Namespaces
	benchmarks

	collision

	constraint

	detail

	internal

	joints

	math

	multibody_plant

	parsers

	test

	test_utilities

Classes
struct	AddMultibodyPlantSceneGraphResult
	Temporary result from `AddMultibodyPlantSceneGraph`. More...

class	AngleBetweenVectorsConstraint
	Constrains that the angle between a vector `a` and another vector `b` is between [θ_lower, θ_upper]. More...

class	ArticulatedBodyInertia
	Articulated Body Inertia is the inertia that a body appears to have when it is the base (or root) of a rigid-body system, also referred to as Articulated Body in the context of articulated body algorithms. More...

class	Body
	Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. More...

class	BodyFrame
	A BodyFrame is a material Frame that serves as the unique reference frame for a Body. More...

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

class	ContactResultsToLcmSystem
	A System that encodes ContactResults into a lcmt_contact_results_for_viz message. More...

class	CoulombFriction
	Parameters for Coulomb's Law of Friction, namely: More...

struct	ExternallyAppliedSpatialForce

class	FixedOffsetFrame
	FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. More...

class	ForceElement
	A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. More...

class	Frame
	Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. More...

class	FrameBase
	FrameBase is an abstract representation of the concept of a frame in multibody dynamics. More...

class	GazeTargetConstraint
	Constrains a target point T to be within a cone K. More...

class	GlobalInverseKinematics
	Solves the inverse kinematics problem as a mixed integer convex optimization problem. More...

class	IiwaKinematicConstraintTest

class	ImplicitStribeckSolver

struct	ImplicitStribeckSolverIterationStats
	Struct used to store information about the iteration process performed by ImplicitStribeckSolver. More...

struct	ImplicitStribeckSolverParameters
	These are the parameters controlling the iteration process of the ImplicitStribeckSolver solver. More...

class	InverseKinematics
	Solves an inverse kinematics (IK) problem on a MultibodyPlant, to find the postures of the robot satisfying certain constraints. More...

class	Joint
	A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. More...

class	JointActuator
	The JointActuator class is mostly a simple bookkeeping structure to represent an actuator acting on a given Joint. More...

class	LinearSpringDamper
	This ForceElement models a spring-damper attached between two points on two different bodies. More...

class	MinimumDistanceConstraint
	Constrain that the pairwise distance between objects should be no smaller than a positive threshold. More...

class	MultibodyForces
	A class to hold a set of forces applied to a MultibodyTree system. More...

class	MultibodyPlant
	MultibodyPlant is a Drake system framework representation (see systems::System) for the model of a physical system consisting of a collection of interconnected bodies. More...

class	MultibodyPlantTester

class	MultibodyTreeElement< ElementType< T >, ElementIndexType >
	A class representing an element or component of a MultibodyTree. More...

class	OrientationConstraint
	Constrains that the angle difference θ between the orientation of frame A and the orientation of frame B to satisfy θ ≤ θ_bound. More...

class	PackageMap
	Maps ROS package names to their full path on the local file system. More...

class	Parser
	Parses SDF and URDF input files into a MultibodyPlant and (optionally) a SceneGraph. More...

class	PointPairContactInfo
	A class containing information regarding contact response between two bodies including: More...

class	PositionConstraint
	Constrains the position of a point Q, rigidly attached to a frame B, to be within a bounding box measured and expressed in frame A. More...

class	PrismaticJoint
	This Joint allows two bodies to translate relative to one another along a common axis. More...

class	RevoluteJoint
	This Joint allows two bodies to rotate relatively to one another around a common axis. More...

class	RevoluteSpring
	This ForceElement models a torsional spring attached to a RevoluteJoint and applies a torque to that joint. More...

class	RigidBody
	The term rigid body implies that the deformations of the body under consideration are so small that they have no significant effect on the overall motions of the body and therefore deformations can be neglected. More...

class	RotationalInertia
	This class helps describe the mass distribution (inertia properties) of a body or composite body about a particular point. More...

class	SpatialAcceleration
	This class is used to represent a spatial acceleration that combines rotational (angular acceleration) and translational (linear acceleration) components. More...

class	SpatialForce
	This class is used to represent a spatial force (also called a wrench) that combines both rotational (torque) and translational force components. More...

class	SpatialInertia
	This class represents the physical concept of a Spatial Inertia. More...

class	SpatialMomentum
	This class is used to represent the spatial momentum of a particle, system of particles or body (whether rigid or soft.) The linear momentum `l_NS` of a system of particles S in a reference frame N is defined by: More...

class	SpatialVector
	This class is used to represent physical quantities that correspond to spatial vectors such as spatial velocities, spatial accelerations and spatial forces. More...

class	SpatialVelocity
	This class is used to represent a spatial velocity (also called a twist) that combines rotational (angular) and translational (linear) velocity components. More...

class	TwoFreeBodiesConstraintTest

class	TwoFreeSpheresTest

class	UniformGravityFieldElement
	This ForceElement allows modeling the effect of a uniform gravity field as felt by bodies on the surface of the Earth. More...

class	UnitInertia
	This class is used to represent rotational inertias for unit mass bodies. More...

class	WeldJoint
	This Joint fixes the relative pose between two frames as if "welding" them together. More...

