velocities).

a𝑠Bias_ABi is the term in a_ABi (Bi's translational acceleration in A) that does not include 𝑠̇, i.e., a𝑠Bias_ABi is Bi's translational acceleration in A when 𝑠̇ = 0.

  a_ABi =  J𝑠_v_ABi ⋅ 𝑠̇  +  J̇𝑠_v_ABi ⋅ 𝑠  (𝑠 = q̇ or 𝑠 = v), hence
a𝑠Bias_ABi = J̇𝑠_v_ABi ⋅ 𝑠


where J𝑠_v_ABi is Bi's translational velocity Jacobian in frame A for s (see CalcJacobianTranslationalVelocity() for details on J𝑠_v_ABi).

Parameters
 [in] context The state of the multibody system. [in] with_respect_to Enum equal to JacobianWrtVariable::kQDot or JacobianWrtVariable::kV, indicating whether the translational accceleration bias is with respect to 𝑠 = q̇ or 𝑠 = v. [in] frame_B The frame on which points Bi are affixed/welded. [in] 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. [in] frame_A The frame that measures a𝑠Bias_ABi. Currently, an exception is thrown if frame_A is not the World frame. [in] 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.
Note
Shown below, a𝑠Bias_ABi_E = J̇𝑠_v_ABp ⋅ 𝑠 is quadratic in 𝑠.
 v_ABi =  J𝑠_v_ABi ⋅ 𝑠        which upon vector differentiation in A gives
a_ABi =  J𝑠_v_ABi ⋅ 𝑠̇ + J̇𝑠_v_ABi ⋅ 𝑠     Since J̇𝑠_v_ABi is linear in 𝑠,
a𝑠Bias_ABi = J̇𝑠_v_ABi ⋅ 𝑠                             is quadratic in 𝑠.

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.
Exceptions
 std::exception if with_respect_to is not JacobianWrtVariable::kV std::exception if frame_A is not the world frame.

## ◆ CalcCenterOfMassPosition() [1/2]

 Vector3 CalcCenterOfMassPosition ( const systems::Context< T > & context ) const

(Deprecated.)

Deprecated:
"Use CalcCenterOfMassPositionInWorld() " "instead of CalcCenterOfMassPosition()."
This will be removed from Drake on or after "2021-04-21" .

## ◆ CalcCenterOfMassPosition() [2/2]

 Vector3 CalcCenterOfMassPosition ( const systems::Context< T > & context, const std::vector< ModelInstanceIndex > & model_instances ) const

(Deprecated.)

Deprecated:
"Use CalcCenterOfMassPositionInWorld() " "instead of CalcCenterOfMassPosition()."
This will be removed from Drake on or after "2021-04-21" .

## ◆ CalcCenterOfMassPositionInWorld() [1/2]

 Vector3 CalcCenterOfMassPositionInWorld ( const systems::Context< T > & context ) const

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.

Parameters
 [in] context Contains the state of the model.
Return values
 p_WScm_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.
Exceptions
 std::exception if this has no body except world_body(). std::exception if mₛ ≤ 0 (mₛ is the mass of this system S).
Note
The world_body() is ignored.

## ◆ CalcCenterOfMassPositionInWorld() [2/2]

 Vector3 CalcCenterOfMassPositionInWorld ( const systems::Context< T > & context, const std::vector< ModelInstanceIndex > & model_instances ) const

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

Parameters
 [in] context Contains the state of the model. [in] model_instances Vector of selected model instances. This method does not distinguish between welded, joint connected, or floating bodies.
Return values
 p_WScm_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 bodies contained in model_instances.
Exceptions
 std::exception if model_instance only has world_model_instance(), i.e., model_instances has no body except world_body(). std::exception if mₛ ≤ 0 (mₛ is the mass of the system S).
Note
The world_body() is ignored.

## ◆ CalcCenterOfMassTranslationalVelocityInWorld() [1/2]

 Vector3 CalcCenterOfMassTranslationalVelocityInWorld ( const systems::Context< T > & context ) const

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

Parameters
 [in] context The context contains the state of the model.
Return values
 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.
Exceptions
 std::exception if this has no body except world_body(). std::exception if mₛ ≤ 0 (mₛ is the mass of this system S).
Note
The world_body() is ignored.

## ◆ CalcCenterOfMassTranslationalVelocityInWorld() [2/2]

 Vector3 CalcCenterOfMassTranslationalVelocityInWorld ( const systems::Context< T > & context, const std::vector< ModelInstanceIndex > & model_instances ) const

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

Parameters
 [in] context The context contains the state of the model. [in] model_instances The vector of selected model instances.
Return values
 v_WScm_W Scm's translational velocity in frame W, expressed in W, where Scm is the center of mass of the system S in model_instances.
Exceptions
 std::exception if this has no body except world_body(). std::exception if mₛ ≤ 0 (mₛ is the mass of this system S).
Note
This method does not distinguish between welded bodies, joint connected bodies, and free bodies. The world_body() is ignored.

## ◆ CalcForceElementsContribution()

 void CalcForceElementsContribution ( const systems::Context< T > & context, MultibodyForces< T > * forces ) const

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.

Parameters
 [in] context The context containing the state of this model. [out] 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.
Exceptions
 std::exception if forces is null or not compatible with this model, per MultibodyForces::CheckInvariants().

## ◆ CalcGravityGeneralizedForces()

 VectorX CalcGravityGeneralizedForces ( const systems::Context< T > & context ) const

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:

  Mv̇ + C(q, v)v = tau_g(q) + tau_app


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

Parameters
 [in] 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()

 VectorX CalcInverseDynamics ( const systems::Context< T > & context, const VectorX< T > & known_vdot, const MultibodyForces< T > & external_forces ) const

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:

  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, C(q, v)v is the bias term containing 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].

Parameters
 [in] context The context containing the state of the model. [in] 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. [in] 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()

 void CalcJacobianAngularVelocity ( const systems::Context< T > & context, const JacobianWrtVariable with_respect_to, const Frame< T > & frame_B, const Frame< T > & frame_A, const Frame< T > & frame_E, EigenPtr< Matrix3X< T >> Js_w_AB_E ) const

Calculates J𝑠_w_AB, a frame B's angular velocity Jacobian in a frame A with respect to "speeds" 𝑠.

     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).

Parameters
 [in] context The state of the multibody system. [in] 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). [in] frame_B The frame B in w_AB (B's angular velocity in A). [in] frame_A The frame A in w_AB (B's angular velocity in A). [in] 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. [out] 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.
Exceptions
 std::exception if J𝑠_w_AB_E is nullptr or not of size 3 x n.

## ◆ CalcJacobianCenterOfMassTranslationalVelocity()

 void CalcJacobianCenterOfMassTranslationalVelocity ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_A, const Frame< T > & frame_E, EigenPtr< Matrix3X< T >> Js_v_ACcm_E ) const

This method computes 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 composite center of mass of the system of all bodies in the MultibodyPlant (except world_body()).

Parameters
 [in] context The state of the multibody system. [in] 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). [in] frame_A The frame in which the translational velocity v_ACcm and its Jacobian J𝑠_v_ACcm are measured. [in] frame_E The frame in which the Jacobian J𝑠_v_ACcm is expressed on output. [out] 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).
Exceptions
 std::runtime_error if CCm does not exist, which occurs if there are no massive bodies in MultibodyPlant (except world_body()). std::exception if composite_mass <= 0, where composite_mass is the total mass of all bodies except world_body() in MultibodyPlant.

## ◆ CalcJacobianSpatialVelocity()

 void CalcJacobianSpatialVelocity ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_B, const Eigen::Ref< const Vector3< T >> & p_BoBp_B, const Frame< T > & frame_A, const Frame< T > & frame_E, EigenPtr< MatrixX< T >> Js_V_ABp_E ) const

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.

     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).

Parameters
 [in] context The state of the multibody system. [in] 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). [in] frame_B The frame on which point Bp is fixed/welded. [in] 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. [in] 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. [in] 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. [out] 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.,  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.
Exceptions
 std::exception if J𝑠_V_ABp_E is nullptr or not sized 6 x n.

## ◆ CalcJacobianTranslationalVelocity()

 void CalcJacobianTranslationalVelocity ( const systems::Context< T > & context, JacobianWrtVariable with_respect_to, const Frame< T > & frame_B, const Eigen::Ref< const Matrix3X< T >> & p_BoBi_B, const Frame< T > & frame_A, const Frame< T > & frame_E, EigenPtr< MatrixX< T >> Js_v_ABi_E ) const

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.

     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).

Parameters
 [in] context The state of the multibody system. [in] 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). [in] frame_B The frame on which point Bi is affixed/welded. [in] 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. [in] 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. [in] 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. [out] 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).
Exceptions
 std::exception 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.
[∂(v_ABi)/∂q̇₁,  ...  ∂(v_ABi)/∂q̇ⱼ] = [∂(p_AoBi)/∂q₁,  ...  ∂(p_AoBi)/∂qⱼ]

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

## ◆ CalcMassMatrix()

 void CalcMassMatrix ( const systems::Context< T > & context, EigenPtr< MatrixX< T >> M ) const

Performs the computation of the mass matrix M(q) of the model, as a function of the generalized positions q stored in context.

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

Parameters
 [in] context The context containing the state of the model. [out] M A valid (non-null) pointer to a squared matrix in ℛⁿˣⁿ with n the number of generalized velocities (num_velocities()) of the model. This method aborts if M is nullptr or if it does not have the proper size.
Warning
This is an O(n²) algorithm. Avoid the explicit computation of the mass matrix whenever possible.

## ◆ CalcMassMatrixViaInverseDynamics()

 void CalcMassMatrixViaInverseDynamics ( const systems::Context< T > & context, EigenPtr< MatrixX< T >> M ) const

Performs the computation of the mass matrix M(q) of the model using inverse dynamics, where the generalized positions q are stored in context.

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

Parameters
 [in] context The context containing the state of the model. [out] M A valid (non-null) pointer to a squared matrix in ℛⁿˣⁿ with n the number of generalized velocities (num_velocities()) of the model. This method aborts if H is nullptr or if it does not have the proper 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:

  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:

  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.

## ◆ CalcPointsPositions()

 void CalcPointsPositions ( const systems::Context< T > & context, const Frame< T > & frame_B, const Eigen::Ref< const MatrixX< T >> & p_BQi, const Frame< T > & frame_A, EigenPtr< MatrixX< T >> p_AQi ) const

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.

Parameters
 [in] context The context containing the state of the model. It stores the generalized positions q of the model. [in] frame_B The frame B in which the positions p_BQi of a set of points Qi are given. [in] 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. [in] frame_A The frame A in which it is desired to compute the positions p_AQi of each point Qi in the set. [out] 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 std::runtime_error exception. This method also throws a std::runtime_error exception if p_BQi and p_AQi differ in the number of columns.

## ◆ CalcRelativeRotationMatrix()

 math::RotationMatrix CalcRelativeRotationMatrix ( const systems::Context< T > & context, const Frame< T > & frame_F, const Frame< T > & frame_G ) const

Calculates the rotation matrix R_FG relating frame F and frame G.

Parameters
 [in] context The state of the multibody system, which includes the system's generalized positions q. Note: R_FG is a function of q. [in] frame_F The frame F designated in the rigid transform R_FG. [in] frame_G The frame G designated in the rigid transform R_FG.
Return values
 R_FG The RigidTransform relating frame F and frame G.

## ◆ CalcRelativeTransform()

 math::RigidTransform CalcRelativeTransform ( const systems::Context< T > & context, const Frame< T > & frame_F, const Frame< T > & frame_G ) const

Calculates the rigid transform (pose) X_FG relating frame F and frame G.

Parameters
 [in] context The state of the multibody system, which includes the system's generalized positions q. Note: X_FG is a function of q. [in] frame_F The frame F designated in the rigid transform X_FG. [in] frame_G The frame G designated in the rigid transform X_FG.
Return values
 X_FG The RigidTransform relating frame F and frame G.

## ◆ CalcSpatialAccelerationsFromVdot()

 void CalcSpatialAccelerationsFromVdot ( const systems::Context< T > & context, const VectorX< T > & known_vdot, std::vector< SpatialAcceleration< T >> * A_WB_array ) const

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.

Parameters
 [in] context The context containing the state of this model. [in] known_vdot A vector with the generalized accelerations for the full model. [out] 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.
Exceptions
 std::exception if A_WB_array is not of size num_bodies().

 SpatialMomentum CalcSpatialMomentumInWorldAboutPoint ( const systems::Context< T > & context, const Vector3< T > & p_WoP_W ) const

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.

Parameters
 [in] context Contains the state of the model. [in] p_WoP_W Position from Wo (origin of the world frame W) to an arbitrary point P, expressed in the world frame W.
Return values
 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:
  MultibodyPlant<T> plant;
// ... code to load a model ....
const Vector3<T> p_WoScm_W =
plant.CalcCenterOfMassPositionInWorld(context);
const SpatialMomentum<T> L_WScm_W =


 SpatialMomentum CalcSpatialMomentumInWorldAboutPoint ( const systems::Context< T > & context, const std::vector< ModelInstanceIndex > & model_instances, const Vector3< T > & p_WoP_W ) const

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.

Parameters
 [in] context Contains the state of the model. [in] model_instances Set of selected model instances. [in] p_WoP_W Position from Wo (origin of the world frame W) to an arbitrary point P, expressed in the world frame W.
Return values
 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:
  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 =
p_WoScm_W);

Exceptions
 std::exception if model_instances contains an invalid ModelInstanceIndex.

## ◆ CollectRegisteredGeometries()

 geometry::GeometrySet CollectRegisteredGeometries ( const std::vector< const Body< T > * > & bodies ) const

For each of the provided bodies, collects up all geometries that have been registered to that body.

Intended to be used in conjunction with SceneGraph::ExcludeCollisionsWithin() and SceneGraph::ExcludeCollisionsBetween() to filter collisions between the geometries registered to the bodies.

For example:

// 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.ExcludeCollisionsWithin(set);
Note
There is a very specific order of operations:
1. Bodies and geometries must be added to the MultibodyPlant.
2. The MultibodyPlant must be finalized (via Finalize()).
3. Create GeometrySet instances from bodies (via this method).
4. Invoke SceneGraph::ExcludeCollisions*() to filter collisions.
5. Allocate context.

Changing the order will cause exceptions to be thrown.

Exceptions
 std::exception if called pre-finalize.

