Drake

MultibodyTree provides a representation for a physical system consisting of a collection of interconnected rigid and deformable bodies. More...
#include <drake/multibody/tree/rigid_body.h>
Public Member Functions  
MultibodyTree ()  
Creates a MultibodyTree containing only a world body. More...  
int  num_frames () const 
Returns the number of Frame objects in the MultibodyTree. More...  
int  num_bodies () const 
Returns the number of bodies in the MultibodyTree including the world body. More...  
int  num_joints () const 
Returns the number of joints added with AddJoint() to the MultibodyTree. More...  
int  num_actuators () const 
Returns the number of actuators in the model. More...  
int  num_mobilizers () const 
Returns the number of mobilizers in the MultibodyTree. More...  
int  num_force_elements () const 
Returns the number of ForceElement objects in the MultibodyTree. More...  
int  num_model_instances () const 
Returns the number of model instances in the MultibodyTree. More...  
int  num_positions () const 
Returns the number of generalized positions of the model. More...  
int  num_positions (ModelInstanceIndex model_instance) const 
Returns the number of generalized positions in a specific model instance. More...  
int  num_velocities () const 
Returns the number of generalized velocities of the model. More...  
int  num_velocities (ModelInstanceIndex model_instance) const 
Returns the number of generalized velocities in a specific model instance. More...  
int  num_states () const 
Returns the total size of the state vector in the model. More...  
int  num_states (ModelInstanceIndex model_instance) const 
Returns the total size of the state vector in a specific model instance. More...  
int  num_actuated_dofs () const 
Returns the total number of Joint degrees of freedom actuated by the set of JointActuator elements added to this model. More...  
int  num_actuated_dofs (ModelInstanceIndex model_instance) const 
Returns the total number of Joint degrees of freedom actuated by the set of JointActuator elements added to a specific model instance. More...  
int  tree_height () const 
Returns the height of the tree data structure of this MultibodyTree. 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...  
const Body< T > &  get_body (BodyIndex body_index) const 
Returns a constant reference to the body with unique index body_index . More...  
const Joint< T > &  get_joint (JointIndex joint_index) const 
Returns a constant reference to the joint with unique index joint_index . 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...  
const Frame< T > &  get_frame (FrameIndex frame_index) const 
Returns a constant reference to the frame with unique index frame_index . More...  
const Mobilizer< T > &  get_mobilizer (MobilizerIndex mobilizer_index) const 
Returns a constant reference to the mobilizer with unique index mobilizer_index . More...  
const std::string &  GetModelInstanceName (ModelInstanceIndex model_instance) const 
Returns the name of a model_instance. More...  
bool  topology_is_valid () const 
Returns true if this MultibodyTree was finalized with Finalize() after all multibody elements were added, and false otherwise. More...  
const MultibodyTreeTopology &  get_topology () const 
Returns the topology information for this multibody tree. More...  
void  Finalize () 
This method must be called after all elements in the tree (joints, bodies, force elements, constraints) were added and before any computations are performed. More...  
std::unique_ptr< systems::LeafContext< T > >  CreateDefaultContext () const 
(Advanced) Allocates a new context for this MultibodyTree uniquely identifying the state of the multibody system. More...  
void  SetDefaultContext (systems::Context< T > *context) const 
Sets default values in the context. More...  
void  SetDefaultState (const systems::Context< T > &context, systems::State< T > *state) const 
Sets default values in the state . More...  
Eigen::VectorBlock< const VectorX< T > >  GetPositionsAndVelocities (const systems::Context< T > &context) const 
Returns a const Eigen vector reference containing the vector [q; v] of the model 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 a Eigen vector containing the multibody state x = [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 
Returns a mutable Eigen vector containing the vector [q; v] of the model with q the vector of generalized positions and v the vector of generalized velocities. More...  
void  SetPositionsAndVelocities (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &instance_state, systems::Context< T > *context) const 
Sets context to store the vector [q; v] with q the vector of generalized positions and v the vector of generalized velocities for model instance model_instance . More...  
void  SetFreeBodyPoseOrThrow (const Body< T > &body, const Isometry3< T > &X_WB, systems::Context< T > *context) const 
Sets context to store the pose X_WB of a given body B in the world frame W. More...  
void  SetFreeBodySpatialVelocityOrThrow (const Body< T > &body, const SpatialVelocity< T > &V_WB, systems::Context< T > *context) const 
Sets context to store the spatial velocity V_WB of a given body B in the world frame W. More...  
void  SetFreeBodyPoseOrThrow (const Body< T > &body, const Isometry3< T > &X_WB, const systems::Context< T > &context, systems::State< T > *state) const 
Sets sate 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  SetFreeBodySpatialVelocityOrThrow (const Body< T > &body, const SpatialVelocity< T > &V_WB, const systems::Context< T > &context, systems::State< T > *state) 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...  
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 >  MakeStateSelectorMatrixFromJointNames (const std::vector< std::string > &selected_joints) const 
Alternative signature to build a state selector matrix from a std::vector of joint names. 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< 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...  
std::unique_ptr< MultibodyTree< T > >  Clone () const 
Creates a deep copy of this MultibodyTree templated on the same scalar type T as this tree. More...  
std::unique_ptr< MultibodyTree< AutoDiffXd > >  ToAutoDiffXd () const 
Creates a deep copy of this MultibodyTree templated on AutoDiffXd. More...  
template<typename ToScalar >  
std::unique_ptr< MultibodyTree< ToScalar > >  CloneToScalar () const 
Creates a deep copy of this MultibodyTree templated on the scalar type ToScalar . More...  
const PositionKinematicsCache< T > &  EvalPositionKinematics (const systems::Context< T > &context) const 
Evaluates position kinematics cached in context. More...  
const VelocityKinematicsCache< T > &  EvalVelocityKinematics (const systems::Context< T > &context) const 
Evaluates velocity kinematics cached in context. More...  
void  set_tree_system (MultibodyTreeSystem< T > *tree_system) 
(Internal use only) Informs the MultibodyTree how to access its resources within a Context. More...  
void  CalcAcrossNodeGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, std::vector< Vector6< T >> *H_PB_W_cache) const 
(Internal) Computes the cache entry associated with the geometric Jacobian H_PB_W for each node. More...  
Does not allow copy, move, or assignment  
MultibodyTree (const MultibodyTree &)=delete  
MultibodyTree &  operator= (const MultibodyTree &)=delete 
MultibodyTree (MultibodyTree &&)=delete  
MultibodyTree &  operator= (MultibodyTree &&)=delete 
Methods to add new MultibodyTree elements.  
To create a MultibodyTree users will add multibody elements like bodies, joints, force elements, constraints, etc, using one of these methods. Once a user is done adding multibody elements, the Finalize() method must be called before invoking any MultibodyTree method. See Finalize() for details.  
template<template< typename Scalar > class BodyType>  
const BodyType< T > &  AddBody (std::unique_ptr< BodyType< T >> body) 
Takes ownership of body and adds it to this MultibodyTree. More...  
template<template< typename Scalar > class BodyType, typename... Args>  
const BodyType< T > &  AddBody (Args &&... args) 
Constructs a new body with type BodyType with the given args , and adds it to this MultibodyTree, which retains ownership. 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, model instance, 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, model instance, and spatial inertia. More...  
template<template< typename Scalar > class FrameType>  
const FrameType< T > &  AddFrame (std::unique_ptr< FrameType< T >> frame) 
Takes ownership of frame and adds it to this MultibodyTree. More...  
template<template< typename Scalar > class FrameType, typename... Args>  
const FrameType< T > &  AddFrame (Args &&... args) 
Constructs a new frame with type FrameType with the given args , and adds it to this MultibodyTree, which retains ownership. More...  
template<template< typename Scalar > class MobilizerType>  
const MobilizerType< T > &  AddMobilizer (std::unique_ptr< MobilizerType< T >> mobilizer) 
Takes ownership of mobilizer and adds it to this MultibodyTree. More...  
template<template< typename Scalar > class MobilizerType, typename... Args>  
const MobilizerType< T > &  AddMobilizer (Args &&... args) 
Constructs a new mobilizer with type MobilizerType with the given args , and adds it to this MultibodyTree, which retains ownership. More...  
template<template< typename Scalar > class ForceElementType>  
const ForceElementType< T > &  AddForceElement (std::unique_ptr< ForceElementType< T >> force_element) 
Creates and adds to this MultibodyTree (which retains ownership) a new ForceElement member with the specific type ForceElementType . 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 MultibodyTree. More...  
template<template< typename Scalar > class ForceElementType, typename... Args>  
std::enable_if< std::is_same< ForceElementType< T >, UniformGravityFieldElement< T > >::value, const ForceElementType< T > & >::type  AddForceElement (Args &&... args) 
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 the frames specified by the joint. More...  
template<template< typename > class JointType, typename... Args>  
const JointType< T > &  AddJoint (const std::string &name, const Body< T > &parent, const optional< Isometry3< double >> &X_PF, const Body< T > &child, const optional< Isometry3< double >> &X_BM, Args &&... args) 
This method helps to create a Joint of type JointType between two bodies. More...  
const JointActuator< T > &  AddJointActuator (const std::string &name, const Joint< T > &joint) 
Creates and adds a JointActuator model for an actuator acting on a given joint . More...  
ModelInstanceIndex  AddModelInstance (const std::string &name) 
Creates a new model instance. More...  
Querying for multibody elements by name  
These methods allow a user to query whether a given multibody element is part of These queries can be performed at any time during the lifetime of a MultibodyTree model, i.e. there is no restriction on whether they must be called before or after Finalize(). That is, these queries can be performed while new multibody elements are being added to the model.  
bool  HasBodyNamed (const std::string &name) const 
bool  HasBodyNamed (const std::string &name, ModelInstanceIndex model_instance) const 
bool  HasFrameNamed (const std::string &name) const 
bool  HasFrameNamed (const std::string &name, ModelInstanceIndex model_instance) const 
bool  HasJointNamed (const std::string &name) const 
bool  HasJointNamed (const std::string &name, ModelInstanceIndex model_instance) const 
bool  HasJointActuatorNamed (const std::string &name) const 
bool  HasJointActuatorNamed (const std::string &name, ModelInstanceIndex model_instance) const 
bool  HasModelInstanceNamed (const std::string &name) const 
Retrieving multibody elements by name  
These methods allow a user to retrieve a reference to a multibody element by its name. A std::logic_error is thrown if there is no element with the requested name. These queries can be performed at any time during the lifetime of a MultibodyTree model, i.e. there is no restriction on whether they must be called before or after Finalize(). This implies that these queries can be performed while new multibody elements are being added to the model. 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.  
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 model. 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 in model_instance . More...  
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...  
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...  
const Joint< T > &  GetJointByName (const std::string &name) const 