Typedefs
using	MinimumDistancePenaltyFunction = std::function< void(double x, double penalty, double dpenalty_dx)>
	Computes the penalty function γ(x) and its derivatives dγ(x)/dx, where x is the scaled (and shifted) signed distance (x = distance / distance_threshold. More...

template<typename T >
using	AccelerationKinematicsCache = internal::AccelerationKinematicsCache< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	ArticulatedBodyInertiaCache = internal::ArticulatedBodyInertiaCache< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	Mobilizer = internal::Mobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T , int A, int B>
using	MobilizerImpl = internal::MobilizerImpl< T, A, B >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	MultibodyTree = internal::MultibodyTree< T >
	Deprecated public alias to internal `MultibodyTree`. More...

using	FrameIndex = TypeSafeIndex< class FrameTag >
	Type used to identify frames by index in a multibody tree system. More...

using	BodyIndex = TypeSafeIndex< class BodyTag >
	Type used to identify bodies by index in a multibody tree system. More...

typedef internal::MobilizerIndex	MobilizerIndex
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::BodyNodeIndex	BodyNodeIndex
	WARNING: This will be removed on or around 2019/03/01. More...

using	ForceElementIndex = TypeSafeIndex< class ForceElementTag >
	Type used to identify force elements by index within a multibody tree system. More...

using	JointIndex = TypeSafeIndex< class JointElementTag >
	Type used to identify joints by index within a multibody tree system. More...

using	JointActuatorIndex = TypeSafeIndex< class JointActuatorElementTag >
	Type used to identify actuators by index within a multibody tree system. More...

using	ModelInstanceIndex = TypeSafeIndex< class ModelInstanceTag >
	Type used to identify model instances by index within a multibody tree system. More...

template<typename T >
using	MultibodyTreeSystem = internal::MultibodyTreeSystem< T >
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::BodyTopology	BodyTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::FrameTopology	FrameTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::MobilizerTopology	MobilizerTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::ForceElementTopology	ForceElementTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::JointActuatorTopology	JointActuatorTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::BodyNodeTopology	BodyNodeTopology
	WARNING: This will be removed on or around 2019/03/01. More...

typedef internal::MultibodyTreeTopology	MultibodyTreeTopology
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	PositionKinematicsCache = internal::PositionKinematicsCache< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	PrismaticMobilizer = internal::PrismaticMobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	QuaternionFloatingMobilizer = internal::QuaternionFloatingMobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	RevoluteMobilizer = internal::RevoluteMobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	SpaceXYZMobilizer = internal::SpaceXYZMobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	VelocityKinematicsCache = internal::VelocityKinematicsCache< T >
	WARNING: This will be removed on or around 2019/03/01. More...

template<typename T >
using	WeldMobilizer = internal::WeldMobilizer< T >
	WARNING: This will be removed on or around 2019/03/01. More...

Enumerations
enum	ImplicitStribeckSolverResult { kSuccess = 0, kMaxIterationsReached = 1, kLinearSolverFailed = 2 }
	The result from ImplicitStribeckSolver::SolveWithGuess() used to report the success or failure of the solver. More...

enum	JacobianWrtVariable { kQDot, kV }
	Enumeration that distinguishes between flavors of Jacobians based on the variable with respect to which they are taken. More...

Functions
void	ApproximateBoundedNormByLinearConstraints (const Eigen::Ref< const Vector3< symbolic::Expression >> &x, double c, solvers::MathematicalProgram *prog)

template<typename T >
lcmt_viewer_load_robot	CreateLoadRobotMessage (const RigidBodyTree< double > &tree)
	Creates and returns an lcmt_viewer_load_robot message containing the visual geometries from the provided RigidBodyTree. More...

template lcmt_viewer_load_robot	CreateLoadRobotMessage< double > (const RigidBodyTree< double > &tree)

void	AddFlatTerrainToWorld (RigidBodyTreed *tree, double box_size=1000, double box_depth=10)
	Adds a box-shaped terrain to `tree`. More...

	TEST_F (RigidBodyTreeKinematicsTests, TestDoKinematicWithValidCache)

	TEST_F (RigidBodyTreeKinematicsTests, TestDoKinematicWithBadCache1)

	TEST_F (RigidBodyTreeKinematicsTests, TestDoKinematicWithBadCache2)

	TEST_F (AcrobotTests, PoseTests)

	TEST_F (AcrobotTests, SpatialVelocityTests)

	TEST_F (RBTDifferentialKinematicsHelperTest, RPYPoseTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, RPYTwistInWorldAlignedBodyTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, RPYJacobianTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, RPYJacobianDotTimeVTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, QuatPoseTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, QuatTwistInWorldAlignedBodyTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, QuatJacobianTest)

	TEST_F (RBTDifferentialKinematicsHelperTest, QuatJacobianDotTimeVTest)

void	ExponentiallySmoothedHingeLoss (double x, double penalty, double dpenalty_dx)
	A hinge loss function smoothed by exponential function. More...

void	QuadraticallySmoothedHingeLoss (double x, double penalty, double dpenalty_dx)
	A linear hinge loss, smoothed with a quadratic loss near the origin. More...

Eigen::Quaterniond	Vector4ToQuaternion (const Eigen::Ref< const Eigen::Vector4d > &q)

	GTEST_TEST (InverseKinematicsTest, ConstructorWithJointLimits)

	TEST_F (TwoFreeBodiesTest, PositionConstraint)

	TEST_F (TwoFreeBodiesTest, OrientationConstraint)

	TEST_F (TwoFreeBodiesTest, GazeTargetConstraint)

	TEST_F (TwoFreeBodiesTest, AngleBetweenVectorsConstraint)

	TEST_F (TwoFreeSpheresTest, MinimalDistanceConstraintTest)

template<typename T >
void	AddTwoFreeBodiesToPlant (MultibodyPlant< T > *model)

template<typename T >
std::unique_ptr< MultibodyPlant< T > >	ConstructTwoFreeBodiesPlant ()
	Constructs a MultibodyPlant consisting of two free bodies. More...

std::unique_ptr< MultibodyPlant< double > >	ConstructIiwaPlant (const std::string &file_path, double time_step)
	Constructs a MultibodyPlant consisting of an Iiwa robot. More...

