Compact representation of spatial transformations. More...

#include <rdl_eigenmath.h>

Public Member Functions
SpatialVector	apply (const SpatialVector &v_sp) const
	Transform a spatial vector. Same as . More...

SpatialVector	applyAdjoint (const SpatialVector &f_sp) const
	Applies where is a spatial force. More...

SpatialVector	applyTranspose (const SpatialVector &f_sp) const
	Applies . More...

SpatialTransform	inverse () const
	Returns inverse of transform. More...

void	invert ()
	Inverts in place. $this = this^{-1}$ . More...

SpatialTransform	operator* (const SpatialTransform &XT) const
	Overloaded * operator for combining transforms. More...

void	operator*= (const SpatialTransform &XT)

	SpatialTransform ()
	Constructor. More...

	SpatialTransform (const Matrix3d &rotation, const double x, const double y, const double z)
	Constructor. More...

	SpatialTransform (const Matrix3d &rotation, const Vector3d &translation)
	Constructor. More...

	SpatialTransform (const Matrix3d &rotation)
	Constructor. More...

	SpatialTransform (const Vector3d &translation)
	Constructor. More...

SpatialMatrix	toMatrix () const
	Return transform as 6x6 spatial matrix. More...

SpatialMatrix	toMatrixAdjoint () const
	Returns Spatial transform that transforms spatial force vectors. More...

SpatialMatrix	toMatrixTranspose () const
	Returns spatial force transform transposed. More...

Public Attributes
Matrix3d	E

Vector3d	r

Detailed Description

Compact representation of spatial transformations.

Instead of using a verbose 6x6 matrix, this structure only stores a 3x3 matrix and a 3-d vector to store spatial transformations. It also encapsulates efficient operations such as concatenations and transformation of spatial vectors.

Definition at line 337 of file rdl_eigenmath.h.

Constructor & Destructor Documentation

RobotDynamics::Math::SpatialTransform::SpatialTransform ( )

inline

Constructor.

Definition at line 342 of file rdl_eigenmath.h.

RobotDynamics::Math::SpatialTransform::SpatialTransform	(	const Matrix3d &	rotation,
		const double	x,
		const double	y,
		const double	z
	)

inline

Constructor.

Parameters

rotation	Orthogonal rotation matrix
x	X component
y	Y component
z	Z component

Definition at line 353 of file rdl_eigenmath.h.

RobotDynamics::Math::SpatialTransform::SpatialTransform	(	const Matrix3d &	rotation,
		const Vector3d &	translation
	)

inline

Constructor.

Parameters

rotation	Orthogonal rotation matrix
translation	3D translational component

Definition at line 362 of file rdl_eigenmath.h.

RobotDynamics::Math::SpatialTransform::SpatialTransform ( const Matrix3d & rotation )

inlineexplicit

Constructor.

Parameters

rotation	Orthogonal rotation matrix
translation	3D translational component

Definition at line 371 of file rdl_eigenmath.h.

RobotDynamics::Math::SpatialTransform::SpatialTransform ( const Vector3d & translation )

inlineexplicit

Constructor.

Parameters

rotation	Orthogonal rotation matrix
translation	3D translational component

Definition at line 380 of file rdl_eigenmath.h.

Member Function Documentation

SpatialVector RobotDynamics::Math::SpatialTransform::apply ( const SpatialVector & v_sp ) const

inline

Transform a spatial vector. Same as $ X * v $ .

Parameters

v_sp	Spatial motion vector to be copied/transformed

Returns: Transformed spatial vector. $\begin{bmatrix} E * w \\ - E * (r \times w) + E * v \end{bmatrix}$

Definition at line 390 of file rdl_eigenmath.h.

SpatialVector RobotDynamics::Math::SpatialTransform::applyAdjoint ( const SpatialVector & f_sp ) const

inline

Applies $ X * f $ where $ f $ is a spatial force.

Parameters

f_sp	Spatial force vector

Returns: $\begin{bmatrix} E * n - E * (r \times f) \\ E * f \end{bmatrix}$

Definition at line 421 of file rdl_eigenmath.h.

SpatialVector RobotDynamics::Math::SpatialTransform::applyTranspose ( const SpatialVector & f_sp ) const

inline

Applies $ X^T * f $ .

Parameters

f_sp	Spatial force

Returns: $\begin{bmatrix} E^T * n + r \times * E^T * f \\ E^T * f \end{bmatrix}$

Definition at line 405 of file rdl_eigenmath.h.

SpatialTransform RobotDynamics::Math::SpatialTransform::inverse ( ) const

inline

Returns inverse of transform.

Returns: $X^{-1}$

Definition at line 488 of file rdl_eigenmath.h.

void RobotDynamics::Math::SpatialTransform::invert ( )

inline

Inverts in place. $this = this^{-1}$ .

Definition at line 496 of file rdl_eigenmath.h.

SpatialTransform RobotDynamics::Math::SpatialTransform::operator* ( const SpatialTransform & XT ) const

inline

Overloaded * operator for combining transforms.

Parameters

XT

Returns: Combined rotation

Definition at line 507 of file rdl_eigenmath.h.

void RobotDynamics::Math::SpatialTransform::operator*= ( const SpatialTransform & XT )

inline

Definition at line 512 of file rdl_eigenmath.h.

SpatialMatrix RobotDynamics::Math::SpatialTransform::toMatrix ( ) const

inline

Return transform as 6x6 spatial matrix.

Returns: $\begin{bmatrix} E & \mathbf{0} \\ -E * r\times & E \end{bmatrix}$

Definition at line 434 of file rdl_eigenmath.h.

SpatialMatrix RobotDynamics::Math::SpatialTransform::toMatrixAdjoint ( ) const

inline

Returns Spatial transform that transforms spatial force vectors.

Returns: $\begin{bmatrix} E & -E * r\times \\ \mathbf{0} & E \end{bmatrix}$

Definition at line 452 of file rdl_eigenmath.h.

SpatialMatrix RobotDynamics::Math::SpatialTransform::toMatrixTranspose ( ) const

inline

Returns spatial force transform transposed.

Returns: $\begin{bmatrix} E^{T} & (-E r\times)^{T} \\ \mathbf{0} & E^{T} \end{bmatrix}$

Definition at line 470 of file rdl_eigenmath.h.

Member Data Documentation

Matrix3d RobotDynamics::Math::SpatialTransform::E

Definition at line 518 of file rdl_eigenmath.h.

Vector3d RobotDynamics::Math::SpatialTransform::r

Definition at line 519 of file rdl_eigenmath.h.

The documentation for this struct was generated from the following file:

rdl_eigenmath.h

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation