Forward Kinematics

Functions
Eigen::Vector3d	spatial_dyn::Position (const ArticulatedBody &ab, int link, const Eigen::Vector3d &offset)
Eigen::Vector3d	spatial_dyn::Position (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link, const Eigen::Vector3d &offset)
Eigen::Quaterniond	spatial_dyn::Orientation (const ArticulatedBody &ab, int link)
Eigen::Quaterniond	spatial_dyn::Orientation (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link)
Eigen::Isometry3d	spatial_dyn::CartesianPose (const ArticulatedBody &ab, int link, const Eigen::Vector3d &offset)
Eigen::Isometry3d	spatial_dyn::CartesianPose (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link, const Eigen::Vector3d &offset)
const Eigen::Matrix6Xd &	spatial_dyn::Jacobian (const ArticulatedBody &ab, int link, const Eigen::Vector3d &offset)
Eigen::Matrix6Xd	spatial_dyn::Jacobian (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link, const Eigen::Vector3d &offset)
Eigen::Ref< const Eigen::Matrix3Xd >	spatial_dyn::LinearJacobian (const ArticulatedBody &ab, int link, const Eigen::Vector3d &offset)
Eigen::Matrix3Xd	spatial_dyn::LinearJacobian (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link, const Eigen::Vector3d &offset)
Eigen::Ref< const Eigen::Matrix3Xd >	spatial_dyn::AngularJacobian (const ArticulatedBody &ab, int link)
Eigen::Matrix3Xd	spatial_dyn::AngularJacobian (const ArticulatedBody &ab, Eigen::Ref< const Eigen::VectorXd > q, int link)
Eigen::Tensor3d	spatial_dyn::Hessian (const ArticulatedBody &ab, int link, const Eigen::Vector3d &offset)

Detailed Description

C++ implementation of spatial_dyn forward kinematics algorithms.

See also

Python: py_forward_kinematics

Function Documentation

AngularJacobian() [1/2]

Eigen::Matrix3Xd spatial_dyn::AngularJacobian	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1
	)

Compute the world frame angular Jacobian of the given operational point.

Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.

Returns

Angular Jacobian (bottom 3 rows of the basic Jacobian) represented in the world frame.

See also

Python: spatialdyn.angular_jacobian()

AngularJacobian() [2/2]

Eigen::Ref< const Eigen::Matrix3Xd > spatial_dyn::AngularJacobian	(	const ArticulatedBody &	ab,
		int	link = -1
	)

Compute the world frame angular Jacobian of the given operational point.

The computation is cached such that the first call to Jacobian() runs in O(n) time, and subsequent calls with the same joint position, link, and offset run in O(1) time. AngularJacobian() uses the last offset passed to Jacobian() or LinearJacobian() for caching, and therefore should be called after Jacobian() or LinearJacobian() to avoid unnecessary computations with a nonzero offset.

Parameters

ab	Articulated body.
link	Index of the desired link.

Returns

Reference to the bottom 3 rows of the cached basic Jacobian represented in the world frame.

See also

Python: spatialdyn.angular_jacobian()

CartesianPose() [1/2]

Eigen::Isometry3d spatial_dyn::CartesianPose	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame pose of an offset vector in link i given articulated body configuration q.

Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.
offset	Vector offset in link i.

Returns

World frame pose of the offset in link i.

See also

Python: spatialdyn.cartesian_pose()

CartesianPose() [2/2]

Eigen::Isometry3d spatial_dyn::CartesianPose	(	const ArticulatedBody &	ab,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame pose of an offset vector in link i.

Uses the articulated body's cached world transforms to run in O(1) time.

Parameters

ab	Articulated body.
link	Index of the desired link.
offset	Vector offset in link i.

Returns

World frame pose of the offset in link i.

See also

Python: spatialdyn.cartesian_pose()

Hessian()

Eigen::Tensor3d spatial_dyn::Hessian	(	const ArticulatedBody &	ab,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame Hessian of the given operational point.

Parameters

ab	Articulated body.
link	Index of the desired link.
offset	Vector offset of the operational point in link i.

Returns

[n x n x 6] Hessian represented in the world frame.

See also

Python: spatialdyn.hessian()

Jacobian() [1/2]

Eigen::Matrix6Xd spatial_dyn::Jacobian	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame basic Jacobian of the given operational point.

Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.
offset	Vector offset of the operational point in link i.

Returns

Basic Jacobian (linear stacked above angular) represented in the world frame.

See also

Python: spatialdyn.jacobian()

Jacobian() [2/2]

const Eigen::Matrix6Xd & spatial_dyn::Jacobian	(	const ArticulatedBody &	ab,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame basic Jacobian of the given operational point.

The computation is cached such that the first call to Jacobian() runs in O(n) time, and subsequent calls with the same joint position, link, and offset run in O(1) time.

Parameters

ab	Articulated body.
link	Index of the desired link.
offset	Vector offset of the operational point in link i.

Returns

Reference to the cached basic Jacobian (linear stacked above angular) represented in the world frame.

See also

Python: spatialdyn.jacobian()

LinearJacobian() [1/2]

Eigen::Matrix3Xd spatial_dyn::LinearJacobian	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame linear Jacobian of the given operational point.

A Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.
offset	Vector offset of the operational point in link i.

Returns

Linear Jacobian (top 3 rows of the basic Jacobian) represented in the world frame.

See also

Python: spatialdyn.linear_jacobian()

LinearJacobian() [2/2]

Eigen::Ref< const Eigen::Matrix3Xd > spatial_dyn::LinearJacobian	(	const ArticulatedBody &	ab,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame linear Jacobian of the given operational point.

The computation is cached such that the first call to Jacobian() runs in O(n) time, and subsequent calls with the same joint position, link, and offset run in O(1) time.

Parameters

ab	Articulated body.
link	Index of the desired link.
offset	Vector offset of the operational point in link i.

Returns

Reference to the top 3 rows of the cached basic Jacobian represented in the world frame.

See also

Python: spatialdyn.linear_jacobian()

Orientation() [1/2]

Eigen::Quaterniond spatial_dyn::Orientation	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1
	)

Compute the world frame orientation of link i given articulated body configuration q.

Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.

Returns

World frame orientation of link i.

See also

Python: spatialdyn.orientation()

Orientation() [2/2]

Eigen::Quaterniond spatial_dyn::Orientation	(	const ArticulatedBody &	ab,
		int	link = -1
	)

Compute the world frame orientation of link i.

Uses the articulated body's cached world transforms to run in O(1) time.

Parameters

ab	Articulated body.
link	Index of the desired link.

Returns

World frame orientation of link i.

See also

Python: spatialdyn.orientation()

Position() [1/2]

Eigen::Vector3d spatial_dyn::Position	(	const ArticulatedBody &	ab,
		Eigen::Ref< const Eigen::VectorXd >	q,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame position of an offset vector in link i given articulated body configuration q.

Runs in O(n) time.

Parameters

ab	Articulated body.
q	Joint configuration.
link	Index of the desired link.
offset	Vector offset in link i.

Returns

World frame position of the offset in link i.

See also

Python: spatialdyn.position()

Position() [2/2]

Eigen::Vector3d spatial_dyn::Position	(	const ArticulatedBody &	ab,
		int	link = -1,
		const Eigen::Vector3d &	offset = Eigen::Vector3d::Zero()
	)

Compute the world frame position of an offset vector in link i.

Uses the articulated body's cached world transforms to run in O(1) time.

Parameters

ab	Articulated body.
link	Index of the desired link.
offset	Vector offset in link i.

Returns

World frame position of the offset in link i.

See also

Python: spatialdyn.position()