Returns a constant reference to a joint that is identified by the string name in this model. More...  
const Joint< T > &  GetJointByName (const std::string &name, ModelInstanceIndex model_instance) const 
Returns a constant reference to the joint that is uniquely identified by the string name in model_instance . More...  
template<template< typename > class JointType>  
const JointType< T > &  GetJointByName (const std::string &name) const 
A templated version of GetJointByName() to return a constant reference of the specified type JointType in place of the base Joint class. More...  
template<template< typename > class JointType>  
const JointType< T > &  GetJointByName (const std::string &name, ModelInstanceIndex model_instance) const 
A templated version of GetJointByName() to return a constant reference of the specified type JointType in place of the base Joint class. More...  
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 model. 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 in model_instance . More...  
ModelInstanceIndex  GetModelInstanceByName (const std::string &name) const 
Returns the index to the model instance that is uniquely identified by the string name in this model. More...  
Model instance accessors  
Many functions on MultibodyTree expect vectors of tree state or joint actuator inputs which encompass the entire tree. Methods in this section are convenience accessors for the portion of those vectors which apply to a single model instance only.  
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 MultibodyTree 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 MultibodyTree 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_array) const 
Returns a vector of generalized velocities for model_instance from a vector v of generalized velocities for the entire MultibodyTree model. More...  
void  SetVelocitiesInArray (ModelInstanceIndex model_instance, const Eigen::Ref< const VectorX< T >> &model_v, EigenPtr< VectorX< T >> v_array) const 
Sets the vector of generalized velocities for model_instance in v using v_instance , leaving all other elements in the array untouched. More...  
Kinematic computations  
Kinematics computations are concerned with the motion of bodies in the model without regard to their mass or the forces and moments that cause the motion. Methods in this category include the computation of poses and spatial velocities.  
void  CalcAllBodyPosesInWorld (const systems::Context< T > &context, std::vector< Isometry3< T >> *X_WB) const 
Computes the world pose X_WB(q) of each body B in the model as a function of the generalized positions q stored in context . More...  
void  CalcAllBodySpatialVelocitiesInWorld (const systems::Context< T > &context, std::vector< SpatialVelocity< T >> *V_WB) const 
Computes the spatial velocity V_WB(q, v) of each body B in the model, measured and expressed in the world frame W. More...  
Isometry3< T >  CalcRelativeTransform (const systems::Context< T > &context, const Frame< T > &frame_A, const Frame< T > &frame_B) const 
Computes the relative transform X_AB(q) from a frame B to a frame A, as a function of the generalized positions q of the model. 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...  
const Isometry3< 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 
Evaluate the spatial velocity V_WB of a body B in the world frame W. More...  
Methods to compute multibody Jacobians.  
void  CalcPointsGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const MatrixX< T >> &p_FP_list, EigenPtr< MatrixX< T >> p_WP_list, EigenPtr< MatrixX< T >> Jv_WFp) const 
Given a list of points with fixed position vectors p_FP in a frame F, (that is, their time derivative DtF(p_FP) in frame F is zero), this method computes the geometric Jacobian Jv_WFp defined by: More...  
void  CalcPointsGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const MatrixX< T >> &p_WP_list, EigenPtr< MatrixX< T >> Jv_WFp) const 
This is a variant to compute the geometric Jacobian Jv_WFp for a list of points P moving with frame_F , given that we know the position p_WP of each point in the list measured and expressed in the world frame W. More...  
VectorX< T >  CalcBiasForPointsGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const MatrixX< T >> &p_FP_list) const 
Computes the bias term b_WFp associated with the translational acceleration a_WFp of a point P instantaneously moving with a frame F. More...  
void  CalcPointsAnalyticalJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const MatrixX< T >> &p_FP_list, EigenPtr< MatrixX< T >> p_WP_list, EigenPtr< MatrixX< T >> Jq_WFp) const 
Given a list of points with fixed position vectors p_FP in a frame F, (that is, their time derivative DtF(p_FP) in frame F is zero), this method computes the analytical Jacobian Jq_WFp(q) . More...  
void  CalcFrameGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const Vector3< T >> &p_FP, EigenPtr< MatrixX< T >> Jv_WFp) const 
Given a frame Fp defined by shifting a frame F from its origin Fo to a new origin P , this method computes the geometric Jacobian Jv_WFp for frame Fp . More...  
void  CalcRelativeFrameGeometricJacobian (const systems::Context< T > &context, const Frame< T > &frame_B, const Eigen::Ref< const Vector3< T >> &p_BP, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< MatrixX< T >> Jv_ABp_E) const 
Computes the geometric Jacobian for a point moving with a given frame. More...  
Vector6< T >  CalcBiasForFrameGeometricJacobianExpressedInWorld (const systems::Context< T > &context, const Frame< T > &frame_F, const Eigen::Ref< const Vector3< T >> &p_FP) const 
Given a frame Fp defined by shifting a frame F from its origin Fo to a new origin P , this method computes the bias term Ab_WFp associated with the spatial acceleration A_WFp a frame Fp instantaneously moving with a frame F at a fixed position p_FP . More...  
void  CalcJacobianSpatialVelocity (const systems::Context< T > &context, JacobianWrtVariable with_respect_to, const Frame< T > &frame_B, const Eigen::Ref< const Vector3< T >> &p_BP, const Frame< T > &frame_A, const Frame< T > &frame_E, EigenPtr< MatrixX< T >> Jw_ABp_E) const 
Computes the Jacobian of spatial velocity for a frame instantaneously moving with a specified frame in the model. More...  
Computational methods  
These methods expose the computational capabilities of MultibodyTree to compute kinematics, forward and inverse dynamics, and Jacobian matrices, among others. These methods follow Drake's naming scheme for methods performing a computation and therefore are named  
void  CalcPositionKinematicsCache (const systems::Context< T > &context, PositionKinematicsCache< T > *pc) const 
Computes into the position kinematics pc all the kinematic quantities that depend on the generalized positions only. More...  
void  CalcVelocityKinematicsCache (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, VelocityKinematicsCache< T > *vc) const 
Computes all the kinematic quantities that depend on the generalized velocities and stores them in the velocity kinematics cache vc . More...  
void  CalcAccelerationKinematicsCache (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, const VelocityKinematicsCache< T > &vc, const VectorX< T > &known_vdot, AccelerationKinematicsCache< T > *ac) const 
Computes all the kinematic quantities that depend on the generalized accelerations that is, the generalized velocities' time derivatives, and stores them in the acceleration kinematics cache ac . More...  
void  CalcSpatialAccelerationsFromVdot (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, const VelocityKinematicsCache< T > &vc, const VectorX< T > &known_vdot, std::vector< SpatialAcceleration< T >> *A_WB_array) const 
Given the state of this MultibodyTree 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 MultibodyTree 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  CalcInverseDynamics (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, const VelocityKinematicsCache< T > &vc, const VectorX< T > &known_vdot, const std::vector< SpatialForce< T >> &Fapplied_Bo_W_array, const Eigen::Ref< const VectorX< T >> &tau_applied_array, std::vector< SpatialAcceleration< T >> *A_WB_array, std::vector< SpatialForce< T >> *F_BMo_W_array, EigenPtr< VectorX< T >> tau_array) const 
(Advanced) Given the state of this MultibodyTree 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 at each Mobilizer in order to attain the specified generalized accelerations. More...  
void  CalcForceElementsContribution (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, const VelocityKinematicsCache< T > &vc, MultibodyForces< T > *forces) const 
Computes the combined force contribution of ForceElement objects in the model. More...  
T  CalcPotentialEnergy (const systems::Context< T > &context) const 
Computes and returns the total potential energy stored in this multibody model for the configuration given by context . More...  
T  CalcConservativePower (const systems::Context< T > &context) const 
Computes and returns the power generated by conservative forces in the multibody model. More...  
void  CalcMassMatrixViaInverseDynamics (const systems::Context< T > &context, EigenPtr< MatrixX< T >> H) 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  CalcBiasTerm (const systems::Context< T > &context, EigenPtr< VectorX< T >> Cv) const 
Computes the bias term C(q, v)v containing Coriolis and gyroscopic effects of the multibody equations of motion: 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...  
void  CalcArticulatedBodyInertiaCache (const systems::Context< T > &context, const PositionKinematicsCache< T > &pc, ArticulatedBodyInertiaCache< T > *abc) const 
Computes all the quantities that are required in the final pass of the articulated body algorithm and stores them in the articulated body cache abc . More...  
Methods to retrieve multibody element variants  
Given two variants of the same MultibodyTree, these methods map an element in one variant, to its corresponding element in the other variant. A concrete case is the call to ToAutoDiffXd() to obtain a MultibodyTree variant templated on AutoDiffXd from a MultibodyTree templated on Consider the following code example: // The user creates a model. MultibodyTree<double> model; // User adds a body and keeps a reference to it. // User creates an AutoDiffXd variant. Variants on other scalar types // can be created with a call to CloneToScalar(). std::unique_ptr<MultibodyTree<Tvariant>> variant_model = model.ToAutoDiffXd(); // User retrieves the AutoDiffXd variant corresponding to the original // body added above. const RigidBody<AutoDiffXd>& variant_body = variant_model.get_variant(body); MultibodyTree::get_variant() is templated on the multibody element type which is deduced from its only input argument. The returned element is templated on the scalar type T of the MultibodyTree on which this method is invoked.  
template<template< typename > class MultibodyElement, typename Scalar >  
std::enable_if_t< std::is_base_of< Frame< T >, MultibodyElement< T > >::value, const MultibodyElement< T > & >  get_variant (const MultibodyElement< Scalar > &element) const 
SFINAE overload for Frame<T> elements. More...  
template<template< typename > class MultibodyElement, typename Scalar >  
std::enable_if_t< std::is_base_of< Body< T >, MultibodyElement< T > >::value, const MultibodyElement< T > & >  get_variant (const MultibodyElement< Scalar > &element) const 
SFINAE overload for Body<T> elements. More...  
template<template< typename > class MultibodyElement, typename Scalar >  
std::enable_if_t< std::is_base_of< Mobilizer< T >, MultibodyElement< T > >::value, const MultibodyElement< T > & >  get_variant (const MultibodyElement< Scalar > &element) const 
SFINAE overload for Mobilizer<T> elements. More...  
template<template< typename > class MultibodyElement, typename Scalar >  
std::enable_if_t< std::is_base_of< Joint< T >, MultibodyElement< T > >::value, const MultibodyElement< T > & >  get_variant (const MultibodyElement< Scalar > &element) const 
SFINAE overload for Joint<T> elements. More...  
Friends  
template<typename >  
class  MultibodyTree 
class  MultibodyTreeTester 
MultibodyTree provides a representation for a physical system consisting of a collection of interconnected rigid and deformable bodies.
As such, it owns and manages each of the elements that belong to this physical system. Multibody dynamics elements include bodies, joints, force elements and constraints.
T  The scalar type. Must be a valid Eigen scalar. 
Instantiated templates for the following kinds of T's are provided:
They are already available to link against in the containing library. No other values for T are currently supported.

