Math types such as vectors and matrices and utility functions. More...

Data Structures
class	Quaternion
	Quaternion that are used for singularity free joints. More...

struct	SpatialRigidBodyInertia
	Compact representation for Spatial Inertia. More...

struct	SpatialTransform
	Compact representation of spatial transformations. More...

Typedefs
typedef Vector1_t	Scalar

typedef Vector2_t	Vector2d

typedef Vector3_t	Vector3d

typedef Vector4_t	Vector4d

typedef Matrix2_t	Matrix2d

typedef Matrix3_t	Matrix3d

typedef SpatialVector_t	SpatialVector

typedef SpatialMatrix_t	SpatialMatrix

typedef Matrix63_t	Matrix63

typedef Matrix43_t	Matrix43

typedef Matrix4_t	Matrix4d

typedef VectorN_t	VectorNd

typedef MatrixN_t	MatrixNd

Functions
RBDL_DLLAPI Vector3d	Vector3dZero (0., 0., 0.)

RBDL_DLLAPI Matrix3d	Matrix3dIdentity (1., 0., 0., 0., 1., 0., 0., 0., 1)

RBDL_DLLAPI Matrix3d	Matrix3dZero (0., 0., 0., 0., 0., 0., 0., 0., 0.)

RBDL_DLLAPI SpatialVector	SpatialVectorZero (0., 0., 0., 0., 0., 0.)

RBDL_DLLAPI bool	LinSolveGaussElimPivot (MatrixNd A, VectorNd b, VectorNd &x)
	Solves a linear system using gaussian elimination with pivoting. More...

RBDL_DLLAPI void	SpatialMatrixSetSubmatrix (SpatialMatrix &dest, unsigned int row, unsigned int col, const Matrix3d &matrix)

RBDL_DLLAPI bool	SpatialMatrixCompareEpsilon (const SpatialMatrix &matrix_a, const SpatialMatrix &matrix_b, Scalar epsilon)

RBDL_DLLAPI bool	SpatialVectorCompareEpsilon (const SpatialVector &vector_a, const SpatialVector &vector_b, Scalar epsilon)

RBDL_DLLAPI Matrix3d	parallel_axis (const Matrix3d &inertia, Scalar mass, const Vector3d &com)
	Translates the inertia matrix to a new center. More...

RBDL_DLLAPI SpatialMatrix	Xtrans_mat (const Vector3d &displacement)
	Creates a transformation of a linear displacement. More...

RBDL_DLLAPI SpatialMatrix	Xrotx_mat (const Scalar &xrot)
	Creates a rotational transformation around the X-axis. More...

RBDL_DLLAPI SpatialMatrix	Xroty_mat (const Scalar &yrot)
	Creates a rotational transformation around the Y-axis. More...

RBDL_DLLAPI SpatialMatrix	Xrotz_mat (const Scalar &zrot)
	Creates a rotational transformation around the Z-axis. More...

RBDL_DLLAPI SpatialMatrix	XtransRotZYXEuler (const Vector3d &displacement, const Vector3d &zyx_euler)
	Creates a spatial transformation for given parameters. More...

RBDL_DLLAPI void	SparseFactorizeLTL (Model &model, Math::MatrixNd &H)

RBDL_DLLAPI void	SparseMultiplyHx (Model &model, Math::MatrixNd &L)

RBDL_DLLAPI void	SparseMultiplyLx (Model &model, Math::MatrixNd &L)

RBDL_DLLAPI void	SparseMultiplyLTx (Model &model, Math::MatrixNd &L)

RBDL_DLLAPI void	SparseSolveLx (Model &model, Math::MatrixNd &L, Math::VectorNd &x)

RBDL_DLLAPI void	SparseSolveLTx (Model &model, Math::MatrixNd &L, Math::VectorNd &x)

RBDL_DLLAPI VectorNd	VectorFromPtr (unsigned int n, Scalar *ptr)

RBDL_DLLAPI MatrixNd	MatrixFromPtr (unsigned int rows, unsigned int cols, Scalar *ptr, bool row_major=true)

RBDL_DLLAPI Matrix3d	rotx (const Scalar &xrot)

RBDL_DLLAPI Matrix3d	roty (const Scalar &yrot)

RBDL_DLLAPI Matrix3d	rotz (const Scalar &zrot)