Eigen::Vector4d	QuaternionToVectorWxyz (const Eigen::Quaterniond &q)
	Convert an Eigen::Quaternion to a vector 4d in the order (w, x, y, z). More...

template std::unique_ptr< MultibodyPlant< double > >	ConstructTwoFreeBodiesPlant< double > ()

template std::unique_ptr< MultibodyPlant< AutoDiffXd > >	ConstructTwoFreeBodiesPlant< AutoDiffXd > ()

template<typename DerivedA , typename DerivedB >
std::enable_if< std::is_same< typename DerivedA::Scalar, typename DerivedB::Scalar >::value &&std::is_same< typename DerivedA::Scalar, AutoDiffXd >::value >::type	CompareAutoDiffVectors (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedB > &b, double tol)
	Compares if two eigen matrices of AutoDiff have the same values and gradients. More...

AutoDiffVecXd	EvalMinimumDistanceConstraintAutoDiff (const systems::Context< AutoDiffXd > &context, const MultibodyPlant< AutoDiffXd > &plant, double minimum_distance, PenaltyType penalty_type)

void	CheckMinimumDistanceConstraintEval (const MinimumDistanceConstraint &constraint, const Eigen::Ref< const AutoDiffVecXd > &x_autodiff, const MultibodyPlant< AutoDiffXd > &plant_autodiff, systems::Context< AutoDiffXd > *context_autodiff, double tol, PenaltyType penalty_type)

template<typename T >
Vector3< T >	ComputeCollisionSphereCenterPosition (const Vector3< T > &p_WB, const Quaternion< T > &quat_WB, const Eigen::Isometry3d &X_BS)

	TEST_F (TwoFreeSpheresMinimumDistanceTest, ExponentialPenalty)

	TEST_F (TwoFreeSpheresMinimumDistanceTest, QuadraticallySmoothedHingePenalty)

	GTEST_TEST (MinimumDistanceConstraintTest, MultibodyPlantWithouthGeometrySource)

	TEST_F (TwoFreeSpheresTest, NonpositiveMinimalDistance)

template<typename T >
SpatialForce< T >	operator+ (const SpatialForce< T > &F1_Sp_E, const SpatialForce< T > &F2_Sp_E)
	Computes the resultant spatial force as the addition of two spatial forces `F1_Sp_E` and `F2_Sp_E` on a same system or body S, at the same point P and expressed in the same frame E. More...

template<typename T >
SpatialMomentum< T >	operator+ (const SpatialMomentum< T > &L1_NSp_E, const SpatialMomentum< T > &L2_NSp_E)
	Computes the resultant spatial momentum as the addition of two spatial momenta `L1_NSp_E` and `L2_NSp_E` on a same system S, about the same point P and expressed in the same frame E. More...

template<typename T >
SpatialVelocity< T >	operator+ (const SpatialVelocity< T > &V_MAb_E, const SpatialVelocity< T > &V_AB_E)
	Performs the addition of two spatial velocities. More...

template<typename T >
SpatialVelocity< T >	operator- (const SpatialVelocity< T > &V_MB_E, const SpatialVelocity< T > &V_MAb_E)
	The addition of two spatial velocities relates to the composition of the spatial velocities for two frames given we know the relative spatial velocity between them, see operator+(const SpatialVelocity<T>&, const SpatialVelocity<T>&) for further details. More...

std::ostream &	operator<< (std::ostream &out, const PackageMap &package_map)

systems::lcm::LcmPublisherSystem *	ConnectContactResultsToDrakeVisualizer (systems::DiagramBuilder< double > builder, const MultibodyPlant< double > &multibody_plant, lcm::DrakeLcmInterface lcm=nullptr)
	Extends a Diagram with the required components to publish contact results to drake_visualizer. More...

systems::lcm::LcmPublisherSystem *	ConnectContactResultsToDrakeVisualizer (systems::DiagramBuilder< double > builder, const MultibodyPlant< double > &multibody_plant, const systems::OutputPort< double > &contact_results_port, lcm::DrakeLcmInterface lcm=nullptr)
	Implements ConnectContactResultsToDrakeVisualizer, but using `contact_results_port` to explicitly specify the output port used to get contact results for `multibody_plant`. More...

template<typename T >
CoulombFriction< T >	CalcContactFrictionFromSurfaceProperties (const CoulombFriction< T > &surface_properties1, const CoulombFriction< T > &surface_properties2)
	Given the surface properties of two different surfaces, this method computes the Coulomb's law coefficients of friction characterizing the interaction by friction of the given surface pair. More...

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

template AddMultibodyPlantSceneGraphResult< double >	AddMultibodyPlantSceneGraph (systems::DiagramBuilder< double > *builder, std::unique_ptr< MultibodyPlant< double >> plant, std::unique_ptr< geometry::SceneGraph< double >> scene_graph)

template AddMultibodyPlantSceneGraphResult< AutoDiffXd >	AddMultibodyPlantSceneGraph (systems::DiagramBuilder< AutoDiffXd > *builder, std::unique_ptr< MultibodyPlant< AutoDiffXd >> plant, std::unique_ptr< geometry::SceneGraph< AutoDiffXd >> scene_graph)

BodyIndex	world_index ()
	For every MultibodyTree the world body always has this unique index and it is always zero. More...