delete 

delete 
MultibodyTree  (  ) 
Creates a MultibodyTree containing only a world body.

inline 
Takes ownership of body
and adds it to this
MultibodyTree.
Returns a constant reference to the body just added, which will remain valid for the lifetime of this
MultibodyTree.
Example of usage:
std::logic_error  if body is a nullptr. 
std::logic_error  if Finalize() was already called on this tree. 
[in]  body  A unique pointer to a body to add to this MultibodyTree. The body class must be specialized on the same scalar type T as this MultibodyTree. 
BodyType
to the created body. This reference which will remain valid for the lifetime of this
MultibodyTree.BodyType  The type of the specific subclass of Body to add. The template needs to be specialized on the same scalar type T of this MultibodyTree. 

inline 
Constructs a new body with type BodyType
with the given args
, and adds it to this
MultibodyTree, which retains ownership.
The BodyType
will be specialized on the scalar type T of this MultibodyTree.
Example of usage:
Note that for dependent names you must use the template keyword (say for instance you have a MultibodyTree<T> member within your custom class):
std::logic_error  if Finalize() was already called on this tree. 
[in]  args  The arguments needed to construct a valid Body of type BodyType . BodyType must provide a public constructor that takes these arguments. 
BodyType
to the created body. This reference which will remain valid for the lifetime of this
MultibodyTree.BodyType  A template for the type of Body to construct. The template will be specialized on the scalar type T of this MultibodyTree. 

inline 
Creates and adds to this
MultibodyTree (which retains ownership) a new ForceElement
member with the specific type ForceElementType
.
The arguments to this method args
are forwarded to ForceElementType
's constructor.
The newly created ForceElementType
object will be specialized on the scalar type T of this MultibodyTree.

inline 
Adds a new force element model of type ForceElementType
to this
MultibodyTree.
The arguments to this method args
are forwarded to ForceElementType
's constructor.
[in]  args  Zero or more parameters provided to the constructor of the new force element. It must be the case that JointType<T>(args) is a valid constructor. 
ForceElementType  The type of the ForceElement to add. This method can only be called once for elements of type UniformGravityFieldElement. That is, gravity can only be specified once and std::runtime_error is thrown if the model already contains a gravity field element. 
ForceElementType<T>
specialized on the scalar type T of this
MultibodyTree. It will remain valid for the lifetime of this
MultibodyTree. std::exception  if gravity was already added to the model. 

inline 

inline 
Takes ownership of frame
and adds it to this
MultibodyTree.
Returns a constant reference to the frame just added, which will remain valid for the lifetime of this
MultibodyTree.
Example of usage:
std::logic_error  if frame is a nullptr. 
std::logic_error  if Finalize() was already called on this tree. 
[in]  frame  A unique pointer to a frame to be added to this MultibodyTree. The frame class must be specialized on the same scalar type T as this MultibodyTree. 
FrameType
to the created frame. This reference which will remain valid for the lifetime of this
MultibodyTree.FrameType  The type of the specific subclass of Frame to add. The template needs to be specialized on the same scalar type T of this MultibodyTree. 

inline 
Constructs a new frame with type FrameType
with the given args
, and adds it to this
MultibodyTree, which retains ownership.
The FrameType
will be specialized on the scalar type T of this MultibodyTree.
Example of usage:
Note that for dependent names you must use the template keyword (say for instance you have a MultibodyTree<T> member within your custom class):
std::logic_error  if Finalize() was already called on this tree. 
[in]  args  The arguments needed to construct a valid Frame of type FrameType . FrameType must provide a public constructor that takes these arguments. 
FrameType
to the created frame. This reference which will remain valid for the lifetime of this
MultibodyTree.FrameType  A template for the type of Frame to construct. The template will be specialized on the scalar type T of this MultibodyTree. 

inline 

inline 
This method helps to create a Joint of type JointType
between two bodies.
The two bodies connected by this Joint object are referred to as the parent and child bodies. Although the terms parent and child are sometimes used synonymously to describe the relationship between inboard and outboard bodies in multibody models, this usage is wholly unrelated and implies nothing about the inboardoutboard relationship between the bodies. 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 create a joint between two bodies with fixed poses X_PF
and X_BM
. Refer to the Joint class's documentation for more details.
The arguments to this method args
are forwarded to JointType
's constructor. The newly created JointType
object will be specialized on the scalar type T of this MultibodyTree.
[in]  name  The name of the joint. 
[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 , provide Isometry3<double>::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 F with pose X_PF , provide Isometry3<double>::Identity() as your input. 
JointType  The type of the new joint to add, which must be a subclass of Joint<T>. 
JointType<T>
specialized on the scalar type T of this
MultibodyTree. It will remain valid for the lifetime of this
MultibodyTree.Example of usage:
std::exception  if this model already contains a joint with the given name . See HasJointNamed(), Joint::name(). 

inline 
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
MultibodyTree.
[in]  name  A string that identifies the new actuator to be added to this model. An exception is thrown if an actuator with the same name already exists in the same model instance as joint . See HasJointActuatorNamed(). 
[in]  joint  The Joint to be actuated by the new JointActuator. 
this
MultibodyTree. std::exception  if this model already contains a joint actuator with the given name . See HasJointActuatorNamed(), JointActuator::get_name(). 

inline 
Takes ownership of mobilizer
and adds it to this
MultibodyTree.
Returns a constant reference to the mobilizer just added, which will remain valid for the lifetime of this
MultibodyTree.
Example of usage:
A Mobilizer effectively connects the two bodies to which the inboard and outboard frames belong.
std::logic_error  if mobilizer is a nullptr. 
std::logic_error  if Finalize() was already called on this tree. 
std::runtime_error  if the new mobilizer attempts to connect a frame with itself. 
std::runtime_error  if attempting to connect two bodies with more than one mobilizer between them. 
[in]  mobilizer  A unique pointer to a mobilizer to add to this MultibodyTree. The mobilizer class must be specialized on the same scalar type T as this MultibodyTree. Notice this is a requirement of this method's signature and therefore an input mobilzer specialized on a different scalar type than that of this MultibodyTree's T will fail to compile. 
MobilizerType
to the created mobilizer. This reference which will remain valid for the lifetime of this
MultibodyTree.MobilizerType  The type of the specific subclass of Mobilizer to add. The template needs to be specialized on the same scalar type T of this MultibodyTree. 