RBDL_DLLAPI Matrix3d	rotxdot (const Scalar &x, const Scalar &xdot)

RBDL_DLLAPI Matrix3d	rotydot (const Scalar &y, const Scalar &ydot)

RBDL_DLLAPI Matrix3d	rotzdot (const Scalar &z, const Scalar &zdot)

RBDL_DLLAPI Vector3d	angular_velocity_from_angle_rates (const Vector3d &zyx_angles, const Vector3d &zyx_angle_rates)

RBDL_DLLAPI Vector3d	global_angular_velocity_from_rates (const Vector3d &zyx_angles, const Vector3d &zyx_rates)

RBDL_DLLAPI Vector3d	angular_acceleration_from_angle_rates (const Vector3d &zyx_angles, const Vector3d &zyx_angle_rates, const Vector3d &zyx_angle_rates_dot)

Matrix3d	VectorCrossMatrix (const Vector3d &vector)

std::ostream &	operator<< (std::ostream &output, const SpatialRigidBodyInertia &rbi)

std::ostream &	operator<< (std::ostream &output, const SpatialTransform &X)

SpatialTransform	Xrot (Scalar angle_rad, const Vector3d &axis)

SpatialTransform	Xrotx (const Scalar &xrot)

SpatialTransform	Xroty (const Scalar &yrot)

SpatialTransform	Xrotz (const Scalar &zrot)

SpatialTransform	Xtrans (const Vector3d &r)

SpatialMatrix	crossm (const SpatialVector &v)

SpatialVector	crossm (const SpatialVector &v1, const SpatialVector &v2)

SpatialMatrix	crossf (const SpatialVector &v)

SpatialVector	crossf (const SpatialVector &v1, const SpatialVector &v2)

Variables
RBDL_DLLAPI Vector3d	Vector3dZero

RBDL_DLLAPI Matrix3d	Matrix3dIdentity

RBDL_DLLAPI Matrix3d	Matrix3dZero

Detailed Description

Math types such as vectors and matrices and utility functions.

Typedef Documentation

◆ Matrix2d

typedef Matrix2_t Matrix2d

Definition at line 59 of file rbdl_math.h.

◆ Matrix3d

typedef Matrix3_t Matrix3d

Definition at line 60 of file rbdl_math.h.

◆ Matrix43

typedef Matrix43_t Matrix43

Definition at line 64 of file rbdl_math.h.

◆ Matrix4d

typedef Matrix4_t Matrix4d

Definition at line 65 of file rbdl_math.h.

◆ Matrix63

typedef Matrix63_t Matrix63

Definition at line 63 of file rbdl_math.h.

◆ MatrixNd

typedef MatrixN_t MatrixNd

Definition at line 67 of file rbdl_math.h.

◆ Scalar

typedef Vector1_t Scalar

Definition at line 55 of file rbdl_math.h.

◆ SpatialMatrix

typedef SpatialMatrix_t SpatialMatrix

Definition at line 62 of file rbdl_math.h.

◆ SpatialVector

typedef SpatialVector_t SpatialVector

Definition at line 61 of file rbdl_math.h.

◆ Vector2d

typedef Vector2_t Vector2d

Definition at line 56 of file rbdl_math.h.

◆ Vector3d

typedef Vector3_t Vector3d

Definition at line 57 of file rbdl_math.h.

◆ Vector4d

typedef Vector4_t Vector4d

Definition at line 58 of file rbdl_math.h.

◆ VectorNd

typedef VectorN_t VectorNd

Definition at line 66 of file rbdl_math.h.

Function Documentation

◆ angular_acceleration_from_angle_rates()

RBDL_DLLAPI Vector3d RigidBodyDynamics::Math::angular_acceleration_from_angle_rates	(	const Vector3d &	zyx_angles,
		const Vector3d &	zyx_angle_rates,
		const Vector3d &	zyx_angle_rates_dot
	)

inline

Definition at line 229 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ angular_velocity_from_angle_rates()

RBDL_DLLAPI Vector3d RigidBodyDynamics::Math::angular_velocity_from_angle_rates	(	const Vector3d &	zyx_angles,
		const Vector3d &	zyx_angle_rates
	)

inline

Definition at line 205 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ crossf() [1/2]

SpatialMatrix RigidBodyDynamics::Math::crossf ( const SpatialVector & v )

inline

Definition at line 425 of file SpatialAlgebraOperators.h.

