Inverse Dynamics

Classes
struct	spatial_dyn::InverseDynamicsOptions

Functions
Eigen::MatrixXd	spatial_dyn::InverseDynamicsPositionDerivative (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > ddq, const std::map< size_t, SpatialForced > &f_external, const InverseDynamicsOptions &options)
Eigen::MatrixXd	spatial_dyn::InverseDynamicsVelocityDerivative (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > ddq, const std::map< size_t, SpatialForced > &f_external, const InverseDynamicsOptions &options)
Eigen::VectorXd	spatial_dyn::InverseDynamics (const ArticulatedBody &ab, const Eigen::VectorXd &ddq, const std::map< size_t, SpatialForced > &f_external, const InverseDynamicsOptions &options)
const Eigen::VectorXd &	spatial_dyn::CentrifugalCoriolis (const ArticulatedBody &ab)
const Eigen::VectorXd &	spatial_dyn::Gravity (const ArticulatedBody &ab)
Eigen::VectorXd	spatial_dyn::ExternalTorques (const ArticulatedBody &ab, const std::map< size_t, SpatialForced > &f_external)
Eigen::VectorXd	spatial_dyn::Friction (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > tau, bool compensate, double stiction_epsilon)
const Eigen::MatrixXd &	spatial_dyn::Inertia (const ArticulatedBody &ab)
const SpatialInertiad &	spatial_dyn::CompositeInertia (const ArticulatedBody &ab, int link)

Detailed Description

C++ implementation of spatial_dyn inverse dynamics algorithms.

See also

Python: py_inverse_dynamics

Function Documentation

CentrifugalCoriolis()

const Eigen::VectorXd & spatial_dyn::CentrifugalCoriolis

(

const ArticulatedBody &

ab

)

Compute the centrifugal/Coriolis compensation torques.

Implements the Recursive Newton Euler Algorithm (RNEA) to compute the inverse dynamic torques in O(n) time. Results are cached such that subsequent calls with the same q and dq will return in O(1) time.

Parameters

ab	ArticulatedBody.

Returns

Reference to the cached centrifugal/Coriolis torques.

See also

Python: spatialdyn.centrifugal_coriolis()

CompositeInertia()

const SpatialInertiad & spatial_dyn::CompositeInertia	(	const ArticulatedBody &	ab,
		int	link = 0
	)

Compute the composite rigid body inertia from the given link to the end-effector.

Calls the Inertia() to compute the inertia with the Composite Rigid Body Algorithm (CRBA) in O(n^2) time. Results are cached such that subsequent calls with the same q will return in O(1) time.

Parameters

ab	ArticulatedBody.

Returns

Spatial Inertia

See also

Python: spatialdyn.composite_inertia()

ExternalTorques()

Eigen::VectorXd spatial_dyn::ExternalTorques	(	const ArticulatedBody &	ab,
		const std::map< size_t, SpatialForced > &	f_external = {}
	)

Compute the torques to compensate external forces applied on the rigid bodies.

Implements the Recursive Newton Euler Algorithm (RNEA) to compute the inverse dynamic torques in O(n) time. Results are cached such that subsequent calls with the same q and dq will return in O(1) time.

Parameters

ab	ArticulatedBody.
f_external	Map of (index, force) pairs where the force is the sum of all external spatial forces (represented in the world frame) applied to the associated rigid body index.

Returns

External torques.

See also

Python: spatialdyn.external_torque()

Friction()

Eigen::VectorXd spatial_dyn::Friction	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	tau,
		bool	compensate = true,
		double	stiction_epsilon = 0.01
	)

Compute Coulomb and viscous joint friction torques.

Friction torques are computed in O(n) time.

Parameters

ab	ArticulatedBody.
tau	Applied torques (for stiction).
compensate	Return friction compensation torques as opposed to resulting friction torques.
stiction_epsilon	Velocity threshold for stiction activation.

Returns

Friction torques.

See also

Python: spatialdyn.friction()

Gravity()

const Eigen::VectorXd & spatial_dyn::Gravity

(

const ArticulatedBody &

ab

)

Compute the gravity compensation torques.

Implements the Recursive Newton Euler Algorithm (RNEA) to compute the inverse dynamic torques in O(n) time. Results are cached such that subsequent calls with the same q and dq will return in O(1) time.

Parameters

ab	ArticulatedBody.

Returns

Reference to the cached gravity torques.

See also

Python: spatialdyn.gravity()

Inertia()

const Eigen::MatrixXd & spatial_dyn::Inertia

(

const ArticulatedBody &

ab

)

Compute the joint space inertia matrix.

Implements the Composite Rigid Body Algorithm (CRBA) to compute the inertia matrix in O(n^2) time. Results are cached such that subsequent calls with the same q will return in O(1) time.

Parameters

ab	ArticulatedBody.

Returns

Inertia matrix.

See also

Forward dynamics: spatial_dyn::InertiaInverse()

Python: spatialdyn.inertia()

InverseDynamics()

Eigen::VectorXd spatial_dyn::InverseDynamics	(	const ArticulatedBody &	ab,
		const Eigen::VectorXd &	ddq,
		const std::map< size_t, SpatialForced > &	f_external = {},
		const InverseDynamicsOptions &	options = {}
	)

Compute the inverse dynamics torques given the desired acceleration ddq.

Implements the Recursive Newton Euler Algorithm (RNEA) to compute the inverse dynamic torques in O(n) time.

Parameters

ab	ArticulatedBody.
ddq	Desired joint acceleration.
f_external	Map of (index, force) pairs where the force is the sum of all external spatial forces (represented in the world frame) applied to the associated rigid body index.
options	InverseDynamicsOptions.

Returns

Inverse dynamics torques.

See also

Python: spatialdyn.inverse_dynamics()

InverseDynamicsPositionDerivative()

Eigen::MatrixXd spatial_dyn::InverseDynamicsPositionDerivative	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	ddq,
		const std::map< size_t, SpatialForced > &	f_external = {},
		const InverseDynamicsOptions &	options = { true, true }
	)

Compute the inverse dynamics torques given the desired acceleration ddq.

Implements the Recursive Newton Euler Algorithm (RNEA) to compute the inverse dynamic torques in O(n) time.

Parameters

ab	ArticulatedBody.
ddq	Desired joint acceleration.
f_external	Map of (index, force) pairs where the force is the sum of all external spatial forces (represented in the world frame) applied to the associated rigid body index.
options	InverseDynamicsOptions.

Returns

Inverse dynamics torques.

See also

Python: spatialdyn.inverse_dynamics()