ModelInstanceIndex	world_model_instance ()
	Returns the model instance containing the world body. More...

ModelInstanceIndex	default_model_instance ()
	Returns the model instance which contains all tree elements with no explicit model instance specified. More...

Drake joint comparison methods.
These methods compare joint `original` with joint `clone`. Since these methods are intended to compare a clone, an exact match is performed. This method will only return `true` if the provided `clone` joint is exactly the same as the provided `original` joint.
bool	CompareDrakeJointToClone (const DrakeJoint &original, const DrakeJoint &clone)

bool	CompareFixedJointToClone (const FixedJoint &original, const FixedJoint &other)

bool	CompareHelicalJointToClone (const HelicalJoint &original, const HelicalJoint &clone)

bool	ComparePrismaticJointToClone (const PrismaticJoint &original, const PrismaticJoint &clone)

bool	CompareQuaternionBallJointToClone (const QuaternionBallJoint &original, const QuaternionBallJoint &clone)

bool	CompareQuaternionFloatingJointToClone (const QuaternionFloatingJoint &original, const QuaternionFloatingJoint &clone)

bool	CompareRevoluteJointToClone (const RevoluteJoint &original, const RevoluteJoint &clone)

bool	CompareRollPitchYawFloatingJointToClone (const RollPitchYawFloatingJoint &original, const RollPitchYawFloatingJoint &clone)

template<typename Derived >
bool	CompareFixedAxisOneDofJointToClone (const FixedAxisOneDoFJoint< Derived > &original, const FixedAxisOneDoFJoint< Derived > &clone)

Variables
const double	kEps = std::numeric_limits<double>::epsilon()

Typedef Documentation

◆ AccelerationKinematicsCache

using AccelerationKinematicsCache = internal::AccelerationKinematicsCache<T>

WARNING: This will be removed on or around 2019/03/01.

◆ ArticulatedBodyInertiaCache

using ArticulatedBodyInertiaCache = internal::ArticulatedBodyInertiaCache<T>

WARNING: This will be removed on or around 2019/03/01.

◆ BodyIndex

using BodyIndex = TypeSafeIndex<class BodyTag>

Type used to identify bodies by index in a multibody tree system.

◆ BodyNodeIndex

typedef internal::BodyNodeIndex BodyNodeIndex

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ BodyNodeTopology

typedef internal::BodyNodeTopology BodyNodeTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ BodyTopology

typedef internal::BodyTopology BodyTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ ForceElementIndex

using ForceElementIndex = TypeSafeIndex<class ForceElementTag>

Type used to identify force elements by index within a multibody tree system.

◆ ForceElementTopology

typedef internal::ForceElementTopology ForceElementTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ FrameIndex

using FrameIndex = TypeSafeIndex<class FrameTag>

Type used to identify frames by index in a multibody tree system.

◆ FrameTopology

typedef internal::FrameTopology FrameTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ JointActuatorIndex

using JointActuatorIndex = TypeSafeIndex<class JointActuatorElementTag>

Type used to identify actuators by index within a multibody tree system.

◆ JointActuatorTopology

typedef internal::JointActuatorTopology JointActuatorTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ JointIndex

using JointIndex = TypeSafeIndex<class JointElementTag>

Type used to identify joints by index within a multibody tree system.

◆ MinimumDistancePenaltyFunction

using MinimumDistancePenaltyFunction = std::function<void(double x, double* penalty, double* dpenalty_dx)>

Computes the penalty function γ(x) and its derivatives dγ(x)/dx, where x is the scaled (and shifted) signed distance (x = distance / distance_threshold.

1). This function is used by MinimumDistanceConstraint, in which we impose the constraint that the pairwise distance are all no smaller than a distance threshold. We do this with the constraint ∑ᵢ γ(dᵢ / distance_threshold - 1) = 0 where dᵢ is the signed distance between the i'th pair of geometries.

◆ Mobilizer

using Mobilizer = internal::Mobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

◆ MobilizerImpl

using MobilizerImpl = internal::MobilizerImpl<T, A, B>

WARNING: This will be removed on or around 2019/03/01.

◆ MobilizerIndex

typedef internal::MobilizerIndex MobilizerIndex

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ MobilizerTopology

typedef internal::MobilizerTopology MobilizerTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ ModelInstanceIndex

using ModelInstanceIndex = TypeSafeIndex<class ModelInstanceTag>

Type used to identify model instances by index within a multibody tree system.

◆ MultibodyTree

using MultibodyTree = internal::MultibodyTree<T>

Deprecated public alias to internal MultibodyTree.

Warning: This alias will be removed 2019-03-01.

◆ MultibodyTreeSystem

using MultibodyTreeSystem = internal::MultibodyTreeSystem<T>

WARNING: This will be removed on or around 2019/03/01.

◆ MultibodyTreeTopology

typedef internal::MultibodyTreeTopology MultibodyTreeTopology

WARNING: This will be removed on or around 2019/03/01.

(Deprecated.)

Deprecated:: "This public alias is deprecated, and will be removed around 2019/03/01."

◆ PositionKinematicsCache

using PositionKinematicsCache = internal::PositionKinematicsCache<T>

WARNING: This will be removed on or around 2019/03/01.

◆ PrismaticMobilizer

using PrismaticMobilizer = internal::PrismaticMobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

◆ QuaternionFloatingMobilizer

using QuaternionFloatingMobilizer = internal::QuaternionFloatingMobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

◆ RevoluteMobilizer

using RevoluteMobilizer = internal::RevoluteMobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

◆ SpaceXYZMobilizer

using SpaceXYZMobilizer = internal::SpaceXYZMobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

◆ VelocityKinematicsCache

using VelocityKinematicsCache = internal::VelocityKinematicsCache<T>

WARNING: This will be removed on or around 2019/03/01.