◆ crossf() [2/2]

SpatialVector RigidBodyDynamics::Math::crossf	(	const SpatialVector &	v1,
		const SpatialVector &	v2
	)

inline

Definition at line 436 of file SpatialAlgebraOperators.h.

◆ crossm() [1/2]

SpatialMatrix RigidBodyDynamics::Math::crossm ( const SpatialVector & v )

inline

Definition at line 403 of file SpatialAlgebraOperators.h.

◆ crossm() [2/2]

SpatialVector RigidBodyDynamics::Math::crossm	(	const SpatialVector &	v1,
		const SpatialVector &	v2
	)

inline

Definition at line 414 of file SpatialAlgebraOperators.h.

◆ global_angular_velocity_from_rates()

RBDL_DLLAPI Vector3d RigidBodyDynamics::Math::global_angular_velocity_from_rates	(	const Vector3d &	zyx_angles,
		const Vector3d &	zyx_rates
	)

inline

Definition at line 218 of file rbdl_mathutils.h.

References roty(), and rotz().

◆ LinSolveGaussElimPivot()

RBDL_DLLAPI bool LinSolveGaussElimPivot	(	MatrixNd	A,
		VectorNd	b,
		VectorNd &	x
	)

Solves a linear system using gaussian elimination with pivoting.

Definition at line 37 of file rbdl_mathutils.cc.

References MX_Xd_dynamic::cols(), std::fabs(), MX_Xd_dynamic::rows(), MX_Xd_dynamic::size(), and MX_Xd_dynamic::Zero().

◆ Matrix3dIdentity()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::Matrix3dIdentity	(	1.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		1
	)

◆ Matrix3dZero()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::Matrix3dZero	(	0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.
	)

◆ MatrixFromPtr()

RBDL_DLLAPI MatrixNd RigidBodyDynamics::Math::MatrixFromPtr	(	unsigned int	rows,
		unsigned int	cols,
		Scalar *	ptr,
		bool	row_major = `true`
	)

inline

Definition at line 51 of file rbdl_mathutils.h.

◆ operator<<() [1/2]

std::ostream & RigidBodyDynamics::Math::operator<<	(	std::ostream &	output,
		const SpatialRigidBodyInertia &	rbi
	)

inline

Definition at line 315 of file SpatialAlgebraOperators.h.

References SpatialRigidBodyInertia::h, SpatialRigidBodyInertia::Ixx, SpatialRigidBodyInertia::Iyx, SpatialRigidBodyInertia::Iyy, SpatialRigidBodyInertia::Izx, SpatialRigidBodyInertia::Izy, SpatialRigidBodyInertia::Izz, and SpatialRigidBodyInertia::m.

◆ operator<<() [2/2]

std::ostream & RigidBodyDynamics::Math::operator<<	(	std::ostream &	output,
		const SpatialTransform &	X
	)

inline

Definition at line 324 of file SpatialAlgebraOperators.h.

References SpatialTransform::E, and SpatialTransform::r.

◆ parallel_axis()

RBDL_DLLAPI Matrix3d parallel_axis	(	const Matrix3d &	inertia,
		Scalar	mass,
		const Vector3d &	com
	)

Translates the inertia matrix to a new center.

Definition at line 190 of file rbdl_mathutils.cc.

References VectorCrossMatrix().

◆ rotx()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::rotx ( const Scalar & xrot )

inline

Definition at line 139 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ rotxdot()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::rotxdot	(	const Scalar &	x,
		const Scalar &	xdot
	)

inline

Definition at line 172 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ roty()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::roty ( const Scalar & yrot )

inline

Definition at line 150 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ rotydot()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::rotydot	(	const Scalar &	y,
		const Scalar &	ydot
	)

inline

Definition at line 183 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ rotz()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::rotz ( const Scalar & zrot )

inline

Definition at line 161 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ rotzdot()

RBDL_DLLAPI Matrix3d RigidBodyDynamics::Math::rotzdot	(	const Scalar &	z,
		const Scalar &	zdot
	)

inline

Definition at line 194 of file rbdl_mathutils.h.

References std::cos(), and std::sin().

◆ SparseFactorizeLTL()

RBDL_DLLAPI void SparseFactorizeLTL	(	Model &	model,
		Math::MatrixNd &	H
	)

Definition at line 261 of file rbdl_mathutils.cc.