## ◆ EvalBodyPoseInWorld()

 const math::RigidTransform& EvalBodyPoseInWorld ( const systems::Context< T > & context, const Body< T > & body_B ) const

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

Parameters
 [in] context The context storing the state of the model. [in] body_B The body B for which the pose is requested.
Return values
 X_WB The pose of body frame B in the world frame W.
Exceptions
 std::logic_error if Finalize() was not called on this model or if body_B does not belong to this model.

## ◆ EvalBodySpatialAccelerationInWorld()

 const SpatialAcceleration& EvalBodySpatialAccelerationInWorld ( const systems::Context< T > & context, const Body< T > & body_B ) const

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

Parameters
 [in] context The context storing the state of the model. [in] body_B The body for which spatial acceleration is requested.
Return values
 A_WB_W Body B's spatial acceleration in the world frame W, expressed in W (for point Bo, the body's origin).
Exceptions
 std::logic_error 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()

 const SpatialVelocity& EvalBodySpatialVelocityInWorld ( const systems::Context< T > & context, const Body< T > & body_B ) const

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

Parameters
 [in] context The context storing the state of the model. [in] body_B The body B for which the spatial velocity is requested.
Return values
 V_WB_W Body B's spatial velocity in the world frame W, expressed in W (for point Bo, the body's origin).
Exceptions
 std::logic_error if Finalize() was not called on this model or if body_B does not belong to this model.

## ◆ EvalPointPairPenetrations()

 const std::vector >& EvalPointPairPenetrations ( const systems::Context< T > & context ) const

Evaluates all point pairs of contact for a given state of the model stored in context.

Each entry in the returned vector corresponds to a single point pair corresponding to two interpenetrating bodies A and B. The size of the returned vector corresponds to the total number of contact penetration pairs. If no geometry was registered, the output vector is empty.

Geometry for geometry registration.
PenetrationAsPointPair for further details on the returned data.
Exceptions
 std::exception if called pre-finalize. See Finalize().

## ◆ ExcludeCollisionGeometriesWithCollisionFilterGroupPair()

 void ExcludeCollisionGeometriesWithCollisionFilterGroupPair ( const std::pair< std::string, geometry::GeometrySet > & collision_filter_group_a, const std::pair< std::string, geometry::GeometrySet > & collision_filter_group_b )

Excludes the collision geometries between two given collision filter groups.

Precondition
RegisterAsSourceForSceneGraph() has been called.
Finalize() has not been called.

## ◆ Finalize()

 void Finalize ( )

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. If this plant registered geometry with a SceneGraph, input and output ports to enable communication with that SceneGraph are declared as well.

If geometry has been registered on a SceneGraph instance, that instance must be provided to the Finalize() method so that any geometric implications of the finalization process can be appropriately handled.

is_finalized().
Exceptions
 std::logic_error if the MultibodyPlant has already been finalized.

## ◆ geometry_source_is_registered()

 bool geometry_source_is_registered ( ) const

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() [1/2]

 const systems::InputPort& get_actuation_input_port ( ModelInstanceIndex model_instance ) const

Returns a constant reference to the input port for external actuation for a specific model instance.

This input port is a vector valued port, which can be set with JointActuator::set_actuation_vector().

Precondition
Finalize() was already called on this plant.
Exceptions
 std::exception if called before Finalize(). std::exception if the model instance does not exist.

## ◆ get_actuation_input_port() [2/2]

 const systems::InputPort& get_actuation_input_port ( ) const

Returns a constant reference to the input port for external actuation for the case where only one model instance has actuated dofs.

This input port is a vector valued port, which can be set with JointActuator::set_actuation_vector().

Precondition
Finalize() was already called on this plant.
Exceptions
 std::exception if called before Finalize(), if the model does not contain any actuators, or if multiple model instances have actuated dofs.

## ◆ get_applied_generalized_force_input_port()

 const systems::InputPort& get_applied_generalized_force_input_port ( ) const

Returns a constant reference to the vector-valued input port for applied generalized forces, and the vector will be added directly into tau (see 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).

Exceptions
 std::exception if called before Finalize().

## ◆ get_applied_spatial_force_input_port()

 const systems::InputPort& get_applied_spatial_force_input_port ( ) const

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()

 const Body& get_body ( BodyIndex body_index ) const

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

Exceptions
 std::exception if body_index does not correspond to a body in this model.

## ◆ get_body_poses_output_port()

 const systems::OutputPort& get_body_poses_output_port ( ) const

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:

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.

Exceptions
 std::exception if called pre-finalize.

## ◆ get_body_spatial_accelerations_output_port()

 const systems::OutputPort& get_body_spatial_accelerations_output_port ( ) const

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 in the world frame W with:

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.

Exceptions
 std::exception if called pre-finalize.

## ◆ get_body_spatial_velocities_output_port()

 const systems::OutputPort& get_body_spatial_velocities_output_port ( ) const

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:

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.

Exceptions
 std::exception if called pre-finalize.

## ◆ get_contact_model()

 ContactModel get_contact_model ( ) const

Returns the model used for contact. See documentation for ContactModel.

## ◆ get_contact_penalty_method_time_scale()

 double get_contact_penalty_method_time_scale ( ) const

Returns a time-scale estimate tc based on the requested penetration allowance δ set with set_penetration_allowance().

For the penalty method in use 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 artificially introduced by the penalty method 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()

 const systems::OutputPort& get_contact_results_output_port ( ) const

Returns a constant reference to the port that outputs ContactResults.

Exceptions
 std::exception if called pre-finalize, see Finalize().

## ◆ get_force_element()

 const ForceElement& get_force_element ( ForceElementIndex force_element_index ) const

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

Exceptions
 std::runtime_error when force_element_index does not correspond to a force element in this model.

## ◆ get_frame()

 const Frame& get_frame ( FrameIndex frame_index ) const

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

Exceptions
 std::exception if frame_index does not correspond to a frame in this plant.

## ◆ get_generalized_acceleration_output_port() [1/2]

 const systems::OutputPort& get_generalized_acceleration_output_port ( ) const

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

Precondition
Finalize() was already called on this plant.
Exceptions
 std::exception if called before Finalize().

## ◆ get_generalized_acceleration_output_port() [2/2]

 const systems::OutputPort& get_generalized_acceleration_output_port ( ModelInstanceIndex model_instance ) const

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

Precondition
Finalize() was already called on this plant.
Exceptions
 std::exception if called before Finalize(). std::exception if the model instance does not exist.

## ◆ get_generalized_contact_forces_output_port()

 const systems::OutputPort& get_generalized_contact_forces_output_port ( ModelInstanceIndex model_instance ) const

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

Precondition
Finalize() was already called on this plant.
Exceptions
 std::exception if called before Finalize(). std::exception if the model instance does not exist.

## ◆ get_geometry_poses_output_port()

 const systems::OutputPort& get_geometry_poses_output_port ( ) const

Returns the output port of frames' poses to communicate with a SceneGraph.

## ◆ get_geometry_query_input_port()

 const systems::InputPort& get_geometry_query_input_port ( ) const

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 Geometry of this class's documentation for further details on collision geometry registration and connection with a SceneGraph.

## ◆ get_joint()

 const Joint& get_joint ( JointIndex joint_index ) const

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

Exceptions
 std::runtime_error when joint_index does not correspond to a joint in this model.