inline 
Constructs a new mobilizer with type MobilizerType
with the given args
, and adds it to this
MultibodyTree, which retains ownership.
The MobilizerType
will be specialized on the scalar type T of this MultibodyTree.
Example of usage:
Note that for dependent names only you must use the template keyword (say for instance you have a MultibodyTree<T> member within your custom class).
std::logic_error  if Finalize() was already called on this tree. 
std::runtime_error  if the new mobilizer attempts to connect a frame with itself. 
std::runtime_error  if attempting to connect two bodies with more than one mobilizer between them. 
[in]  args  The arguments needed to construct a valid Mobilizer of type MobilizerType . MobilizerType must provide a public constructor that takes these arguments. 
MobilizerType
to the created mobilizer. This reference which will remain valid for the lifetime of this
MultibodyTree.MobilizerType  A template for the type of Mobilizer to construct. The template will be specialized on the scalar type T of this MultibodyTree. 

inline 
Creates a new model instance.
Returns the index for a new model instance (as there is no concrete object beyond the index).
[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(). 
std::logic_error  if Finalize() was already called on this tree. 

inline 
Creates a rigid body with the provided name, model instance, and spatial inertia.
This method returns a constant reference to the body just added, which will remain valid for the lifetime of this
MultibodyTree.
Example of usage:
[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 model, computed about the body frame origin Bo and expressed in the body frame B. 
this
MultibodyTree. std::logic_error  if a body named name already exists in this model instance. 
std::logic_error  if the model instance does not exist. 