◆ WeldMobilizer

using WeldMobilizer = internal::WeldMobilizer<T>

WARNING: This will be removed on or around 2019/03/01.

Enumeration Type Documentation

◆ ImplicitStribeckSolverResult

enum ImplicitStribeckSolverResult

strong

The result from ImplicitStribeckSolver::SolveWithGuess() used to report the success or failure of the solver.

Enumerator

kSuccess

Successful computation.

kMaxIterationsReached

The maximum number of iterations was reached.

kLinearSolverFailed

The linear solver used within the Newton-Raphson loop failed.

This might be caused by a divergent iteration that led to an invalid Jacobian matrix.

◆ JacobianWrtVariable

enum JacobianWrtVariable

strong

Enumeration that distinguishes between flavors of Jacobians based on the variable with respect to which they are taken.

Enumerator

kQDot

kV

J = ∂V/∂q̇

J = ∂V/∂v

Function Documentation

◆ AddFlatTerrainToWorld()

void AddFlatTerrainToWorld	(	RigidBodyTreed *	tree,
		double	box_size = `1000`,
		double	box_depth = `10`
	)

Adds a box-shaped terrain to tree.

This directly modifies the existing world rigid body within tree and thus does not need to return a model_instance_id value.

Two opposite corners of the resulting axis-aligned box are: (box_size / 2, box_size / 2, 0) and (-box_size / 2, -box_size / 2, -box_depth).

Parameters

[in]	tree	The RigidBodyTreed to which to add the terrain.
[in]	box_size	The length and width of the terrain aligned with the world's X and Y axes.
[in]	box_depth	The depth of the terrain aligned with the world's Z axis. Note that regardless of how deep the terrain is, the top surface of the terrain will be at Z = 0.

◆ AddMultibodyPlantSceneGraph() [1/3]

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

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

Parameters

[in,out]	builder	Builder to add to.
[in]	plant	(optional) Constructed plant (e.g. for using a discrete plant). By default, a continuous plant is used.
[in]	scene_graph	(optional) Constructed scene graph. If none is provided, one will be created and used.

Returns: Pair of the registered plant and scene graph.

Precondition: builder must be non-null.

Recommended usages:

Assign to a MultibodyPlant reference (ignoring the SceneGraph):

MultibodyPlant<double>& plant = AddMultibodyPlantSceneGraph(&builder);

plant.DoFoo(...);

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

Assign to auto, and use the named public fields:

auto items = AddMultibodyPlantSceneGraph(&builder);
items.plant.DoFoo(...);
items.scene_graph.DoBar(...);

or

auto items = AddMultibodyPlantSceneGraph(&builder);
MultibodyPlant<double>& plant = items.plant;
SceneGraph<double>& scene_graph = items.scene_graph;
...
plant.DoFoo(...);
scene_graph.DoBar(...);

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

Assign to already-declared pointer variables:

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

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

◆ AddMultibodyPlantSceneGraph() [2/3]

template AddMultibodyPlantSceneGraphResult<double> drake::multibody::AddMultibodyPlantSceneGraph	(	systems::DiagramBuilder< double > *	builder,
		std::unique_ptr< MultibodyPlant< double >>	plant,
		std::unique_ptr< geometry::SceneGraph< double >>	scene_graph
	)

◆ AddMultibodyPlantSceneGraph() [3/3]

template AddMultibodyPlantSceneGraphResult<AutoDiffXd> drake::multibody::AddMultibodyPlantSceneGraph	(	systems::DiagramBuilder< AutoDiffXd > *	builder,
		std::unique_ptr< MultibodyPlant< AutoDiffXd >>	plant,
		std::unique_ptr< geometry::SceneGraph< AutoDiffXd >>	scene_graph
	)

◆ AddTwoFreeBodiesToPlant()

void drake::multibody::AddTwoFreeBodiesToPlant ( MultibodyPlant< T > * model )

◆ ApproximateBoundedNormByLinearConstraints()

void drake::multibody::ApproximateBoundedNormByLinearConstraints	(	const Eigen::Ref< const Vector3< symbolic::Expression >> &	x,
		double	c,
		solvers::MathematicalProgram *	prog
	)

◆ CalcContactFrictionFromSurfaceProperties()

CoulombFriction<T> drake::multibody::CalcContactFrictionFromSurfaceProperties	(	const CoulombFriction< T > &	surface_properties1,
		const CoulombFriction< T > &	surface_properties2
	)

Given the surface properties of two different surfaces, this method computes the Coulomb's law coefficients of friction characterizing the interaction by friction of the given surface pair.

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

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

  μ = 2μₘμₙ/(μₘ + μₙ)

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

Parameters

[in]	surface_properties1	Surface properties for surface 1. Specified as an individual set of Coulomb's law coefficients of friction.
[in]	surface_properties2	Surface properties for surface 2. Specified as an individual set of Coulomb's law coefficients of friction.

Returns: the combined friction coefficients for the interacting surfaces.

◆ CheckMinimumDistanceConstraintEval()

void drake::multibody::CheckMinimumDistanceConstraintEval	(	const MinimumDistanceConstraint &	constraint,
		const Eigen::Ref< const AutoDiffVecXd > &	x_autodiff,
		const MultibodyPlant< AutoDiffXd > &	plant_autodiff,
		systems::Context< AutoDiffXd > *	context_autodiff,
		double	tol,
		PenaltyType	penalty_type
	)

◆ CompareAutoDiffVectors()

std::enable_if< std::is_same<typename DerivedA::Scalar, typename DerivedB::Scalar>::value && std::is_same<typename DerivedA::Scalar, AutoDiffXd>::value>::type drake::multibody::CompareAutoDiffVectors	(	const Eigen::MatrixBase< DerivedA > &	a,
		const Eigen::MatrixBase< DerivedB > &	b,
		double	tol
	)

Compares if two eigen matrices of AutoDiff have the same values and gradients.