## ◆ get_joint_actuator()

 const JointActuator& get_joint_actuator ( JointActuatorIndex actuator_index ) const

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

Exceptions
 std::exception if actuator_index does not correspond to a joint actuator in this tree.

## ◆ get_mutable_joint()

 Joint& get_mutable_joint ( JointIndex joint_index )

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

Exceptions
 std::runtime_error when joint_index does not correspond to a joint in this model.

## ◆ get_mutable_joint_actuator()

 JointActuator& get_mutable_joint_actuator ( JointActuatorIndex actuator_index ) const

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

Exceptions
 std::exception if actuator_index does not correspond to a joint actuator in this tree.

## ◆ get_reaction_forces_output_port()

 const systems::OutputPort& get_reaction_forces_output_port ( ) const

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.

Exceptions
 std::exception if called pre-finalize.

## ◆ get_source_id()

 std::optional get_source_id ( ) const

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() [1/2]

 const systems::OutputPort& get_state_output_port ( ) const

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.
Exceptions
 std::exception if called before Finalize().

## ◆ get_state_output_port() [2/2]

 const systems::OutputPort& get_state_output_port ( ModelInstanceIndex model_instance ) const

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.
Exceptions
 std::exception if called before Finalize(). std::exception if the model instance does not exist.

## ◆ GetAccelerationLowerLimits()

 VectorX GetAccelerationLowerLimits ( ) const

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.

Exceptions
 std::logic_error if called pre-finalize.

## ◆ GetAccelerationUpperLimits()

 VectorX GetAccelerationUpperLimits ( ) const

Upper limit analog of GetAccelerationsLowerLimits(), where any unbounded or unspecified limits will be +infinity.

## ◆ GetActuationFromArray()

 VectorX GetActuationFromArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & u ) const

Returns a vector of actuation values for model_instance from a vector u of actuation values for the entire model.

This method throws an exception if u is not of size MultibodyPlant::num_actuated_dofs().

## ◆ GetBodiesWeldedTo()

 std::vector*> GetBodiesWeldedTo ( const Body< T > & body ) const

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

1. 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:

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.
Exceptions
 std::exception if body is not part of this plant.

## ◆ GetBodyByName() [1/2]

 const Body& GetBodyByName ( const std::string & name ) const

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

Exceptions
 std::logic_error if there is no body with the requested name. std::logic_error if the body name occurs in multiple model instances.
HasBodyNamed() to query if there exists a body in this MultibodyPlant with a given specified name.

## ◆ GetBodyByName() [2/2]

 const Body& GetBodyByName ( const std::string & name, ModelInstanceIndex model_instance ) const

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

Exceptions
 std::logic_error if there is no body with the requested name.
HasBodyNamed() to query if there exists a body in this MultibodyPlant with a given specified name.

## ◆ GetBodyFrameIdIfExists()

 std::optional GetBodyFrameIdIfExists ( BodyIndex body_index ) const

If the body with body_index belongs to the called plant, it returns the geometry::FrameId associated with it.

Otherwise, it returns nullopt.

## ◆ GetBodyFrameIdOrThrow()

 geometry::FrameId GetBodyFrameIdOrThrow ( BodyIndex body_index ) const

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.

Exceptions
 std::exception if the called plant does not have the body indicated by body_index.

## ◆ GetBodyFromFrameId()

 const Body* GetBodyFromFrameId ( geometry::FrameId frame_id ) const

Given a geometry frame identifier, returns a pointer to the body associated with that id (nullptr if there is no such body).

## ◆ GetBodyIndices()

 std::vector GetBodyIndices ( ModelInstanceIndex model_instance ) const

Returns a list of body indices associated with model_instance.

## ◆ GetCollisionGeometriesForBody()

 const std::vector& GetCollisionGeometriesForBody ( const Body< T > & body ) const

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.
RegisterCollisionGeometry(), Finalize()

## ◆ GetDefaultFreeBodyPose()

 const math::RigidTransform& GetDefaultFreeBodyPose ( const Body< T > & body ) const

Gets the default pose of body as set by SetDefaultFreeBodyPose().

Parameters
 [in] body Body whose default pose will be retrieved.

## ◆ GetFloatingBaseBodies()

 std::unordered_set GetFloatingBaseBodies ( ) const

Returns the set of body indexes corresponding to the free (floating) bodies in the model, in no particular order.

Exceptions
 std::exception if called pre-finalize, see Finalize().

## ◆ GetForceElement()

 const ForceElementType& GetForceElement ( ForceElementIndex force_element_index ) const

Returns a constant reference to a force element identified by its unique index in this MultibodyPlant.

If the optional template argument is supplied, then the returned value is downcast to the specified ForceElementType.

Template Parameters
 ForceElementType The specific type of the ForceElement to be retrieved. It must be a subclass of ForceElement.
Exceptions
 std::logic_error if the force element is not of type ForceElementType or if there is no ForceElement with that index.

## ◆ GetFrameByName() [1/2]

 const Frame& GetFrameByName ( const std::string & name ) const

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

Exceptions
 std::logic_error if there is no frame with the requested name. std::logic_error if the frame name occurs in multiple model instances.
HasFrameNamed() to query if there exists a frame in this model with a given specified name.

## ◆ GetFrameByName() [2/2]

 const Frame& GetFrameByName ( const std::string & name, ModelInstanceIndex model_instance ) const

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

Exceptions
 std::logic_error if there is no frame with the requested name. std::runtime_error if model_instance is not valid for this model.
HasFrameNamed() to query if there exists a frame in this model with a given specified name.

## ◆ GetFreeBodyPose()

 math::RigidTransform GetFreeBodyPose ( const systems::Context< T > & context, const Body< T > & body ) const

Gets the pose of a given body in the world frame W.

Note
In general getting the pose of a body in the model would involve solving the kinematics. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ GetJointActuatorByName() [1/2]

 const JointActuator& GetJointActuatorByName ( const std::string & name ) const

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

Exceptions
 std::logic_error if there is no actuator with the requested name. std::logic_error if the actuator name occurs in multiple model instances.
HasJointActuatorNamed() to query if there exists an actuator in this MultibodyPlant with a given specified name.

## ◆ GetJointActuatorByName() [2/2]

 const JointActuator& GetJointActuatorByName ( const std::string & name, ModelInstanceIndex model_instance ) const

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

Exceptions
 std::logic_error if there is no actuator with the requested name. std::exception if model_instance is not valid for this model.
HasJointActuatorNamed() to query if there exists an actuator in this MultibodyPlant with a given specified name.

## ◆ GetJointByName()

 const JointType& GetJointByName ( const std::string & name, std::optional< ModelInstanceIndex > model_instance = std::nullopt ) const

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 Parameters
 JointType The specific type of the Joint to be retrieved. It must be a subclass of Joint.
Exceptions
 std::logic_error if the named joint is not of type JointType or if there is no Joint with that name. std::exception if model_instance is not valid for this model.
HasJointNamed() to query if there exists a joint in this MultibodyPlant with a given specified name.

## ◆ GetJointIndices()

 std::vector GetJointIndices ( ModelInstanceIndex model_instance ) const

Returns a list of joint indices associated with model_instance.