References std::sqrt().

◆ SparseMultiplyHx()

RBDL_DLLAPI void SparseMultiplyHx	(	Model &	model,
		Math::MatrixNd &	L
	)

Definition at line 288 of file rbdl_mathutils.cc.

◆ SparseMultiplyLTx()

RBDL_DLLAPI void SparseMultiplyLTx	(	Model &	model,
		Math::MatrixNd &	L
	)

Definition at line 296 of file rbdl_mathutils.cc.

◆ SparseMultiplyLx()

RBDL_DLLAPI void SparseMultiplyLx	(	Model &	model,
		Math::MatrixNd &	L
	)

Definition at line 292 of file rbdl_mathutils.cc.

◆ SparseSolveLTx()

RBDL_DLLAPI void SparseSolveLTx	(	Model &	model,
		Math::MatrixNd &	L,
		Math::VectorNd &	x
	)

Definition at line 311 of file rbdl_mathutils.cc.

◆ SparseSolveLx()

RBDL_DLLAPI void SparseSolveLx	(	Model &	model,
		Math::MatrixNd &	L,
		Math::VectorNd &	x
	)

Definition at line 300 of file rbdl_mathutils.cc.

◆ SpatialMatrixCompareEpsilon()

RBDL_DLLAPI bool SpatialMatrixCompareEpsilon	(	const SpatialMatrix &	matrix_a,
		const SpatialMatrix &	matrix_b,
		Scalar	epsilon
	)

Definition at line 147 of file rbdl_mathutils.cc.

References std::fabs().

◆ SpatialMatrixSetSubmatrix()

RBDL_DLLAPI void SpatialMatrixSetSubmatrix	(	SpatialMatrix &	dest,
		unsigned int	row,
		unsigned int	col,
		const Matrix3d &	matrix
	)

Definition at line 126 of file rbdl_mathutils.cc.

◆ SpatialVectorCompareEpsilon()

RBDL_DLLAPI bool SpatialVectorCompareEpsilon	(	const SpatialVector &	vector_a,
		const SpatialVector &	vector_b,
		Scalar	epsilon
	)

Definition at line 169 of file rbdl_mathutils.cc.

References std::fabs().

◆ SpatialVectorZero()

RBDL_DLLAPI SpatialVector RigidBodyDynamics::Math::SpatialVectorZero	(	0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.
	)

◆ Vector3dZero()

RBDL_DLLAPI Vector3d RigidBodyDynamics::Math::Vector3dZero	(	0.	,
		0.	,
		0.
	)

◆ VectorCrossMatrix()

Matrix3d RigidBodyDynamics::Math::VectorCrossMatrix ( const Vector3d & vector )

inline

Definition at line 18 of file SpatialAlgebraOperators.h.

◆ VectorFromPtr()

RBDL_DLLAPI VectorNd RigidBodyDynamics::Math::VectorFromPtr	(	unsigned int	n,
		Scalar *	ptr
	)

inline

Definition at line 40 of file rbdl_mathutils.h.

◆ Xrot()

SpatialTransform RigidBodyDynamics::Math::Xrot	(	Scalar	angle_rad,
		const Vector3d &	axis
	)

inline

Definition at line 330 of file SpatialAlgebraOperators.h.

References std::cos(), and std::sin().

◆ Xrotx()

SpatialTransform RigidBodyDynamics::Math::Xrotx ( const Scalar & xrot )

inline

Definition at line 354 of file SpatialAlgebraOperators.h.

References std::cos(), and std::sin().

◆ Xrotx_mat()

RBDL_DLLAPI SpatialMatrix Xrotx_mat ( const Scalar & xrot )

Creates a rotational transformation around the X-axis.

Creates a rotation around the current X-axis by the given angle (specified in radians).

Parameters

xrot	Rotation angle in radians.

Definition at line 210 of file rbdl_mathutils.cc.

References std::cos(), and std::sin().

◆ Xroty()

SpatialTransform RigidBodyDynamics::Math::Xroty ( const Scalar & yrot )

inline

Definition at line 368 of file SpatialAlgebraOperators.h.

References std::cos(), and std::sin().

◆ Xroty_mat()

RBDL_DLLAPI SpatialMatrix Xroty_mat ( const Scalar & yrot )

Creates a rotational transformation around the Y-axis.

Creates a rotation around the current Y-axis by the given angle (specified in radians).

Parameters

yrot	Rotation angle in radians.

Definition at line 225 of file rbdl_mathutils.cc.

References std::cos(), and std::sin().

◆ Xrotz()

SpatialTransform RigidBodyDynamics::Math::Xrotz ( const Scalar & zrot )

inline

Definition at line 382 of file SpatialAlgebraOperators.h.

References std::cos(), and std::sin().

◆ Xrotz_mat()

RBDL_DLLAPI SpatialMatrix Xrotz_mat ( const Scalar & zrot )

Creates a rotational transformation around the Z-axis.

Creates a rotation around the current Z-axis by the given angle (specified in radians).

Parameters

zrot	Rotation angle in radians.

Definition at line 240 of file rbdl_mathutils.cc.

References std::cos(), and std::sin().

◆ Xtrans()

SpatialTransform RigidBodyDynamics::Math::Xtrans ( const Vector3d & r )

inline

Definition at line 396 of file SpatialAlgebraOperators.h.

◆ Xtrans_mat()

RBDL_DLLAPI SpatialMatrix Xtrans_mat ( const Vector3d & displacement )

Creates a transformation of a linear displacement.

This can be used to specify the translation to the joint center when adding a body to a model. See also section 2.8 in RBDA.

Note: The transformation returned is for motions. For a transformation for forces; one has to conjugate the matrix.

Parameters

displacement The displacement as a 3D vector

Definition at line 199 of file rbdl_mathutils.cc.

◆ XtransRotZYXEuler()

RBDL_DLLAPI SpatialMatrix XtransRotZYXEuler	(	const Vector3d &	displacement,
		const Vector3d &	zyx_euler
	)

Creates a spatial transformation for given parameters.

Creates a transformation to a coordinate system that is first rotated and then translated.

Parameters

displacement	The displacement to the new origin
zyx_euler	The orientation of the new coordinate system, specifyed by ZYX-Euler angles.

Definition at line 255 of file rbdl_mathutils.cc.

References Xrotx_mat(), Xroty_mat(), Xrotz_mat(), and Xtrans_mat().

Variable Documentation

◆ Matrix3dIdentity

RBDL_DLLAPI Matrix3d Matrix3dIdentity

extern

◆ Matrix3dZero

RBDL_DLLAPI Matrix3d Matrix3dZero

extern

◆ Vector3dZero

RBDL_DLLAPI Vector3d Vector3dZero

extern

Data Structures

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ Matrix2d

◆ Matrix3d

◆ Matrix43

◆ Matrix4d

◆ Matrix63

◆ MatrixNd

◆ Scalar

◆ SpatialMatrix

◆ SpatialVector

◆ Vector2d

◆ Vector3d

◆ Vector4d

◆ VectorNd

Function Documentation

◆ angular_acceleration_from_angle_rates()

◆ angular_velocity_from_angle_rates()

◆ crossf() [1/2]

◆ crossf() [2/2]

◆ crossm() [1/2]

◆ crossm() [2/2]

◆ global_angular_velocity_from_rates()

◆ LinSolveGaussElimPivot()

◆ Matrix3dIdentity()

◆ Matrix3dZero()

◆ MatrixFromPtr()

◆ operator<<() [1/2]

◆ operator<<() [2/2]

◆ parallel_axis()

◆ rotx()

◆ rotxdot()

◆ roty()

◆ rotydot()

◆ rotz()

◆ rotzdot()

◆ SparseFactorizeLTL()

◆ SparseMultiplyHx()

◆ SparseMultiplyLTx()

◆ SparseMultiplyLx()

◆ SparseSolveLTx()

◆ SparseSolveLx()

◆ SpatialMatrixCompareEpsilon()

◆ SpatialMatrixSetSubmatrix()

◆ SpatialVectorCompareEpsilon()

◆ SpatialVectorZero()

◆ Vector3dZero()

◆ VectorCrossMatrix()

◆ VectorFromPtr()

◆ Xrot()

◆ Xrotx()

◆ Xrotx_mat()

◆ Xroty()

◆ Xroty_mat()

◆ Xrotz()

◆ Xrotz_mat()

◆ Xtrans()

◆ Xtrans_mat()

◆ XtransRotZYXEuler()

Variable Documentation

◆ Matrix3dIdentity

◆ Matrix3dZero

◆ Vector3dZero