Jacobian Kinematics

Jacobian matrix for robotics. More...

Classes
struct	fsb::Jacobian
	Jacobian matrix. More...
struct	fsb::JointMatrix
	Square matrix of size nxn for n joints. More...
struct	fsb::Hessian
	Hessian tensor. More...
struct	fsb::SingularityEllipsoid
struct	fsb::Mat3Singularity
struct	fsb::JacobianMetrics

Enumerations
enum class	fsb::JacobianError : uint8_t { JacobianError::SUCCESS , JacobianError::BODY_NOT_IN_TREE }
	Error values for Jacobian calculations. More...

Functions
size_t	fsb::jacobian_index (const size_t row, const size_t col)
	Helper function for indexing jacobian matrix.
size_t	fsb::joint_matrix_index (const size_t row, const size_t col, const size_t dofs)
	Helper function for indexing joint matrix.
MotionVector	fsb::jacobian_multiply (const Jacobian &jacobian, const JointSpace &joint_motion, size_t dofs=MaxSize::dofs)
	Jacobian multiply joint velocity.
JointSpace	fsb::jacobian_transpose_multiply (const Jacobian &jacobian, const MotionVector &cartesian_motion, size_t dofs=MaxSize::dofs)
	Jacobian transpose multiply cartesian motion.
JointMatrix	fsb::jacobian_transpose_multiply_jacobian (const Jacobian &jacobian, const MotionVector &cartesian_weights, size_t dofs=MaxSize::dofs)
	Jacobian transpose multiply jacobian.
Jacobian	fsb::jacobian_derivative (const Hessian &hessian, const JointSpace &joint_velocity, size_t dofs=MaxSize::dofs)
	Compute derivative of Jacobian matrix.
JacobianError	fsb::calculate_jacobian (size_t body_index, const BodyTree &body_tree, const BodyCartesianPva &cartesian_pva, Jacobian &jacobian)
	Determine Jacobian matrix for a single body in tree.
JacobianMetrics	fsb::calculate_jacobian_metrics (const Jacobian &jacobian, size_t dofs=MaxSize::dofs)
	Calculate Jacobian metrics for a given Jacobian matrix.

Detailed Description

Jacobian matrix for robotics.

Enumeration Type Documentation

JacobianError

enum class fsb::JacobianError : uint8_t

strong

Error values for Jacobian calculations.

Enumerator
SUCCESS	No error.
BODY_NOT_IN_TREE	Body index not found in tree.

Function Documentation

calculate_jacobian()

JacobianError fsb::calculate_jacobian	(	size_t	body_index,
		const BodyTree &	body_tree,
		const BodyCartesianPva &	cartesian_pva,
		Jacobian &	jacobian
	)

Determine Jacobian matrix for a single body in tree.

Cartesian pose for all bodies should be determined by forward kinematics prior to calling this function.

Parameters

[in]	body_index	Body index of Jacobian
[in]	body_tree	Body tree with body and joint data
[in]	cartesian_pva	Cartesian pose, velocity and acceleration data for all bodies
[out]	jacobian	Jacobian matrix for body

Returns

Jacobian error code

calculate_jacobian_metrics()

JacobianMetrics fsb::calculate_jacobian_metrics	(	const Jacobian &	jacobian,
		size_t	dofs = MaxSize::dofs
	)

Calculate Jacobian metrics for a given Jacobian matrix.

Parameters

jacobian	Jacobian matrix
dofs	Number of dofs (elements in joint velocity vector)

Returns

Jacobian metrics including condition number, manipulability, and singularity ellipsoids

jacobian_derivative()

Jacobian fsb::jacobian_derivative	(	const Hessian &	hessian,
		const JointSpace &	joint_velocity,
		size_t	dofs = MaxSize::dofs
	)

Compute derivative of Jacobian matrix.

Parameters

hessian	Hessian matrix
joint_velocity	Joint velocity vector
dofs	Number of dofs (elements in joint velocity vector)

Returns

Jacobian derivative

jacobian_index()

size_t fsb::jacobian_index ( const size_t  row, const size_t  col  )

inline

Helper function for indexing jacobian matrix.

Matrix is ordered column-major with 6 rows

Parameters

row	Row index
col	Column index

Returns

Jacobian index

jacobian_multiply()

MotionVector fsb::jacobian_multiply	(	const Jacobian &	jacobian,
		const JointSpace &	joint_motion,
		size_t	dofs = MaxSize::dofs
	)

Jacobian multiply joint velocity.

Parameters

jacobian	Jacobian matrix
joint_motion	Joint velocity
dofs	Number of degrees of freedom (elements in joint velocity vector)

Returns

Cartesian velocity

jacobian_transpose_multiply()

JointSpace fsb::jacobian_transpose_multiply	(	const Jacobian &	jacobian,
		const MotionVector &	cartesian_motion,
		size_t	dofs = MaxSize::dofs
	)

Jacobian transpose multiply cartesian motion.

Parameters

jacobian	Jacobian matrix
cartesian_motion	Cartesian motion
dofs	Number of degrees of freedom (elements in joint motion vector)

Returns

Joint motion

jacobian_transpose_multiply_jacobian()

JointMatrix fsb::jacobian_transpose_multiply_jacobian	(	const Jacobian &	jacobian,
		const MotionVector &	cartesian_weights,
		size_t	dofs = MaxSize::dofs
	)

Jacobian transpose multiply jacobian.

\( J^T \cdot \text{diag}(w) J \)

Parameters

jacobian	Jacobian matrix
cartesian_weights	Weighted cartesian motion
dofs

Returns

joint_matrix_index()

size_t fsb::joint_matrix_index ( const size_t  row, const size_t  col, const size_t  dofs  )

inline

Helper function for indexing joint matrix.

Matrix is ordered column-major with n rows for n joints

Parameters

row	Row index
col	Column index
dofs	Number of degrees of freedom (elements in joint velocity vector)

Returns

Array index for joint matrix