◆ CompareDrakeJointToClone()

bool CompareDrakeJointToClone	(	const DrakeJoint &	original,
		const DrakeJoint &	clone
	)

◆ CompareFixedAxisOneDofJointToClone()

bool drake::multibody::CompareFixedAxisOneDofJointToClone	(	const FixedAxisOneDoFJoint< Derived > &	original,
		const FixedAxisOneDoFJoint< Derived > &	clone
	)

◆ CompareFixedJointToClone()

bool CompareFixedJointToClone	(	const FixedJoint &	original,
		const FixedJoint &	other
	)

◆ CompareHelicalJointToClone()

bool CompareHelicalJointToClone	(	const HelicalJoint &	original,
		const HelicalJoint &	clone
	)

◆ ComparePrismaticJointToClone()

bool ComparePrismaticJointToClone	(	const PrismaticJoint &	original,
		const PrismaticJoint &	clone
	)

◆ CompareQuaternionBallJointToClone()

bool CompareQuaternionBallJointToClone	(	const QuaternionBallJoint &	original,
		const QuaternionBallJoint &	clone
	)

◆ CompareQuaternionFloatingJointToClone()

bool CompareQuaternionFloatingJointToClone	(	const QuaternionFloatingJoint &	original,
		const QuaternionFloatingJoint &	clone
	)

◆ CompareRevoluteJointToClone()

bool CompareRevoluteJointToClone	(	const RevoluteJoint &	original,
		const RevoluteJoint &	clone
	)

◆ CompareRollPitchYawFloatingJointToClone()

bool CompareRollPitchYawFloatingJointToClone	(	const RollPitchYawFloatingJoint &	original,
		const RollPitchYawFloatingJoint &	clone
	)

◆ ComputeCollisionSphereCenterPosition()

Vector3<T> drake::multibody::ComputeCollisionSphereCenterPosition	(	const Vector3< T > &	p_WB,
		const Quaternion< T > &	quat_WB,
		const Eigen::Isometry3d &	X_BS
	)

◆ ConstructIiwaPlant()

std::unique_ptr< MultibodyPlant< double > > ConstructIiwaPlant	(	const std::string &	file_path,
		double	time_step
	)

Constructs a MultibodyPlant consisting of an Iiwa robot.

◆ ConstructTwoFreeBodiesPlant()

std::unique_ptr< MultibodyPlant< T > > ConstructTwoFreeBodiesPlant ( )

Constructs a MultibodyPlant consisting of two free bodies.

◆ ConstructTwoFreeBodiesPlant< AutoDiffXd >()

template std::unique_ptr<MultibodyPlant<AutoDiffXd> > drake::multibody::ConstructTwoFreeBodiesPlant< AutoDiffXd > ( )

◆ ConstructTwoFreeBodiesPlant< double >()

template std::unique_ptr<MultibodyPlant<double> > drake::multibody::ConstructTwoFreeBodiesPlant< double > ( )

◆ CreateLoadRobotMessage()

lcmt_viewer_load_robot CreateLoadRobotMessage ( const RigidBodyTree< double > & tree )

Creates and returns an lcmt_viewer_load_robot message containing the visual geometries from the provided RigidBodyTree.

Note that this includes any visual geometries attached to the world body.

Instantiated templates for the following ScalarTypes are provided:

double

They are already available to link against in the containing library.

◆ CreateLoadRobotMessage< double >()

template lcmt_viewer_load_robot drake::multibody::CreateLoadRobotMessage< double > ( const RigidBodyTree< double > & tree )

◆ default_model_instance()

ModelInstanceIndex drake::multibody::default_model_instance ( )

Returns the model instance which contains all tree elements with no explicit model instance specified.

◆ EvalMinimumDistanceConstraintAutoDiff()

AutoDiffVecXd drake::multibody::EvalMinimumDistanceConstraintAutoDiff	(	const systems::Context< AutoDiffXd > &	context,
		const MultibodyPlant< AutoDiffXd > &	plant,
		double	minimum_distance,
		PenaltyType	penalty_type
	)

◆ ExponentiallySmoothedHingeLoss()

void ExponentiallySmoothedHingeLoss	(	double	x,
		double *	penalty,
		double *	dpenalty_dx
	)

A hinge loss function smoothed by exponential function.

This loss function is differentiable everywhere. The fomulation is described in section II.C of [2] The penalty is

       ⎧ 0            if x ≥ 0
γ(x) = ⎨
       ⎩  -x exp(1/x) if x < 0.

[2] "Whole-body Motion Planning with Centroidal Dynamics and Full Kinematics" by Hongkai Dai, Andres Valenzuela and Russ Tedrake, IEEE-RAS International Conference on Humanoid Robots, 2014.

◆ GTEST_TEST() [1/2]

drake::multibody::GTEST_TEST	(	InverseKinematicsTest	,
		ConstructorWithJointLimits
	)

◆ GTEST_TEST() [2/2]

drake::multibody::GTEST_TEST	(	MinimumDistanceConstraintTest	,
		MultibodyPlantWithouthGeometrySource
	)

◆ operator+() [1/3]

SpatialForce<T> drake::multibody::operator+	(	const SpatialForce< T > &	F1_Sp_E,
		const SpatialForce< T > &	F2_Sp_E
	)

Computes the resultant spatial force as the addition of two spatial forces F1_Sp_E and F2_Sp_E on a same system or body S, at the same point P and expressed in the same frame E.