## ◆ GetModelInstanceByName()

 ModelInstanceIndex GetModelInstanceByName ( const std::string & name ) const

Returns the index to the model instance that is uniquely identified by the string name in this MultibodyPlant.

Exceptions
 std::logic_error if there is no instance with the requested name.
HasModelInstanceNamed() to query if there exists an instance in this MultibodyPlant with a given specified name.

## ◆ GetModelInstanceName()

 const std::string& GetModelInstanceName ( ModelInstanceIndex model_instance ) const

Returns the name of a model_instance.

Exceptions
 std::logic_error when model_instance does not correspond to a model in this model.

## ◆ GetMutableJointByName()

 JointType& GetMutableJointByName ( const std::string & name, std::optional< ModelInstanceIndex > model_instance = std::nullopt )

A version of GetJointByName that returns a mutable reference.

GetJointByName.

## ◆ GetMutablePositions() [1/2]

 Eigen::VectorBlock > GetMutablePositions ( systems::Context< T > * context ) const

(Advanced) Returns a mutable vector reference containing the vector of generalized positions (see warning).

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.
Warning
You should use SetPositions() instead of this method unless you are fully aware of the possible interactions with the caching mechanism (see dangerous_get_mutable).
Exceptions
 std::exception if the context is nullptr or if it does not correspond to the context for a multibody model.

## ◆ GetMutablePositions() [2/2]

 Eigen::VectorBlock > GetMutablePositions ( const systems::Context< T > & context, systems::State< T > * state ) const

(Advanced) Returns a mutable vector reference containing the vector of generalized positions (see warning).

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.
Warning
You should use SetPositions() instead of this method unless you are fully aware of the possible interactions with the caching mechanism (see dangerous_get_mutable).
Exceptions
 std::exception if the state is nullptr or if the context does not correspond to the context for a multibody model.
Precondition
state comes from this MultibodyPlant.

## ◆ GetMutablePositionsAndVelocities()

 Eigen::VectorBlock > GetMutablePositionsAndVelocities ( systems::Context< T > * context ) const

(Advanced) Returns a mutable vector containing the vector [q; v] of the model with q the vector of generalized positions and v the vector of generalized velocities (see warning).

Warning
You should use SetPositionsAndVelocities() instead of this method unless you are fully aware of the interactions with the caching mechanism (see dangerous_get_mutable).
Exceptions
 std::exception if the context is nullptr or if it does not correspond to the context for a multibody model.

## ◆ GetMutableVelocities() [1/2]

 Eigen::VectorBlock > GetMutableVelocities ( const systems::Context< T > & context, systems::State< T > * state ) const

(Advanced) Returns a mutable vector reference containing the vector of generalized velocities (see warning).

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.
Warning
You should use SetVelocities() instead of this method unless you are fully aware of the possible interactions with the caching mechanism (see dangerous_get_mutable).
Exceptions
 std::exception if the context is nullptr or the context does not correspond to the context for a multibody model.
Precondition
state comes from this MultibodyPlant.

## ◆ GetMutableVelocities() [2/2]

 Eigen::VectorBlock > GetMutableVelocities ( systems::Context< T > * context ) const

See GetMutableVelocities() method above.

## ◆ GetPositionLowerLimits()

 VectorX GetPositionLowerLimits ( ) const

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.

Exceptions
 std::logic_error if called pre-finalize.

## ◆ GetPositions() [1/2]

 Eigen::VectorBlock > GetPositions ( const systems::Context< T > & context ) const

Returns a const vector reference containing the vector of generalized positions.

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.
Exceptions
 std::exception if the context does not correspond to the context for a multibody model.

## ◆ GetPositions() [2/2]

 VectorX GetPositions ( const systems::Context< T > & context, ModelInstanceIndex model_instance ) const

Returns an vector containing the generalized positions (q) for the given model instance.

Exceptions
 std::exception if the context does not correspond to the context for a multibody model.
Note
returns a dense vector of dimension q.size() associated with model_instance in O(q.size()) time.

## ◆ GetPositionsAndVelocities() [1/2]

 Eigen::VectorBlock > GetPositionsAndVelocities ( const systems::Context< T > & context ) const

Returns a const vector reference containing the vector [q; v] with q the vector of generalized positions and v the vector of generalized velocities.

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.
Exceptions
 std::exception if the context does not correspond to the context for a multibody model.

## ◆ GetPositionsAndVelocities() [2/2]

 VectorX GetPositionsAndVelocities ( const systems::Context< T > & context, ModelInstanceIndex model_instance ) const

Returns the vector [q; v] of the model with q the vector of generalized positions and v the vector of generalized velocities for model instance model_instance.

Exceptions
 std::exception if the context does not correspond to the context for a multibody model or model_instance is invalid.
Note
returns a dense vector of dimension q.size() + v.size() associated with model_instance in O(q.size()) time.

## ◆ GetPositionsFromArray()

 VectorX GetPositionsFromArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & q ) const

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()

 VectorX GetPositionUpperLimits ( ) const

Upper limit analog of GetPositionsLowerLimits(), where any unbounded or unspecified limits will be +infinity.

## ◆ GetRigidBodyByName() [1/2]

 const RigidBody& GetRigidBodyByName ( const std::string & name ) const

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

Exceptions
 std::logic_error if there is no body with the requested name. std::logic_error if the body name occurs in multiple model instances. std::logic_error if the requested body is not a RigidBody.
HasBodyNamed() to query if there exists a body in this model with a given specified name.

## ◆ GetRigidBodyByName() [2/2]

 const RigidBody& GetRigidBodyByName ( const std::string & name, ModelInstanceIndex model_instance ) const

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

Exceptions
 std::logic_error if there is no body with the requested name. std::logic_error if the requested body is not a RigidBody. std::runtime_error if model_instance is not valid for this model.
HasBodyNamed() to query if there exists a body in this model with a given specified name.

## ◆ GetTopologyGraphvizString()

 std::string GetTopologyGraphvizString ( ) const

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()

 const Body& GetUniqueFreeBaseBodyOrThrow ( ModelInstanceIndex model_instance ) const

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.

Exceptions
 std::exception if called pre-finalize. std::exception if model_instance is not valid. std::exception if HasUniqueFreeBaseBody(model_instance) == false.

## ◆ GetVelocities() [1/2]

 Eigen::VectorBlock > GetVelocities ( const systems::Context< T > & context ) const

Returns a const vector reference containing the generalized velocities.

Note
This method returns a reference to existing data, exhibits constant i.e., O(1) time complexity, and runs very quickly.

## ◆ GetVelocities() [2/2]

 VectorX GetVelocities ( const systems::Context< T > & context, ModelInstanceIndex model_instance ) const

Returns a vector containing the generalized velocities (v) for the given model instance.

Exceptions
 std::exception if the context does not correspond to the context for a multibody model.
Note
returns a dense vector of dimension v.size() associated with model_instance in O(v.size()) time.

## ◆ GetVelocitiesFromArray()

 VectorX GetVelocitiesFromArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & v ) const

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()

 VectorX GetVelocityLowerLimits ( ) const

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.

Exceptions
 std::logic_error if called pre-finalize.

## ◆ GetVelocityUpperLimits()

 VectorX GetVelocityUpperLimits ( ) const

Upper limit analog of GetVelocitysLowerLimits(), where any unbounded or unspecified limits will be +infinity.