inline 
Creates a rigid body with the provided name, model instance, and spatial inertia.
The newly created body will be placed in the default model instance. This method returns a constant reference to the body just added, which will remain valid for the lifetime of this
MultibodyTree.
Example of usage:
[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 model, computed about the body frame origin Bo and expressed in the body frame B. 
this
MultibodyTree. std::logic_error  if a body named name already exists. 
std::logic_error  if additional model instances have been created beyond the world and default instances. 
void CalcAccelerationKinematicsCache  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
const VelocityKinematicsCache< T > &  vc,  
const VectorX< T > &  known_vdot,  
AccelerationKinematicsCache< T > *  ac  
)  const 
Computes all the kinematic quantities that depend on the generalized accelerations that is, the generalized velocities' time derivatives, and stores them in the acceleration kinematics cache ac
.
These include:
A_WB
for each body B in the model as measured and expressed in the world frame W.[in]  context  The context containing the state of the MultibodyTree model. 
[in]  pc  A position kinematics cache object already updated to be in sync with context . 
[in]  vc  A velocity kinematics cache object already updated to be in sync with context . 
[in]  known_vdot  A vector with the generalized accelerations for the full MultibodyTree model. 
[out]  ac  A pointer to a valid, non nullptr, acceleration kinematics cache. This method aborts if ac is nullptr. 
pc
must have been previously updated with a call to CalcPositionKinematicsCache(). vc
must have been previously updated with a call to CalcVelocityKinematicsCache(). void CalcAcrossNodeGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
std::vector< Vector6< T >> *  H_PB_W_cache  
)  const 
(Internal) Computes the cache entry associated with the geometric Jacobian H_PB_W for each node.
The geometric Jacobian H_PB_W
relates to the spatial velocity of B in P by V_PB_W = H_PB_W(q)⋅v_B
, where v_B
corresponds to the generalized velocities associated to body B. H_PB_W
has size 6 x nm
with nm
the number of mobilities associated with body B. H_PB_W_cache
stores the Jacobian matrices for all nodes in the tree as a vector of the columns of these matrices. Therefore H_PB_W_cache
has as many entries as number of generalized velocities in the tree.
void CalcAllBodyPosesInWorld  (  const systems::Context< T > &  context, 
std::vector< Isometry3< T >> *  X_WB  
)  const 
Computes the world pose X_WB(q)
of each body B in the model as a function of the generalized positions q stored in context
.
[in]  context  The context containing the state of the model. It stores the generalized positions q of the model. 
[out]  X_WB  On output this vector will contain the pose of each body in the model ordered by BodyIndex. The index of a body in the model can be obtained with Body::index(). This method throws an exception if X_WB is nullptr . Vector X_WB is resized when needed to have size num_bodies(). 
std::exception  if X_WB is nullptr. 
void CalcAllBodySpatialVelocitiesInWorld  (  const systems::Context< T > &  context, 
std::vector< SpatialVelocity< T >> *  V_WB  
)  const 
Computes the spatial velocity V_WB(q, v)
of each body B in the model, measured and expressed in the world frame W.
The body spatial velocities are a function of the generalized positions q and generalized velocities v, both stored in context
.
[in]  context  The context containing the state of the model. It stores the generalized positions q and velocities v of the model. 
[out]  V_WB  On output this vector will contain the spatial velocity of each body in the model ordered by BodyIndex. The index of a body in the model can be obtained with Body::index(). This method throws an exception if V_WB is nullptr . Vector V_WB is resized when needed to have size num_bodies(). 
std::exception  if V_WB is nullptr. 
void CalcArticulatedBodyInertiaCache  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
ArticulatedBodyInertiaCache< T > *  abc  
)  const 
Computes all the quantities that are required in the final pass of the articulated body algorithm and stores them in the articulated body cache abc
.
These include:
Pplus_PB_W
, which can be thought of as the articulated body inertia of parent body P as though it were inertialess, but taken about Bo and expressed in W.[in]  context  The context containing the state of the MultibodyTree model. 
[in]  pc  A position kinematics cache object already updated to be in sync with context . 
[out]  abc  A pointer to a valid, non nullptr, articulated body cache. This method throws an exception if abc is a nullptr. 
pc
must have been previously updated with a call to CalcPositionKinematicsCache() using the same context
. Vector6< T > CalcBiasForFrameGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const Vector3< T >> &  p_FP  
)  const 
Given a frame Fp
defined by shifting a frame F from its origin Fo
to a new origin P
, this method computes the bias term Ab_WFp
associated with the spatial acceleration A_WFp
a frame Fp
instantaneously moving with a frame F at a fixed position p_FP
.
That is, the spatial acceleration of frame Fp
can be computed as:
A_WFp = Jv_WFp(q)⋅v̇ + Ab_WFp(q, v)
where Ab_WFp(q, v) = J̇v_WFp(q, v)⋅v
.
Jv_WFp(q)
.[in]  context  The context containing the state of the model. It stores the generalized positions q and generalized velocities v. 
[in]  frame_F  The position p_FP of frame Fp is measured and expressed in this frame F. 
[in]  p_FP  The (fixed) position of the origin P of frame Fp as measured and expressed in frame F. 
context
. The returned vector is of size 6, with the first three elements related to the bias in angular acceleration and the with the last three elements related to the bias in translational acceleration. VectorX< T > CalcBiasForPointsGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const MatrixX< T >> &  p_FP_list  
)  const 
Computes the bias term b_WFp
associated with the translational acceleration a_WFp
of a point P
instantaneously moving with a frame F.
That is, the translational acceleration of point P
can be computed as:
a_WFp = Jv_WFp(q)⋅v̇ + b_WFp(q, v)
where b_WFp = J̇v_WFp(q, v)⋅v
.
This method computes b_WFp
for each point P
in p_FP_list
defined by its position p_FP
in frame_F
.
Jv_WFp(q)
.[in]  context  The context containing the state of the model. It stores the generalized positions q and generalized velocities v. 
[in]  frame_F  Points P in the list instantaneously move with this frame. 
[in]  p_FP_list  A matrix with the fixed position of a list of points P measured and expressed in frame_F . Each column of this matrix contains the position vector p_FP for a point P measured and expressed in frame F. Therefore this input matrix lives in ℝ³ˣⁿᵖ with np the number of points in the list. 
context
. The returned vector has size 3⋅np
, with np the number of points in p_FP_list
, and concatenates the bias terms for each point P
in the list in the same order they are specified on input.std::exception  if p_FP_list does not have 3 rows. 
void CalcBiasTerm  (  const systems::Context< T > &  context, 
EigenPtr< VectorX< T >>  Cv  
)  const 
Computes the bias term C(q, v)v
containing Coriolis and gyroscopic effects of the multibody equations of motion:
M(q)v̇ + C(q, v)v = tau_app + ∑ J_WBᵀ(q) Fapp_Bo_W
where M(q)
is the multibody model's mass matrix 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 geometric Jacobian J_WB(q)
which maps generalized velocities into body B spatial velocity as V_WB = J_WB(q)v
.
[in]  context  The context containing the state of the MultibodyTree 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 (nonnull) 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. 
T CalcConservativePower  (  const systems::Context< T > &  context  )  const 
Computes and returns the power generated by conservative forces in the multibody model.
This quantity is defined to be positive when the potential energy is decreasing. In other words, if U(q)
is the potential energy as defined by CalcPotentialEnergy(), then the conservative power, Pc
, is Pc = U̇(q)
.
void CalcForceElementsContribution  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
const VelocityKinematicsCache< T > &  vc,  
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. Therefore this method provides outputs for both spatial forces per body (with F_Bo_W_array
) and generalized forces (with tau_array
). 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.
[in]  context  The context containing the state of the MultibodyTree model. 
[in]  pc  A position kinematics cache object already updated to be in sync with context . 
[in]  vc  A velocity kinematics cache object already updated to be in sync with context . 
[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. This method will abort if the forces pointer is null or if the forces object is not compatible with this MultibodyTree, see MultibodyForces::CheckInvariants(). 
pc
must have been previously updated with a call to CalcPositionKinematicsCache(). vc
must have been previously updated with a call to CalcVelocityKinematicsCache(). void CalcFrameGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const Vector3< T >> &  p_FP,  
EigenPtr< MatrixX< T >>  Jv_WFp  
)  const 
Given a frame Fp
defined by shifting a frame F from its origin Fo
to a new origin P
, this method computes the geometric Jacobian Jv_WFp
for frame Fp
.
The new origin P
is specified by the position vector p_FP
in frame F. The frame geometric Jacobian Jv_WFp
is defined by:
V_WFp(q, v) = Jv_WFp(q)⋅v
where V_WFp(q, v)
is the spatial velocity of frame Fp
measured and expressed in the world frame W and q and v are the vectors of generalized position and velocity, respectively. The geometric Jacobian Jv_WFp(q)
is a function of the generalized coordinates q only.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  frame_F  The position p_FP of frame Fp is measured and expressed in this frame F. 
[in]  p_FP  The (fixed) position of the origin P of frame Fp as measured and expressed in frame F. 
[out]  Jv_WFp  The geometric Jacobian Jv_WFp(q) , function of the generalized positions q only. This Jacobian relates to the spatial velocity V_WFp of frame Fp by: V_WFp(q, v) = Jv_WFp(q)⋅vTherefore Jv_WFp is a matrix of size 6 x nv , with nv the number of generalized velocities. On input, matrix Jv_WFp must have size 6 x nv or this method throws an exception. The top rows of this matrix (which can be accessed with Jv_WFp.topRows<3>()) is the Jacobian Hw_WFp related to the angular velocity of Fp in W by w_WFp = Hw_WFp⋅v . The bottom rows of this matrix (which can be accessed with Jv_WFp.bottomRows<3>()) is the Jacobian Hv_WFp related to the translational velocity of the origin P of frame Fp in W by v_WFpo = Hv_WFp⋅v . This ordering is consistent with the internal storage of the SpatialVelocity class. Therefore the following operations results in a valid spatial velocity: SpatialVelocity<double> Jv_WFp_times_v(Jv_WFp * v); 
std::exception  if J_WFp is nullptr or if it is not of size 6 x nv . 
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
.
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.
[in]  context  The context storing the state of the multibody model. 
v
for this
MultibodyTree model 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. VectorX< T > CalcInverseDynamics  (  const systems::Context< T > &  context, 
const VectorX< T > &  known_vdot,  
const MultibodyForces< T > &  external_forces  
)  const 
Given the state of this
MultibodyTree 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 MultibodyTree 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 geometric Jacobian J_WB(q)
which maps generalized velocities into body B spatial velocity as V_WB = J_WB(q)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)
NewtonEuler recursive algorithm, where n is the number of bodies in the MultibodyTree. 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 NewtonEuler algorithm is the most efficient currently known general method for solving inverse dynamics [Featherstone 2008].
[in]  context  The context containing the state of the model. 
[in]  known_vdot  A vector with the known generalized accelerations vdot for the full MultibodyTree 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. 
known_vdot
. void CalcInverseDynamics  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
const VelocityKinematicsCache< T > &  vc,  
const VectorX< T > &  known_vdot,  
const std::vector< SpatialForce< T >> &  Fapplied_Bo_W_array,  
const Eigen::Ref< const VectorX< T >> &  tau_applied_array,  
std::vector< SpatialAcceleration< T >> *  A_WB_array,  
std::vector< SpatialForce< T >> *  F_BMo_W_array,  
EigenPtr< VectorX< T >>  tau_array  
)  const 
(Advanced) Given the state of this
MultibodyTree 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 at each Mobilizer 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 MultibodyTree 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 geometric Jacobian J_WB(q)
which maps generalized velocities into body B spatial velocity as V_WB = J_WB(q)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)
NewtonEuler recursive algorithm, where n is the number of bodies in the MultibodyTree. 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 NewtonEuler algorithm is the most efficient currently known general method for solving inverse dynamics [Featherstone 2008].
[in]  context  The context containing the state of the MultibodyTree model. 
[in]  pc  A position kinematics cache object already updated to be in sync with context . 
[in]  vc  A velocity kinematics cache object already updated to be in sync with context . 
[in]  known_vdot  A vector with the known generalized accelerations vdot for the full MultibodyTree model. Use Mobilizer::get_accelerations_from_array() to access entries into this array for a particular Mobilizer. You can use the mutable version of this method to write into this array. 
[in]  Fapplied_Bo_W_array  A vector containing the spatial force Fapplied_Bo_W applied on each body at the body's frame origin Bo and expressed in the world frame W. Fapplied_Bo_W_array can have zero size which means there are no applied forces. To apply nonzero forces, Fapplied_Bo_W_array must be of size equal to the number of bodies in this MultibodyTree model. This array must be ordered by BodyNodeIndex, which for a given body can be retrieved with Body::node_index(). This method will abort if provided with an array that does not have a size of either num_bodies() or zero. 
[in]  tau_applied_array  An array of applied generalized forces for the entire model. For a given mobilizer, entries in this array can be accessed using the method Mobilizer::get_generalized_forces_from_array() while its mutable counterpart, Mobilizer::get_mutable_generalized_forces_from_array(), allows writing into this array. tau_applied_array can have zero size, which means there are no applied forces. To apply nonzero forces, tau_applied_array must be of size equal to the number to the number of generalized velocities in the model, see MultibodyTree::num_velocities(). This method will abort if provided with an array that does not have a size of either MultibodyTree::num_velocities() or zero. 
[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. This method will abort if the the pointer is null or if A_WB_array is not of size num_bodies() . On output, entries will be ordered by BodyNodeIndex. To access the acceleration A_WB of given body B in this array, use the index returned by Body::node_index(). 
[out]  F_BMo_W_array  A pointer to a valid, non nullptr, vector of spatial forces containing, for each body B, the spatial force F_BMo_W corresponding to its inboard mobilizer reaction forces on body B applied at the origin Mo of the inboard mobilizer, expressed in the world frame W. It must be of size equal to the number of bodies in the MultibodyTree. This method will abort if the the pointer is null or if F_BMo_W_array is not of size num_bodies() . On output, entries will be ordered by BodyNodeIndex. To access a mobilizer's reaction force on given body B in this array, use the index returned by Body::node_index(). 