Return values

Fr_Sp_E The resultant spatial force on system or body S from combining F1_Sp_E and F2_Sp_E, applied at the same point P and in the same expressed-in frame E as the operand spatial forces.

◆ operator+() [2/3]

SpatialMomentum<T> drake::multibody::operator+	(	const SpatialMomentum< T > &	L1_NSp_E,
		const SpatialMomentum< T > &	L2_NSp_E
	)

Computes the resultant spatial momentum as the addition of two spatial momenta L1_NSp_E and L2_NSp_E on a same system S, about the same point P and expressed in the same frame E.

Return values

Lc_NSp_E The combined spatial momentum of system S from combining L1_NSp_E and L2_NSp_E, applied about the same point P, and in the same expressed-in frame E as the operand spatial momenta.

◆ operator+() [3/3]

SpatialVelocity<T> drake::multibody::operator+	(	const SpatialVelocity< T > &	V_MAb_E,
		const SpatialVelocity< T > &	V_AB_E
	)

Performs the addition of two spatial velocities.

This operator returns the spatial velocity that results from adding the operands as if they were 6-dimensional vectors. In other words, the resulting spatial velocity contains a rotational component which is the 3-dimensional addition of the operand's rotational components and a translational component which is the 3-dimensional addition of the operand's translational components.

The addition of two spatial velocities has a clear physical meaning but can only be performed if the operands meet strict conditions. In addition the the usual requirement of common expressed-in frames, both spatial velocities must be for frames with the same origin point. The general idea is that if frame A has a spatial velocity with respect to M, and frame B has a spatial velocity with respect to A, we want to "compose" them so that we get frame B's spatial velocity in M. But that can't be done directly since frames A and B don't have the same origin. So:

Given the velocity V_MA_E of a frame A in a measured-in frame M, and the velocity V_AB_E of a frame B measured in frame A (both expressed in a common frame E), we can calculate V_MB_E as their sum after shifting A's velocity to point Bo:

  V_MB_E = V_MA_E.Shift(p_AB_E) + V_AB_E

where p_AB_E is the position vector from A's origin to B's origin, expressed in E. This shift can also be thought of as yielding the spatial velocity of a new frame Ab, which is an offset frame rigidly aligned with A, but with its origin shifted to B's origin:

  V_MAb_E = V_MA_E.Shift(p_AB_E)
  V_MB_E = V_MAb_E + V_AB_E

The addition in the last expression is what is carried out by this operator; the caller must have already performed the necessary shift.

◆ operator-()

SpatialVelocity<T> drake::multibody::operator-	(	const SpatialVelocity< T > &	V_MB_E,
		const SpatialVelocity< T > &	V_MAb_E
	)

The addition of two spatial velocities relates to the composition of the spatial velocities for two frames given we know the relative spatial velocity between them, see operator+(const SpatialVelocity<T>&, const SpatialVelocity<T>&) for further details.

Mathematically, operator-(v1, v2) is equivalent ot operator+(v1, -v2).

Physically, the subtraction operation allow us to compute the relative velocity between two frames. As an example, consider having the the spatial velocities V_MA and V_MB of two frames A and B respectively measured in the same frame M. The velocity of B in A can be obtained as:

  V_AB_E = V_MB_E - V_MAb_E = V_AB_E = V_MB_E - V_MA_E.Shift(p_AB_E)

where we have expressed all quantities in a common frame E. Notice that, as explained in the documentation for operator+(const SpatialVelocity<T>&, const SpatialVelocity<T>&) a shift operation with SpatialVelocity::Shift() operation is needed.

◆ operator<<()

std::ostream& drake::multibody::operator<<	(	std::ostream &	out,
		const PackageMap &	package_map
	)

◆ QuadraticallySmoothedHingeLoss()

void QuadraticallySmoothedHingeLoss	(	double	x,
		double *	penalty,
		double *	dpenalty_dx
	)

A linear hinge loss, smoothed with a quadratic loss near the origin.

The formulation is in equation (6) of [1]. The penalty is

       ⎧  0        if x ≥ 0
γ(x) = ⎨  x²/2     if -1 < x < 0
       ⎩  -0.5 - x if x ≤ -1.

[1] "Loss Functions for Preference Levels: Regression with Discrete Ordered Labels." by Jason Rennie and Nathan Srebro, Proceedings of IJCAI multidisciplinary workshop on Advances in preference handling.

◆ QuaternionToVectorWxyz()

Eigen::Vector4d QuaternionToVectorWxyz ( const Eigen::Quaterniond & q )

Convert an Eigen::Quaternion to a vector 4d in the order (w, x, y, z).

◆ TEST_F() [1/21]

drake::multibody::TEST_F	(	RigidBodyTreeKinematicsTests	,
		TestDoKinematicWithValidCache
	)

◆ TEST_F() [2/21]

drake::multibody::TEST_F	(	RigidBodyTreeKinematicsTests	,
		TestDoKinematicWithBadCache1
	)

◆ TEST_F() [3/21]

drake::multibody::TEST_F	(	RigidBodyTreeKinematicsTests	,
		TestDoKinematicWithBadCache2
	)

◆ TEST_F() [4/21]

drake::multibody::TEST_F	(	TwoFreeBodiesTest	,
		PositionConstraint
	)

◆ TEST_F() [5/21]

drake::multibody::TEST_F	(	TwoFreeBodiesTest	,
		OrientationConstraint
	)

◆ TEST_F() [6/21]

drake::multibody::TEST_F	(	TwoFreeBodiesTest	,
		GazeTargetConstraint
	)

◆ TEST_F() [7/21]

drake::multibody::TEST_F	(	TwoFreeBodiesTest	,
		AngleBetweenVectorsConstraint
	)

◆ TEST_F() [8/21]

drake::multibody::TEST_F	(	AcrobotTests	,
		PoseTests
	)

◆ TEST_F() [9/21]

drake::multibody::TEST_F	(	AcrobotTests	,
		SpatialVelocityTests
	)

◆ TEST_F() [10/21]

drake::multibody::TEST_F	(	TwoFreeSpheresTest	,
		MinimalDistanceConstraintTest
	)

◆ TEST_F() [11/21]

drake::multibody::TEST_F	(	TwoFreeSpheresMinimumDistanceTest	,
		ExponentialPenalty
	)

◆ TEST_F() [12/21]

drake::multibody::TEST_F	(	TwoFreeSpheresMinimumDistanceTest	,
		QuadraticallySmoothedHingePenalty
	)

◆ TEST_F() [13/21]

drake::multibody::TEST_F	(	TwoFreeSpheresTest	,
		NonpositiveMinimalDistance
	)

◆ TEST_F() [14/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		RPYPoseTest
	)

◆ TEST_F() [15/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		RPYTwistInWorldAlignedBodyTest
	)

◆ TEST_F() [16/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		RPYJacobianTest
	)

◆ TEST_F() [17/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		RPYJacobianDotTimeVTest
	)

◆ TEST_F() [18/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		QuatPoseTest
	)

◆ TEST_F() [19/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		QuatTwistInWorldAlignedBodyTest
	)

◆ TEST_F() [20/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		QuatJacobianTest
	)

◆ TEST_F() [21/21]

drake::multibody::TEST_F	(	RBTDifferentialKinematicsHelperTest	,
		QuatJacobianDotTimeVTest
	)

◆ Vector4ToQuaternion()

Eigen::Quaterniond drake::multibody::Vector4ToQuaternion ( const Eigen::Ref< const Eigen::Vector4d > & q )

◆ world_index()

BodyIndex drake::multibody::world_index ( )

For every MultibodyTree the world body always has this unique index and it is always zero.

◆ world_model_instance()

ModelInstanceIndex drake::multibody::world_model_instance ( )

Returns the model instance containing the world body.

For every MultibodyTree the world body always has this unique model instance and it is always zero (as described in #3088).

Variable Documentation

◆ kEps

const double kEps = std::numeric_limits<double>::epsilon()

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ AccelerationKinematicsCache

◆ ArticulatedBodyInertiaCache

◆ BodyIndex

◆ BodyNodeIndex

◆ BodyNodeTopology

◆ BodyTopology

◆ ForceElementIndex

◆ ForceElementTopology

◆ FrameIndex

◆ FrameTopology

◆ JointActuatorIndex

◆ JointActuatorTopology

◆ JointIndex

◆ MinimumDistancePenaltyFunction

◆ Mobilizer

◆ MobilizerImpl

◆ MobilizerIndex

◆ MobilizerTopology

◆ ModelInstanceIndex

◆ MultibodyTree

◆ MultibodyTreeSystem

◆ MultibodyTreeTopology

◆ PositionKinematicsCache

◆ PrismaticMobilizer

◆ QuaternionFloatingMobilizer

◆ RevoluteMobilizer

◆ SpaceXYZMobilizer

◆ VelocityKinematicsCache

◆ WeldMobilizer

Enumeration Type Documentation

◆ ImplicitStribeckSolverResult

◆ JacobianWrtVariable

Function Documentation

◆ AddFlatTerrainToWorld()

◆ AddMultibodyPlantSceneGraph() [1/3]

◆ AddMultibodyPlantSceneGraph() [2/3]

◆ AddMultibodyPlantSceneGraph() [3/3]

◆ AddTwoFreeBodiesToPlant()

◆ ApproximateBoundedNormByLinearConstraints()

◆ CalcContactFrictionFromSurfaceProperties()

◆ CheckMinimumDistanceConstraintEval()

◆ CompareAutoDiffVectors()

◆ CompareDrakeJointToClone()

◆ CompareFixedAxisOneDofJointToClone()

◆ CompareFixedJointToClone()

◆ CompareHelicalJointToClone()

◆ ComparePrismaticJointToClone()

◆ CompareQuaternionBallJointToClone()

◆ CompareQuaternionFloatingJointToClone()

◆ CompareRevoluteJointToClone()

◆ CompareRollPitchYawFloatingJointToClone()

◆ ComputeCollisionSphereCenterPosition()

◆ ConstructIiwaPlant()

◆ ConstructTwoFreeBodiesPlant()

◆ ConstructTwoFreeBodiesPlant< AutoDiffXd >()

◆ ConstructTwoFreeBodiesPlant< double >()

◆ CreateLoadRobotMessage()

◆ CreateLoadRobotMessage< double >()

◆ default_model_instance()

◆ EvalMinimumDistanceConstraintAutoDiff()

◆ ExponentiallySmoothedHingeLoss()

◆ GTEST_TEST() [1/2]

◆ GTEST_TEST() [2/2]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-()

◆ operator<<()

◆ QuadraticallySmoothedHingeLoss()

◆ QuaternionToVectorWxyz()

◆ TEST_F() [1/21]

◆ TEST_F() [2/21]

◆ TEST_F() [3/21]