## ◆ GetVisualGeometriesForBody()

 const std::vector& GetVisualGeometriesForBody ( const Body< T > & body ) const

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.
RegisterVisualGeometry(), Finalize()

## ◆ gravity_field()

 const UniformGravityFieldElement& gravity_field ( ) const

An accessor to the current gravity field.

## ◆ HasBodyNamed() [1/2]

 bool HasBodyNamed ( const std::string & name ) const
Returns
true if a body named name was added to the MultibodyPlant.
Exceptions
 std::logic_error if the body name occurs in multiple model instances.

## ◆ HasBodyNamed() [2/2]

 bool HasBodyNamed ( const std::string & name, ModelInstanceIndex model_instance ) const
Returns
true if a body named name was added to the MultibodyPlant in model_instance.
Exceptions
 std::exception if model_instance is not valid for this model.

## ◆ HasFrameNamed() [1/2]

 bool HasFrameNamed ( const std::string & name ) const
Returns
true if a frame named name was added to the model.
Exceptions
 std::logic_error if the frame name occurs in multiple model instances.

## ◆ HasFrameNamed() [2/2]

 bool HasFrameNamed ( const std::string & name, ModelInstanceIndex model_instance ) const
Returns
true if a frame named name was added to model_instance.
Exceptions
 std::exception if model_instance is not valid for this model.

## ◆ HasJointActuatorNamed() [1/2]

 bool HasJointActuatorNamed ( const std::string & name ) const
Returns
true if an actuator named name was added to this model.
Exceptions
 std::logic_error if the actuator name occurs in multiple model instances.

## ◆ HasJointActuatorNamed() [2/2]

 bool HasJointActuatorNamed ( const std::string & name, ModelInstanceIndex model_instance ) const
Returns
true if an actuator named name was added to model_instance.
Exceptions
 std::exception if model_instance is not valid for this model.

## ◆ HasJointNamed() [1/2]

 bool HasJointNamed ( const std::string & name ) const
Returns
true if a joint named name was added to this model.
Exceptions
 std::logic_error if the joint name occurs in multiple model instances.

## ◆ HasJointNamed() [2/2]

 bool HasJointNamed ( const std::string & name, ModelInstanceIndex model_instance ) const
Returns
true if a joint named name was added to model_instance.
Exceptions
 std::exception if model_instance is not valid for this model.

## ◆ HasModelInstanceNamed()

 bool HasModelInstanceNamed ( const std::string & name ) const
Returns
true if a model instance named name was added to this model.

## ◆ HasUniqueFreeBaseBody()

 bool HasUniqueFreeBaseBody ( ModelInstanceIndex model_instance ) const

Return true if there exists a unique base body in the model given by model_instance and that unique base body is free.

Exceptions
 std::exception if called pre-finalize. std::exception if model_instance is not valid.

## ◆ is_finalized()

 bool is_finalized ( ) const

Returns true if this MultibodyPlant was finalized with a call to Finalize().

Finalize().

## ◆ IsAnchored()

 bool IsAnchored ( const Body< T > & body ) const

Returns true if body is anchored (i.e.

the kinematic path between body and the world only contains weld joints.)

Exceptions
 std::exception if called pre-finalize.

## ◆ MakeActuationMatrix()

 MatrixX MakeActuationMatrix ( ) const

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_actuators() and nv equal to num_velocities().

The vector u of actuation values is of size num_actuators(). For a given JointActuator, u[JointActuator::index()] stores the value for the external actuation corresponding to that actuator. tau_u on the other hand is indexed by generalized velocity indexes 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.

## ◆ MakeActuatorSelectorMatrix() [1/2]

 MatrixX MakeActuatorSelectorMatrix ( const std::vector< JointActuatorIndex > & user_to_actuator_index_map ) const

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 full vector of actuation values u is ordered by JointActuatorIndex.

## ◆ MakeActuatorSelectorMatrix() [2/2]

 MatrixX MakeActuatorSelectorMatrix ( const std::vector< JointIndex > & user_to_joint_index_map ) const

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 (ordered by JointActuatorIndex) 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.

Exceptions
 std::logic_error if any of the joints in user_to_joint_index_map does not have an actuator.

## ◆ MakeStateSelectorMatrix()

 MatrixX MakeStateSelectorMatrix ( const std::vector< JointIndex > & user_to_joint_index_map ) const

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.

Exceptions
 std::logic_error if there are repeated indexes in user_to_joint_index_map.

## ◆ MapQDotToVelocity()

 void MapQDotToVelocity ( const systems::Context< T > & context, const Eigen::Ref< const VectorX< T >> & qdot, EigenPtr< VectorX< T >> v ) const

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.

Parameters
 [in] context The context containing the state of the model. [in] qdot A vector containing the time derivatives of the generalized positions. This method aborts if qdot is not of size num_positions(). [out] 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().
MapVelocityToQDot()
Mobilizer::MapQDotToVelocity()

## ◆ MapVelocityToQDot()

 void MapVelocityToQDot ( const systems::Context< T > & context, const Eigen::Ref< const VectorX< T >> & v, EigenPtr< VectorX< T >> qdot ) const

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.

Parameters
 [in] context The context containing the state of the model. [in] v A vector of of generalized velocities for this model. This method aborts if v is not of size num_velocities(). [out] 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().
MapQDotToVelocity()
Mobilizer::MapVelocityToQDot()

## ◆ mutable_gravity_field()

 UniformGravityFieldElement& mutable_gravity_field ( )

A mutable accessor to the current gravity field.

## ◆ num_actuated_dofs() [1/2]

 int num_actuated_dofs ( ) const

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() [2/2]

 int num_actuated_dofs ( ModelInstanceIndex model_instance ) const

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().

## ◆ num_actuators()

 int num_actuators ( ) const

Returns the number of joint actuators in the model.

## ◆ num_bodies()

 int num_bodies ( ) const

Returns the number of bodies in the model, including the "world" body, which is always part of the model.

## ◆ num_collision_geometries()

 int num_collision_geometries ( ) const

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_force_elements()

 int num_force_elements ( ) const

Returns the number of ForceElement objects.

## ◆ num_frames()

 int num_frames ( ) const

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()

 int num_joints ( ) const

Returns the number of joints in the model.

## ◆ num_model_instances()

 int num_model_instances ( ) const

Returns the number of model instances in the model.

## ◆ num_multibody_states() [1/2]

 int num_multibody_states ( ) const

Returns the size of the multibody system state vector x = [q v].

This will be num_positions() plus num_velocities().

## ◆ num_multibody_states() [2/2]

 int num_multibody_states ( ModelInstanceIndex model_instance ) const

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).

## ◆ num_positions() [1/2]

 int num_positions ( ) const

Returns the size of the generalized position vector q for this model.

## ◆ num_positions() [2/2]

 int num_positions ( ModelInstanceIndex model_instance ) const

Returns the size of the generalized position vector qᵢ for model instance i.

## ◆ num_velocities() [1/2]

 int num_velocities ( ) const

Returns the size of the generalized velocity vector v for this model.

## ◆ num_velocities() [2/2]

 int num_velocities ( ModelInstanceIndex model_instance ) const

Returns the size of the generalized velocity vector vᵢ for model instance i.

## ◆ num_visual_geometries()

 int num_visual_geometries ( ) const

Returns the number of geometries registered for visualization.