[out]  tau_array  On output this array will contain the generalized forces that must be applied in order to achieve the desired generalized accelerations given by the input argument known_vdot . It must not be nullptr and it must be of size MultibodyTree::num_velocities(). Generalized forces for each Mobilizer can be accessed with Mobilizer::get_generalized_forces_from_array(). 
A_WB_array
nor F_BMo_W_array
are ordered by BodyNodeIndex. You can use Body::node_index() to obtain the node index for a given body.F_BMo_W_array
and tau_array
as the only local temporaries and therefore no additional dynamic memory allocation is performed.F_BMo_W_array
(tau_array
) and Fapplied_Bo_W_array
(tau_applied_array
) can actually be the same array in order to reduce memory footprint and/or dynamic memory allocations. However the information in Fapplied_Bo_W_array
(tau_applied_array
) would be overwritten through F_BMo_W_array
(tau_array
). Make a copy if data must be preserved.pc
must have been previously updated with a call to CalcPositionKinematicsCache(). vc
must have been previously updated with a call to CalcVelocityKinematicsCache(). void CalcJacobianSpatialVelocity  (  const systems::Context< T > &  context, 
JacobianWrtVariable  with_respect_to,  
const Frame< T > &  frame_B,  
const Eigen::Ref< const Vector3< T >> &  p_BP,  
const Frame< T > &  frame_A,  
const Frame< T > &  frame_E,  
EigenPtr< MatrixX< T >>  Jw_ABp_E  
)  const 
Computes the Jacobian of spatial velocity for a frame instantaneously moving with a specified frame in the model.
Consider a point P instantaneously moving with a frame B with position p_BP
in that frame. Frame Bp
is the frame defined by shifting frame B with origin at Bo
to a new origin at point P. The spatial velocity V_ABp_E
of frame Bp
measured in a frame A and expressed in a frame E can be expressed as:
V_ABp_E(q, w) = Jw_ABp_E(q)⋅w
where w represents
with_respect_to
is JacobianWrtVariable::kQDot.with_respect_to
is JacobianWrtVariable::kV.This method computes Jw_ABp_E(q)
.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  with_respect_to  Enum indicating whether Jw_ABp_E converts generalized velocities or timederivatives of generalized positions to spatial velocities. 
[in]  frame_B  The position p_BP of point P is measured and expressed in this frame. 
[in]  p_BP  The (fixed) position of the origin P of frame Bp as measured and expressed in frame B. 
[in]  frame_A  The second frame in which the spatial velocity V_ABp is measured. 
[in]  frame_E  Frame in which the velocity V_ABp_E, and therefore the Jacobian Jw_ABp_E is expressed. 
[out]  Jw_ABp_E  The Jacobian Jw_ABp_E(q) , function of the generalized positions q only. This Jacobian relates to the spatial velocity V_ABp_E of frame Bp in A and expressed in E by: V_ABp_E(q, w) = Jw_ABp_E(q)⋅wTherefore Jw_ABp_E is a matrix of size 6 x nz , where nz is the number of elements in w. On input, matrix Jv_ABp_E must have size 6 x nz or this method throws an exception. Given a 6 x nz Jacobian J, let Jr be the 3 x nz rotational part (top 3 rows) and Jt be the translational part (bottom 3 rows). These can be obtained as follows: Jr_ABp_E = Jw_ABp_E.topRows<3>(); Jt_ABp_E = Jw_ABp_E.bottomRows<3>(); SpatialVelocity<double> V_ABp(Jw_ABp * w); 
std::exception  if Jw_ABp_E is nullptr or if it is not of size 6 x nz . 
void CalcMassMatrixViaInverseDynamics  (  const systems::Context< T > &  context, 
EigenPtr< MatrixX< T >>  H  
)  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
.
[in]  context  The context containing the state of the MultibodyTree model. 
[out]  H  A valid (nonnull) 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 ith
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:
H.ᵢ(q) = M(q) * e_i
where H.ᵢ(q)
(notice the dot for the rows index) denotes the ith
column in M(q).
void CalcPointsAnalyticalJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const MatrixX< T >> &  p_FP_list,  
EigenPtr< MatrixX< T >>  p_WP_list,  
EigenPtr< MatrixX< T >>  Jq_WFp  
)  const 
Given a list of points with fixed position vectors p_FP
in a frame F, (that is, their time derivative DtF(p_FP)
in frame F is zero), this method computes the analytical Jacobian Jq_WFp(q)
.
The analytical Jacobian Jq_WFp(q)
is defined by:
Jq_WFp(q) = d(p_WFp(q))/dq
where p_WFp(q)
is the position of point P, which moves with frame F, in the world frame W.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  frame_F  The positions p_FP of each point in the input set are measured and expressed in this frame F and are constant (fixed) in this frame. 
[in]  p_FP_list  A matrix with the fixed position of a set of points P measured and expressed in frame_F . Each column of this matrix contains the position vector p_FP for a point P measured and expressed in frame F. Therefore this input matrix lives in ℝ³ˣⁿᵖ with np the number of points in the set. 
[out]  p_WP_list  The output positions of each point P now measured and expressed in computing the geometric Jacobian J_WP and therefore external storage must be provided. The output p_WP_list must have the same size as the input set p_FP_list or otherwise this method throws a std::runtime_error exception. That is p_WP_list must be in ℝ³ˣⁿᵖ . 
[out]  Jq_WFp  The analytical Jacobian Jq_WFp(q) , function of the generalized positions q only. We stack the positions of each point P in the world frame W into a column vector p_WFp = [p_WFp1; p_WFp2; ...] of size 3⋅np, with np the number of points in p_FP_list. Then the analytical Jacobian is defined as: Jq_WFp(q) = ∇(p_WFp(q))with ∇(⋅) the gradient operator with respect to the generalized positions q. Therefore Jq_WFp is a matrix of size 3⋅np x nq , with nq the number of generalized positions. On input, matrix Jq_WFp must have size 3⋅np x nq or this method throws a std::runtime_error exception. 
std::exception  if the output p_WP_list is nullptr or does not have the same size as the input array p_FP_list . 
std::exception  if Jq_WFp is nullptr or if it does not have the appropriate size, see documentation for Jq_WFp for details. 
void CalcPointsGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const MatrixX< T >> &  p_FP_list,  
EigenPtr< MatrixX< T >>  p_WP_list,  
EigenPtr< MatrixX< T >>  Jv_WFp  
)  const 
Given a list of points with fixed position vectors p_FP
in a frame F, (that is, their time derivative DtF(p_FP)
in frame F is zero), this method computes the geometric Jacobian Jv_WFp
defined by:
v_WP(q, v) = Jv_WFp(q)⋅v
where v_WP(q, v)
is the translational velocity of point P
in the world frame W and q and v are the vectors of generalized position and velocity, respectively.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  frame_F  The positions p_FP of each point in the input set are measured and expressed in this frame F and are constant (fixed) in this frame. 
[in]  p_FP_list  A matrix with the fixed position of a set of points P measured and expressed in frame_F . Each column of this matrix contains the position vector p_FP for a point P measured and expressed in frame F. Therefore this input matrix lives in ℝ³ˣⁿᵖ with np the number of points in the set. 
[out]  p_WP_list  The output positions of each point P now measured and expressed in computing the geometric Jacobian J_WP and therefore external storage must be provided. The output p_WP_list must have the same size as the input set p_FP_list or otherwise this method throws a std::runtime_error exception. That is p_WP_list must be in ℝ³ˣⁿᵖ . 
[out]  Jv_WFp  The geometric Jacobian Jv_WFp(q) , function of the generalized positions q only. This Jacobian relates the translational velocity v_WP of each point P in the input set by: v_WP(q, v) = Jv_WFp(q)⋅vso that v_WP is a column vector of size 3⋅np concatenating the velocity of all points P in the same order they were given in the input set. Therefore J_WFp is a matrix of size 3⋅np x nv , with nv the number of generalized velocities. On input, matrix J_WFp must have size 3⋅np x nv or this method throws a std::runtime_error exception. 
std::exception  if the output p_WP_list is nullptr or does not have the same size as the input array p_FP_list . 
std::exception  if Jv_WFp is nullptr or if it does not have the appropriate size, see documentation for Jv_WFp for details. 
void CalcPointsGeometricJacobianExpressedInWorld  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_F,  
const Eigen::Ref< const MatrixX< T >> &  p_WP_list,  
EigenPtr< MatrixX< T >>  Jv_WFp  
)  const 
This is a variant to compute the geometric Jacobian Jv_WFp
for a list of points P
moving with frame_F
, given that we know the position p_WP
of each point in the list measured and expressed in the world frame W.
The geometric Jacobian Jv_WFp
is defined such that:
v_WP(q, v) = Jv_WFp(q)⋅v
where v_WP(q, v)
is the translational velocity of point P
in the world frame W and q and v are the vectors of generalized position and velocity, respectively. Since the spatial velocity of each point P
is linear in the generalized velocities, the geometric Jacobian Jv_WFp
is a function of the generalized coordinates q only.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  frame_F  Points P in the list instantaneously move with this frame. 
[in]  p_WP_list  A matrix with the fixed position of a list of points P measured and expressed in the world frame W. Each column of this matrix contains the position vector p_WP for a point P measured and expressed in the world frame W. Therefore this input matrix lives in ℝ³ˣⁿᵖ with np the number of points in the list. 
[out]  Jv_WFp  The geometric Jacobian Jv_WFp(q) , function of the generalized positions q only. This Jacobian relates the translational velocity v_WP of each point P in the input list by: `v_WP(q, v) = Jv_WFp(q)⋅v`so that v_WP is a column vector of size 3⋅np concatenating the velocity of all points P in the same order they were given in the input list. Therefore J_WP is a matrix of size 3⋅np x nv , with nv the number of generalized velocities. On input, matrix J_WP must have size 3⋅np x nv or this method throws a std::runtime_error exception. 
std::exception  if Jv_WFp is nullptr or if it does not have the appropriate size, see documentation for Jv_WFp for details. 
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.
[in]  context  The context containing the state of the MultibodyTree 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 . 
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. void CalcPositionKinematicsCache  (  const systems::Context< T > &  context, 
PositionKinematicsCache< T > *  pc  
)  const 
Computes into the position kinematics pc
all the kinematic quantities that depend on the generalized positions only.
These include:
X_BF
of each of the frames F attached to body B.X_WB
of each body B in the model as measured and expressed in the world frame W.H_FM
and H_PB_W
.com_W
and M_Bo_W
.Aborts if pc
is nullptr.
T CalcPotentialEnergy  (  const systems::Context< T > &  context  )  const 
Computes and returns the total potential energy stored in this
multibody model for the configuration given by context
.
[in]  context  The context containing the state of the MultibodyTree model. 
this
multibody model. void CalcRelativeFrameGeometricJacobian  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_B,  
const Eigen::Ref< const Vector3< T >> &  p_BP,  
const Frame< T > &  frame_A,  
const Frame< T > &  frame_E,  
EigenPtr< MatrixX< T >>  Jv_ABp_E  
)  const 
Computes the geometric Jacobian for a point moving with a given frame.
Consider a point P instantaneously moving with a frame B with position p_BP
in that frame. Frame Bp
is the frame defined by shifting frame B with origin at Bo
to a new origin at point P. The spatial velocity V_ABp_E
of frame Bp
measured in a frame A and expressed in a frame E relates to the generalized velocities of the system by the geometric Jacobian Jv_ABp_E(q)
by:
V_ABp_E(q, v) = Jv_ABp_E(q)⋅v
This method computes the geometric Jacobian Jv_ABp_E(q)
.
[in]  context  The context containing the state of the model. It stores the generalized positions q. 
[in]  frame_B  The position p_BP of point P is measured and expressed in this frame. 
[in]  p_BP  The (fixed) position of the origin P of frame Bp as measured and expressed in frame B. 
[in]  frame_A  The second frame in which the spatial velocity V_ABp is measured and expressed. 
[in]  frame_E  Frame in which the velocity V_ABp_E is expressed. 
[out]  Jv_ABp_E  The geometric Jacobian Jv_ABp_E(q) , function of the generalized positions q only. This Jacobian relates to the spatial velocity V_ABp_E of frame Bp in A and expressed in E by: V_ABp_E(q, v) = Jv_ABp_E(q)⋅vTherefore Jv_ABp_E is a matrix of size 6 x nv , with nv the number of generalized velocities. On input, matrix Jv_ABp_E must have size 6 x nv or this method throws an exception. Given a 6 x nv spatial Jacobian Jv, let Jvr be the 3 x nv rotational part (top 3 rows) and Jvt be the translational part (bottom 3 rows). These can be obtained as follows: Jvr_ABp = Jv_ABp.topRows<3>(); Jvt_ABp = Jv_ABp.bottomRows<3>();This ordering is consistent with the internal storage of the SpatialVelocity class. Therefore the following operations results in a valid spatial velocity: SpatialVelocity<double> V_ABp(Jv_ABp * v); 
std::exception  if J_ABp is nullptr or if it is not of size 6 x nv . 
Isometry3< T > CalcRelativeTransform  (  const systems::Context< T > &  context, 
const Frame< T > &  frame_A,  
const Frame< T > &  frame_B  
)  const 
Computes the relative transform X_AB(q)
from a frame B to a frame A, as a function of the generalized positions q of the model.
That is, the position p_AQ
of a point Q measured and expressed in frame A can be computed from the position p_BQ
of this point measured and expressed in frame B using the transformation p_AQ = X_AB⋅p_BQ
.
[in]  context  The context containing the state of the MultibodyTree model. It stores the generalized positions q of the model. 
[in]  frame_A  The target frame A in the computed relative transform X_AB . 
[in]  frame_B  The source frame B in the computed relative transform X_AB . 
X_AB  The relative transform from frame B to frame A, such that p_AQ = X_AB⋅p_BQ . 
void CalcSpatialAccelerationsFromVdot  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
const VelocityKinematicsCache< T > &  vc,  
const VectorX< T > &  known_vdot,  
std::vector< SpatialAcceleration< T >> *  A_WB_array  
)  const 
Given the state of this
MultibodyTree 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.
[in]  context  The context containing the state of the MultibodyTree model. 
[in]  pc  A position kinematics cache object already updated to be in sync with context . 
[in]  vc  A velocity kinematics cache object already updated to be in sync with context . 
[in]  known_vdot  A vector with the generalized accelerations for the full MultibodyTree 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 MultibodyTree. This method will abort if the the pointer is null or if A_WB_array is not of size num_bodies() . On output, entries will be ordered by BodyNodeIndex. These accelerations can be read in the proper order with Body::get_from_spatial_acceleration_array(). 
pc
must have been previously updated with a call to CalcPositionKinematicsCache(). vc
must have been previously updated with a call to CalcVelocityKinematicsCache(). void CalcVelocityKinematicsCache  (  const systems::Context< T > &  context, 
const PositionKinematicsCache< T > &  pc,  
VelocityKinematicsCache< T > *  vc  
)  const 
Computes all the kinematic quantities that depend on the generalized velocities and stores them in the velocity kinematics cache vc
.
These include:
V_WB
for each body B in the model as measured and expressed in the world frame W.V_PB
for each body B in the model as measured and expressed in the inboard (or parent) body frame P.pc
must have been previously updated with a call to CalcPositionKinematicsCache().Aborts if vc
is nullptr.

inline 
Creates a deep copy of this
MultibodyTree templated on the same scalar type T as this
tree.

inline 
Creates a deep copy of this
MultibodyTree templated on the scalar type ToScalar
.
The new deep copy is guaranteed to have exactly the same MultibodyTreeTopology as the original tree the method is called on. This method ensures the following cloning order:
Consider the following code example:
MultibodyTree::get_variant() is templated on the multibody element type which is deduced from its only input argument. The returned element is templated on the scalar type T of the MultibodyTree on which this method is invoked. In the example above, the user could have also invoked the method ToAutoDiffXd().

inline 
(Advanced) Allocates a new context for this MultibodyTree uniquely identifying the state of the multibody system.
std::runtime_error  if this is not owned by a MultibodyPlant / MultibodyTreeSystem. 
const Isometry3< 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.
[in]  context  The context storing the state of the MultibodyTree model. 
[in]  body_B  The body B for which the pose is requested. 
X_WB  The pose of body frame B in the world frame W. 
std::exception  if Finalize() was not called on this model or if body_B does not belong to this model. 
const SpatialVelocity< T > & EvalBodySpatialVelocityInWorld  (  const systems::Context< T > &  context, 
const Body< T > &  body_B  
)  const 
Evaluate the spatial velocity V_WB
of a body B in the world frame W.
[in]  context  The context storing the state of the MultibodyTree model. 
[in]  body_B  The body B for which the spatial velocity is requested. 
std::exception  if Finalize() was not called on this model or if body_B does not belong to this model. 

inline 
Evaluates position kinematics cached in context.
context  A Context whose position kinematics cache will be updated and returned. 

inline 
Evaluates velocity kinematics cached in context.
This will also force position kinematics to be updated if it hasn't already.
context  A Context whose velocity kinematics cache will be updated and returned. 
void Finalize  (  ) 
This method must be called after all elements in the tree (joints, bodies, force elements, constraints) were 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 preprocessing to perform computations at a later stage.
If the finalize stage is successful, the topology of this MultibodyTree is validated, meaning that the topology is uptodate after this call. No more multibody tree elements can be added after a call to Finalize().
std::exception  if called postfinalize. 
Returns a constant reference to the body with unique index body_index
.
std::exception  if body_index does not correspond to a body in this multibody tree. 

inline 
Returns a constant reference to the frame with unique index frame_index
.
std::exception  if frame_index does not correspond to a frame in this multibody tree. 

inline 
Returns a constant reference to the joint with unique index joint_index
.
std::runtime_error  when joint_index does not correspond to a joint in this multibody tree. 

inline 
Returns a constant reference to the joint actuator with unique index actuator_index
.
std::exception  if actuator_index does not correspond to a joint actuator in this multibody tree. 

inline 
Returns a constant reference to the mobilizer with unique index mobilizer_index
.
std::runtime_error  when mobilizer_index does not correspond to a mobilizer in this multibody tree. 

inline 
Returns the topology information for this multibody tree.
Users should not need to call this method since MultibodyTreeTopology is an internal bookkeeping detail. Used at Finalize() stage by multibody elements to retrieve a local copy of their topology.

inline 
SFINAE overload for Frame<T> elements.

inline 
SFINAE overload for Body<T> elements.

inline 
SFINAE overload for Mobilizer<T> elements.

inline 
SFINAE overload for Joint<T> elements.

inline 
Returns a constant reference to a body that is identified by the string name
in this
model.
std::logic_error  if there is no body with the requested name. 
std::logic_error  if the body name occurs in multiple model instances. 
this
model with a given specified name.

inline 
Returns a constant reference to the body that is uniquely identified by the string name
in model_instance
.
std::logic_error  if there is no body with the requested name. 
std::runtime_error  if model_instance is not valid for this model. 
this
model with a given specified name.

inline 
Returns a constant reference to a frame that is identified by the string name
in this
model.
std::logic_error  if there is no frame with the requested name. 
std::logic_error  if the frame name occurs in multiple model instances. 
this
model with a given specified name.

inline 
Returns a constant reference to the frame that is uniquely identified by the string name
in model_instance
.
std::logic_error  if there is no frame with the requested name. 
std::runtime_error  if model_instance is not valid for this model. 
this
model with a given specified name.

inline 
Returns a constant reference to an actuator that is identified by the string name
in this
model.
std::logic_error  if there is no actuator with the requested name. 
std::logic_error  if the actuator name occurs in multiple model instances. 
this
model with a given specified name.

inline 
Returns a constant reference to the actuator that is uniquely identified by the string name
in model_instance
.
std::logic_error  if there is no actuator with the requested name. 
std::runtime_error  if model_instance is not valid for this model. 
this
model with a given specified name.

inline 
Returns a constant reference to a joint that is identified by the string name
in this
model.
std::logic_error  if there is no joint with the requested name. 
std::logic_error  if the joint name occurs in multiple model instances. 
this
model with a given specified name.

inline 
Returns a constant reference to the joint that is uniquely identified by the string name
in model_instance
.
std::logic_error  if there is no joint with the requested name. 
std::runtime_error  if model_instance is not valid for this model. 
this
model with a given specified name.

inline 
A templated version of GetJointByName() to return a constant reference of the specified type JointType
in place of the base Joint class.
See GetJointByName() for details.
JointType  The specific type of the Joint to be retrieved. It must be a subclass of Joint. 
std::logic_error  if the named joint is not of type JointType or if there is no Joint with that name. 
std::logic_error  if the joint name occurs in multiple model instances. 
this
model with a given specified name.

inline 
A templated version of GetJointByName() to return a constant reference of the specified type JointType
in place of the base Joint class.
See GetJointByName() for details.
JointType  The specific type of the Joint to be retrieved. It must be a subclass of Joint. 
std::logic_error  if the named joint is not of type JointType or 
std::runtime_error  if model_instance is not valid for this model. if there is no Joint with that name. 
this
model with a given specified name.

inline 
Returns the index to the model instance that is uniquely identified by the string name
in this
model.
std::logic_error  if there is no instance with the requested name. 
this
model with a given specified name.

inline 
Returns the name of a model_instance.
std::logic_error  when model_instance does not correspond to a model in this multibody tree. 
Eigen::VectorBlock< VectorX< T > > GetMutablePositionsAndVelocities  (  systems::Context< T > *  context  )  const 
Returns a mutable Eigen vector containing the vector [q; v]
of the model with q
the vector of generalized positions and v
the vector of generalized velocities.
std::exception  if the context is nullptr or if it does not correspond to the context for a multibody model. 
Eigen::VectorBlock< const VectorX< T > > GetPositionsAndVelocities  (  const systems::Context< T > &  context  )  const 
Returns a const Eigen vector reference containing the vector [q; v]
of the model with q
the vector of generalized positions and v
the vector of generalized velocities.
std::exception  if the context does not correspond to the context for a multibody model. 
VectorX< T > GetPositionsAndVelocities  (  const systems::Context< T > &  context, 
ModelInstanceIndex  model_instance  
)  const 
Returns a Eigen vector containing the multibody state x = [q; v]
of the model with q
the vector of generalized positions and v
the vector of generalized velocities for model instance model_instance
.
std::exception  if the context does not correspond to the context for a multibody model or model_instance is invalid. 
q.size() + v.size()
associated with model_instance
in O(q.size()
) time. 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 MultibodyTree model.
This method throws an exception if q
is not of size MultibodyTree::num_positions().

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

inline 
Returns a constant reference to the rigid body that is uniquely identified by the string name
in model_instance
.
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. 
this
model with a given specified name. VectorX< T > GetVelocitiesFromArray  (  ModelInstanceIndex  model_instance, 
const Eigen::Ref< const VectorX< T >> &  v_array  
)  const 
Returns a vector of generalized velocities for model_instance
from a vector v
of generalized velocities for the entire MultibodyTree model.
This method throws an exception if the input array is not of size MultibodyTree::num_velocities().

inline 
true
if a body named name
was added to the model. std::logic_error  if the body name occurs in multiple model instances. 

inline 
true
if a body named name
was added to model_instance
. std::exception  if model_instance is not valid for this model. 

inline 
true
if a frame named name
was added to the model. std::logic_error  if the frame name occurs in multiple model instances. 

inline 
true
if a frame named name
was added to model_instance
. std::exception  if model_instance is not valid for this model. 

inline 
true
if a joint actuator named name
was added to the model. std::logic_error  if the actuator name occurs in multiple model instances. 

inline 
true
if a joint actuator named name
was added to model_instance
. std::exception  if model_instance is not valid for this model. 

inline 
true
if a joint named name
was added to the model. std::logic_error  if the joint name occurs in multiple model instances. 

inline 
true
if a joint named name
was added to model_instance
. std::exception  if model_instance is not valid for this model. 

inline 
true
if a model instance named name
was added to the model. 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.
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.
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
.
It is assumed that all joints referenced by user_to_joint_index_map
are actuated. See MakeActuatorSelectorMatrix(const std::vector<JointActuatorIndex>&) for details.
std::logic_error  if any of the joints in user_to_joint_index_map does not have an actuator. 
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.
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.
std::logic_error  if there are repeated indexes in user_to_joint_index_map . 
MatrixX< double > MakeStateSelectorMatrixFromJointNames  (  const std::vector< std::string > &  selected_joints  )  const 
Alternative signature to build a state selector matrix from a std::vector of joint names.
See MakeStateSelectorMatrixFromJointNames(const std::vector<JointIndex>&) for details. selected_joints
must not contain any duplicates.
A user specifies the preferred order in the selected states vector xₛ via selected_joints
. 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 selected_joints
. That is, the positions for selected_joints[0]
are first, followed by the positions for selected_joints[1]
, etc. Similarly for the selected velocities vₛ.
std::logic_error  if there are any duplicates in selected_joints . 
std::logic_error  if there is no joint in the model with a name specified in selected_joints . 
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 pseudoinverse 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
.
[in]  context  The context containing the state of the MultibodyTree 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 (nonnull) 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(). 
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
.
[in]  context  The context containing the state of the MultibodyTree model. 
[in]  v  A vector of of generalized velocities for this MultibodyTree model. This method aborts if v is not of size num_velocities(). 
[out]  qdot  A valid (nonnull) pointer to a vector in ℝⁿ with n being the number of generalized positions in this MultibodyTree model, given by num_positions() . This method aborts if qdot is nullptr or if it is not of size num_positions(). 

inline 
Returns the total number of Joint degrees of freedom actuated by the set of JointActuator elements added to this
model.

inline 
Returns the total number of Joint degrees of freedom actuated by the set of JointActuator elements added to a specific model instance.

inline 
Returns the number of actuators in the model.

inline 
Returns the number of bodies in the MultibodyTree including the world body.
Therefore the minimum number of bodies in a MultibodyTree is one.

inline 
Returns the number of ForceElement objects in the MultibodyTree.

inline 
Returns the number of Frame objects in the MultibodyTree.
Frames include body frames associated with each of the bodies in the MultibodyTree including the world body. Therefore the minimum number of frames in a MultibodyTree is one.

inline 
Returns the number of joints added with AddJoint() to the MultibodyTree.

inline 
Returns the number of mobilizers in the MultibodyTree.
Since the world has no Mobilizer, the number of mobilizers equals the number of bodies minus one, i.e. num_mobilizers() returns num_bodies()  1.

inline 
Returns the number of model instances in the MultibodyTree.

inline 
Returns the number of generalized positions of the model.

inline 
Returns the number of generalized positions in a specific model instance.

inline 
Returns the total size of the state vector in the model.

inline 
Returns the total size of the state vector in a specific model instance.

inline 
Returns the number of generalized velocities of the model.

inline 
Returns the number of generalized velocities in a specific model instance.

delete 

delete 

inline 
(Internal use only) Informs the MultibodyTree how to access its resources within a Context.
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 MultibodyTree 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
.
[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 MultibodyTree. 
void SetDefaultContext  (  systems::Context< T > *  context  )  const 
Sets default values in the context.
For mobilizers, this method sets them to their zero configuration according to Mobilizer::set_zero_configuration().
void SetDefaultState  (  const systems::Context< T > &  context, 
systems::State< T > *  state  
)  const 
Sets default values in the state
.
For mobilizers, this method sets them to their zero configuration according to Mobilizer::set_zero_configuration().
void SetFreeBodyPoseOrThrow  (  const Body< T > &  body, 
const Isometry3< T > &  X_WB,  
systems::Context< T > *  context  
)  const 
Sets context
to store the pose X_WB
of a given body
B in the world frame W.
std::exception  if body is not a free body in the model. 
std::exception  if called prefinalize. 
void SetFreeBodyPoseOrThrow  (  const Body< T > &  body, 
const Isometry3< T > &  X_WB,  
const systems::Context< T > &  context,  
systems::State< T > *  state  
)  const 
Sets sate
to store the pose X_WB
of a given body
B in the world frame W, for a given context
of this
model.
std::exception  if body is not a free body in the model. 
std::exception  if called prefinalize. 
void SetFreeBodySpatialVelocityOrThrow  (  const Body< T > &  body, 
const SpatialVelocity< T > &  V_WB,  
systems::Context< T > *  context  
)  const 
Sets context
to store the spatial velocity V_WB
of a given body
B in the world frame W.
std::exception  if body is not a free body in the model. 
std::exception  if called prefinalize. 
void SetFreeBodySpatialVelocityOrThrow  (  const Body< T > &  body, 
const SpatialVelocity< T > &  V_WB,  
const systems::Context< T > &  context,  
systems::State< T > *  state  
)  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.
std::exception  if body is not a free body in the model. 
std::exception  if called prefinalize. 
void SetPositionsAndVelocities  (  ModelInstanceIndex  model_instance, 
const Eigen::Ref< const VectorX< T >> &  instance_state,  
systems::Context< T > *  context  
)  const 
Sets context
to store the vector [q; v]
with q
the vector of generalized positions and v
the vector of generalized velocities for model instance model_instance
.
std::exception  if the context does not correspond to the context for a multibody model, context is nullptr, model_instance is invalid, or instance_state.size() does not equal num_positions(model_instance)

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 MultibodyTree::num_positions() or q_instance
is not of size MultibodyTree::num_positions(model_instance)
.
void SetVelocitiesInArray  (  ModelInstanceIndex  model_instance, 
const Eigen::Ref< const VectorX< T >> &  model_v,  
EigenPtr< VectorX< T >>  v_array  
)  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 MultibodyTree::num_velocities() or v_instance
is not of size MultibodyTree::num_positions(model_instance)
.

inline 
Creates a deep copy of this
MultibodyTree templated on AutoDiffXd.

inline 
Returns true
if this MultibodyTree was finalized with Finalize() after all multibody elements were added, and false
otherwise.
When a MultibodyTree is instantiated, its topology remains invalid until Finalize() is called, which validates the topology.

inline 
Returns the height of the tree data structure of this
MultibodyTree.
That is, the number of bodies in the longest kinematic path between the world and any other leaf body. For a model that only contains the world body, the height of the tree is one. Kinematic paths are created by Mobilizer objects connecting a chain of frames. Therefore, this method does not count kinematic cycles, which could only be considered in the model using constraints.

inline 
Returns a constant reference to the world body.

inline 
Returns a constant reference to the world frame.

friend 

friend 