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.

## ◆ operator=() [1/2]

 MultibodyPlant& operator= ( const MultibodyPlant< T > & )
delete

## ◆ operator=() [2/2]

 MultibodyPlant& operator= ( MultibodyPlant< T > && )
delete

## ◆ RegisterAsSourceForSceneGraph()

 geometry::SourceId RegisterAsSourceForSceneGraph ( geometry::SceneGraph< T > * scene_graph )

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.

Parameters
 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().
Exceptions
 std::exception if called post-finalize. std::exception if scene_graph is the nullptr. std::exception if called more than once.

## ◆ RegisterCollisionGeometry() [1/2]

 geometry::GeometryId RegisterCollisionGeometry ( const Body< T > & body, const math::RigidTransform< double > & X_BG, const geometry::Shape & shape, const std::string & name, geometry::ProximityProperties properties )

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.

Parameters
 [in] body The body for which geometry is being registered. [in] X_BG The fixed pose of the geometry frame G in the body frame B. [in] shape The geometry::Shape used for visualization. E.g.: geometry::Sphere, geometry::Cylinder, etc. [in] properties The proximity properties associated with the collision geometry. They must include the (material, coulomb_friction) property of type CoulombFriction.
Exceptions
 std::exception if called post-finalize or if the properties are missing the coulomb friction property (or if it is of the wrong type).

## ◆ RegisterCollisionGeometry() [2/2]

 geometry::GeometryId RegisterCollisionGeometry ( const Body< T > & body, const math::RigidTransform< double > & X_BG, const geometry::Shape & shape, const std::string & name, const CoulombFriction< double > & coulomb_friction )

Overload which specifies a single property: coulomb_friction.

## ◆ RegisterVisualGeometry() [1/3]

 geometry::GeometryId RegisterVisualGeometry ( const Body< T > & body, const math::RigidTransform< double > & X_BG, const geometry::Shape & shape, const std::string & name, const geometry::IllustrationProperties & properties )

Registers geometry in a SceneGraph with a given geometry::Shape to be used for visualization of a given body.

Note
Currently, the visual geometry will also be assigned a perception role. Its render label's value will be equal to the body's index and its perception color will be the same as its illustration color (defaulting to gray if no color is provided). This behavior will change in the near future and code that directly relies on this behavior will break.
Parameters
 [in] body The body for which geometry is being registered. [in] X_BG The fixed pose of the geometry frame G in the body frame B. [in] shape The geometry::Shape used for visualization. E.g.: geometry::Sphere, geometry::Cylinder, etc. [in] name The name for the geometry. It must satisfy the requirements defined in drake::geometry::GeometryInstance. [in] properties The illustration properties for this geometry.
Exceptions
 std::exception if called post-finalize. std::exception if scene_graph does not correspond to the same instance with which RegisterAsSourceForSceneGraph() was called.
Returns
the id for the registered geometry.

## ◆ RegisterVisualGeometry() [2/3]

 geometry::GeometryId RegisterVisualGeometry ( const Body< T > & body, const math::RigidTransform< double > & X_BG, const geometry::Shape & shape, const std::string & name, const Vector4< double > & diffuse_color )

Overload for visual geometry registration; it converts the diffuse_color (RGBA with values in the range [0, 1]) into a geometry::DrakeVisualizer-compatible set of geometry::IllustrationProperties.

## ◆ RegisterVisualGeometry() [3/3]

 geometry::GeometryId RegisterVisualGeometry ( const Body< T > & body, const math::RigidTransform< double > & X_BG, const geometry::Shape & shape, const std::string & name )

Overload for visual geometry registration; it relies on the downstream geometry::IllustrationProperties consumer to provide default parameter values (see Geometry Queries and Roles for details).

## ◆ set_contact_model()

 void set_contact_model ( ContactModel model )

Sets the contact model to be used by this MultibodyPlant, see ContactModel for available options.

The default contact model is ContactModel::kPointContactOnly.

Exceptions
 std::exception iff called post-finalize.

## ◆ set_penetration_allowance()

 void set_penetration_allowance ( double penetration_allowance = 0.001 )

Sets the penetration allowance used to estimate the coefficients in the penalty method used to impose non-penetration among bodies.

Refer to the section Contact by penalty method for further details.

Exceptions
 std::logic_error if penetration_allowance is not positive.

## ◆ set_stiction_tolerance()

 void set_stiction_tolerance ( double v_stiction = 0.001 )

### 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 Choice of Time Advancement Strategy). See Continuous Approximation of Coulomb 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 Continuous Approximation of Coulomb.

Exceptions
 std::exception if v_stiction is non-positive.

## ◆ SetActuationInArray()

 void SetActuationInArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & u_instance, EigenPtr< VectorX< T >> u ) const

Given the actuation values u_instance for all actuators in model_instance, this method sets the actuation vector u for the entire model to which this actuator belongs to.

This method throws an exception if the size of u_instance is not equal to the number of degrees of freedom of all of the actuated joints in model_instance.

Parameters
 [in] u_instance Actuation values for the actuators. It must be of size equal to the number of degrees of freedom of all of the actuated joints in model_instance. [out] u The vector containing the actuation values for the entire model.

## ◆ SetDefaultFreeBodyPose()

 void SetDefaultFreeBodyPose ( const Body< T > & body, const math::RigidTransform< double > & X_WB )

Sets the default pose of body.

If body.is_floating() is true, this will affect subsequent calls to SetDefaultState(); otherwise, this value is effectively ignored.

Parameters
 [in] body Body whose default pose will be set. [in] X_WB Default pose of the body.

## ◆ SetDefaultState()

 void SetDefaultState ( const systems::Context< T > & context, systems::State< T > * state ) const
override

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.

Exceptions
 std::exception if called pre-finalize. See Finalize().

## ◆ SetFreeBodyPose() [1/2]

 void SetFreeBodyPose ( systems::Context< T > * context, const Body< T > & body, const math::RigidTransform< T > & X_WB ) const

Sets context to store the pose X_WB of a given body B in the world frame W.

Note
In general setting the pose and/or velocity of a body in the model would involve a complex inverse kinematics problem. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ SetFreeBodyPose() [2/2]

 void SetFreeBodyPose ( const systems::Context< T > & context, systems::State< T > * state, const Body< T > & body, const math::RigidTransform< T > & X_WB ) const

Sets state to store the pose X_WB of a given body B in the world frame W, for a given context of this model.

Note
In general setting the pose and/or velocity of a body in the model would involve a complex inverse kinematics problem. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.
Precondition
state comes from this MultibodyPlant.

## ◆ SetFreeBodyPoseInAnchoredFrame()

 void SetFreeBodyPoseInAnchoredFrame ( systems::Context< T > * context, const Frame< T > & frame_F, const Body< T > & body, const math::RigidTransform< T > & X_FB ) const

Updates context to store the pose X_FB of a given body B in a frame F.

Frame F must be anchored, meaning that it is either directly welded to the world frame W or, more generally, that there is a kinematic path between frame F and the world frame W that only includes weld joints.

Exceptions
 std::logic_error if called pre-finalize. std::logic_error if frame F is not anchored to the world.

## ◆ SetFreeBodyPoseInWorldFrame()

 void SetFreeBodyPoseInWorldFrame ( systems::Context< T > * context, const Body< T > & body, const math::RigidTransform< T > & X_WB ) const

Sets context to store the pose X_WB of a given body B in the world frame W.

Parameters
 [in] context The context to store the pose X_WB of body_B. [in] body_B The body B corresponding to the pose X_WB to be stored in context.
Return values
 X_WB The pose of body frame B in the world frame W.
Note
In general setting the pose and/or velocity of a body in the model would involve a complex inverse kinematics problem. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::logic_error if called pre-finalize.

## ◆ SetFreeBodyRandomPositionDistribution()

 void SetFreeBodyRandomPositionDistribution ( const Body< T > & body, const Vector3< symbolic::Expression > & position )

Sets the distribution used by SetRandomState() to populate the free body's x-y-z position with respect to World.

Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ SetFreeBodyRandomRotationDistribution()

 void SetFreeBodyRandomRotationDistribution ( const Body< T > & body, const Eigen::Quaternion< symbolic::Expression > & rotation )

Sets the distribution used by SetRandomState() to populate the free body's rotation with respect to World.

Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ SetFreeBodyRandomRotationDistributionToUniform()

 void SetFreeBodyRandomRotationDistributionToUniform ( const Body< T > & body )

Sets the distribution used by SetRandomState() to populate the free body's rotation with respect to World using uniformly random rotations.

Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ SetFreeBodySpatialVelocity() [1/2]

 void SetFreeBodySpatialVelocity ( systems::Context< T > * context, const Body< T > & body, const SpatialVelocity< T > & V_WB ) const

Sets context to store the spatial velocity V_WB of a given body B in the world frame W.

Note
In general setting the pose and/or velocity of a body in the model would involve a complex inverse kinematics problem. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.

## ◆ SetFreeBodySpatialVelocity() [2/2]

 void SetFreeBodySpatialVelocity ( const systems::Context< T > & context, systems::State< T > * state, const Body< T > & body, const SpatialVelocity< T > & V_WB ) const

Sets state to store the spatial velocity V_WB of a given body B in the world frame W, for a given context of this model.

Note
In general setting the pose and/or velocity of a body in the model would involve a complex inverse kinematics problem. This method allows us to simplify this process when we know the body is free in space.
Exceptions
 std::exception if body is not a free body in the model. std::exception if called pre-finalize.
Precondition
state comes from this MultibodyPlant.

## ◆ SetPositions() [1/3]

 void SetPositions ( systems::Context< T > * context, const VectorX< T > & q ) const

Sets all generalized positions from the given vector.

Exceptions
 std::exception if the context is nullptr, if the context does not correspond to the context for a multibody model, or if the length of q is not equal to num_positions().

## ◆ SetPositions() [2/3]

 void SetPositions ( systems::Context< T > * context, ModelInstanceIndex model_instance, const VectorX< T > & q_instance ) const

Sets the positions for a particular model instance from the given vector.

Exceptions
 std::exception if the context is nullptr, if the context does not correspond to the context for a multibody model, if the model instance index is invalid, or if the length of q_instance is not equal to num_positions(model_instance).

## ◆ SetPositions() [3/3]

 void SetPositions ( const systems::Context< T > & context, systems::State< T > * state, ModelInstanceIndex model_instance, const VectorX< T > & q_instance ) const

Sets the positions for a particular model instance from the given vector.

Exceptions
 std::exception if the state is nullptr, if the context does not correspond to the context for a multibody model, if the model instance index is invalid, or if the length of q_instance is not equal to num_positions(model_instance).
Precondition
state comes from this MultibodyPlant.

## ◆ SetPositionsAndVelocities() [1/2]

 void SetPositionsAndVelocities ( systems::Context< T > * context, const VectorX< T > & q_v ) const

Sets all generalized positions and velocities from the given vector [q; v].

Exceptions
 std::exception if the context is nullptr, if the 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() [2/2]

 void SetPositionsAndVelocities ( systems::Context< T > * context, ModelInstanceIndex model_instance, const VectorX< T > & q_v ) const

Sets generalized positions and velocities from the given vector [q; v] for the specified model instance.

Exceptions
 std::exception if the context is nullptr, if the 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()

 void SetPositionsInArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & q_instance, EigenPtr< VectorX< T >> q ) const

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).

## ◆ SetRandomState()

 void SetRandomState ( const systems::Context< T > & context, systems::State< T > * state, RandomGenerator * generator ) const
override

Assigns random values to all elements of the state, by drawing samples independently for each joint/free body (coming soon: and then solving a mathematical program to "project" these samples onto the registered system constraints).

Stochastic Systems

## ◆ SetVelocities() [1/3]

 void SetVelocities ( systems::Context< T > * context, const VectorX< T > & v ) const

Sets all generalized velocities from the given vector.

Exceptions
 std::exception 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() [2/3]

 void SetVelocities ( const systems::Context< T > & context, systems::State< T > * state, ModelInstanceIndex model_instance, const VectorX< T > & v_instance ) const

Sets the generalized velocities for a particular model instance from the given vector.

Exceptions
 std::exception if the context is nullptr, if the 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).
Precondition
state comes from this MultibodyPlant.

## ◆ SetVelocities() [3/3]

 void SetVelocities ( systems::Context< T > * context, ModelInstanceIndex model_instance, const VectorX< T > & v_instance ) const

Sets the generalized velocities for a particular model instance from the given vector.

Exceptions
 std::exception if the context is nullptr, if the 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()

 void SetVelocitiesInArray ( ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> & v_instance, EigenPtr< VectorX< T >> v ) const

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()

 double time_step ( ) const

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().

MultibodyPlant::MultibodyPlant(double)

## ◆ WeldFrames()

 const WeldJoint& WeldFrames ( const Frame< T > & A, const Frame< T > & B, const math::RigidTransform< double > & X_AB = math::RigidTransform< double >::Identity() )

Welds frames A and B with relative pose X_AB.

That is, the pose of frame B in frame A is fixed, with value X_AB. The call to this method creates and adds a new WeldJoint to the model. The new WeldJoint is named as: A.name() + "_welds_to_" + B.name().

Returns
a constant reference to the WeldJoint welding frames A and B.

## ◆ world_body()

 const RigidBody& world_body ( ) const

Returns a constant reference to the world body.

## ◆ world_frame()

 const BodyFrame& world_frame ( ) const

Returns a constant reference to the world frame.

## Friends And Related Function Documentation

 AddMultibodyPlantSceneGraphResult< T > AddMultibodyPlantSceneGraph ( systems::DiagramBuilder< T > * builder, double time_step, std::unique_ptr< geometry::SceneGraph< T >> scene_graph = nullptr )
related

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
Parameters
 [in,out] builder Builder to add to. [in] 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. [in] 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.

 AddMultibodyPlantSceneGraphResult< T > AddMultibodyPlantSceneGraph ( systems::DiagramBuilder< T > * builder, std::unique_ptr< MultibodyPlant< T >> plant, std::unique_ptr< geometry::SceneGraph< T >> scene_graph = nullptr )
related

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

Note
Parameters
 [in,out] builder Builder to add to. [in] plant Plant to be added to the builder. [in] 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.

## ◆ MultibodyPlant

 friend class MultibodyPlant
friend

## ◆ MultibodyPlantTester

 friend class MultibodyPlantTester
friend

The documentation for this class was generated from the following file: