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

Classes
class	ForceVector
	A ForceVector is a SpatialVector containing 3 moments and 3 linear forces. More...

class	FrameOrientation
	A Frame object that represents an orientation(quaternion) relative to a reference frame. More...

class	FramePoint
	A FramePoint is a 3D point that is expressed in a ReferenceFrame. To change the ReferenceFrame a FramePoint is expressed in, you may call the inhereted FrameObject::changeFrame method and supply it a pointer to the ReferenceFrame you wish to have the FramePoint expressed in. This class and its implementation are an adaptation of FramePoint.java by Jerry Pratt and the IHMC Robotics Group. More...

class	FrameVector
	A FrameVector is a 3D vector with a ReferenceFrame, and all operations between FrameVectors and other frame objects will perform runtime checks that objects are expressed in the same frames. This class and its implementation are an adaptation of FrameVector.java by Jerry Pratt and the IHMC Robotics Group. More...

class	FrameVectorPair
	A FrameVector is a pair of 3D vector with a ReferenceFrame. More...

class	Matrix3d

class	Matrix4d

class	Momentum
	Momentum is mass/inertia multiplied by velocity. More...

class	MotionVector

class	Point3d

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

class	RigidBodyInertia
	This class stores a bodies mass, center of mass, and inertia information. The inertia elements are stored individually since the inertia matrix is a 3x3 symmetric matrix. The bodies inertia matrix, expressed about its center of mass, can be reconstructed as $I_c = \begin{bmatrix} I_xx & I_yx & I_zx \\ I_yx & I_yy & I_zy \\ I_zx & I_zy & I_zz \end{bmatrix}$ The full RigidBodyInertia matrix has the following structure, $\begin{bmatrix} I_c + (h\times)h & h\times \\ -h\times & \mathbf{1}_{3\times3}m \end{bmatrix}$ where $\mathbf{1}_{3\times 3}$ is a 3x3 identity matrix. More...

class	SpatialAcceleration
	SpatialAcceleration. For clarity, the ReferenceFrames are stated as follows. A spatial acceleration is the acceleration of the SpatialAcceleration::bodyFrame with respect to the SpatialAcceleration::baseFrame expressed in the SpatialAcceleration::expressedInFrame. More...

class	SpatialForce
	A SpatialForce is a spatial vector with the angular part being three moments and the linear part being 3 linear forces. More...

class	SpatialInertia
	A Math::SpatialInertia is a RigidBodyInertia explicitly expressed in a RobotDynamics::ReferenceFrame. The frame a Math::SpatialInertia is expressed in can be changed by calling RobotDynamics::FrameObject::changeFrame. More...

class	SpatialMatrix

class	SpatialMomentum
	A SpatialMomentum is a Momentum expressed in a RobotDynamics::ReferenceFrame. The angular portion of the vector is referred to as and the linear portion as . More...

class	SpatialMotion
	A SpatialMotion vector is a MotionVector with a RobotDynamics::ReferenceFrame it is expressed in. This allows for runtime checks that frame rules are obeyed and makes it easy to change the frame the metion vector is expressed in. As with a SpatialAcceleration, a SpatialMotion vector is the spatial velocity of a SpatialMotion::bodyFrame relative to a SpatialMotion::baseFrame and is expressed in RobotDynamics::FrameObject::referenceFrame. More...

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

class	SpatialVector

class	TransformableGeometricObject
	The TransformableGeometricObject class is an essential interface because it forces all geometric objects to implement a method that tells how to transform them. This makes in possible for frame transformations of any TransformableGeometricObject can be done via the FrameObject::changeFrame method. More...

class	Vector3d

class	Vector4d

Typedefs
typedef Eigen::AngleAxisd	AxisAngle

typedef std::vector< ForceVector, Eigen::aligned_allocator< ForceVector > >	ForceVectorV

typedef std::vector< FramePoint, Eigen::aligned_allocator< FramePoint > >	FramePointV

typedef std::vector< FrameVector, Eigen::aligned_allocator< FrameVector > >	FrameVectorV

typedef Eigen::Matrix< double, 6, 3 >	Matrix63

typedef Eigen::MatrixXd	MatrixNd

typedef std::vector< MotionVector, Eigen::aligned_allocator< MotionVector > >	MotionVectorV

typedef std::vector< Point3d, Eigen::aligned_allocator< Point3d > >	Point3V

typedef std::vector< RigidBodyInertia, Eigen::aligned_allocator< RigidBodyInertia > >	RigidBodyInertiaV

typedef std::vector< SpatialAcceleration, Eigen::aligned_allocator< SpatialAcceleration > >	SpatialAccelerationV

typedef std::vector< SpatialForce, Eigen::aligned_allocator< SpatialForce > >	SpatialForceV

typedef std::vector< SpatialInertia, Eigen::aligned_allocator< SpatialInertia > >	SpatialInertiaV

typedef std::vector< SpatialMomentum, Eigen::aligned_allocator< SpatialMomentum > >	SpatialMomentumV

typedef std::vector< SpatialMotion, Eigen::aligned_allocator< SpatialMotion > >	SpatialMotionV

typedef Eigen::VectorXd	VectorNd

Enumerations
enum	LinearSolver { LinearSolverUnknown = 0, LinearSolverPartialPivLU, LinearSolverColPivHouseholderQR, LinearSolverHouseholderQR, LinearSolverLLT, LinearSolverLast }
	Available solver methods for the linear systems. More...

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

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

static RigidBodyInertia	createFromMassComInertiaC (double mass, const Vector3d &com, const Matrix3d &inertia_C)

SpatialMatrix	crossf (const SpatialVector &v)
	Get the spatial force cross matrix. More...

SpatialVector	crossf (const SpatialVector &v1, const SpatialVector &v2)
	Spatial motion cross spatial force. More...

SpatialMatrix	crossm (const SpatialVector &v)
	Get the spatial motion cross matrix. More...

SpatialVector	crossm (const SpatialVector &v1, const SpatialVector &v2)
	Spatial motion cross times spatial motion. More...

Vector3d	getLinearPartTransformed (const SpatialVector &v, const SpatialTransform &X)
	Get the rotated linear portion of the spatial vector. More...

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

static Quaternion	intrinsicXYZAnglesToQuaternion (double roll, double pitch, double yaw)
	Convert RPY angles to quaternion. More...

static Quaternion	intrinsicXYZAnglesToQuaternion (const Vector3d &xyz_angles)
	Convert RPY angles to quaternion. More...

static Quaternion	intrinsicYXZAnglesToQuaternion (double pitch, double roll, double yaw)
	Convert PRY angles to quaternion. More...

static Quaternion	intrinsicYXZAnglesToQuaternion (const Vector3d &yxz_angles)
	Convert PRY angles to quaternion. More...

static Quaternion	intrinsicZYXAnglesToQuaternion (double yaw, double pitch, double roll)
	Convert YPR angles to quaternion. More...

static Quaternion	intrinsicZYXAnglesToQuaternion (const Vector3d &zyx_angles)
	Convert YPR angles to quaternion. More...

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

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

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

MatrixNd	matrixFromPtr (unsigned int rows, unsigned int cols, double *ptr, bool row_major=true)

bool	operator!= (const FramePoint &lhs, const FramePoint &rhs)
	Check if two FramePoints are not equal. More...

EIGEN_STRONG_INLINE SpatialMotion	operator% (SpatialMotion v1, const SpatialMotion &v2)

MotionVector	operator% (MotionVector v, const MotionVector &v2)

ForceVector	operator% (MotionVector v, const ForceVector &v2)

SpatialMomentum	operator* (const SpatialInertia &inertia, const SpatialMotion &vector)

static Momentum	operator* (const RigidBodyInertia &I, const MotionVector &v)
	Multiplying a Math::RigidBodyInertia by a Math::MotionVector returns a Momentum. More...

SpatialForce	operator* (SpatialForce f1, double scale)
	Overloaded * operator to scale a spatial force by a scalar value. More...

template<typename T >
FrameVector	operator* (FrameVector v1, const T scale)

SpatialVector	operator* (const RigidBodyInertia &I, const SpatialVector &v)
	Operator for multiplying a Math::RigidBodyInertia by a Math::SpatialVector. More...

ForceVector	operator* (const SpatialTransform &X, ForceVector f)
	Operator for transforming a ForceVector. Calls the ForceVector::transform method. More...

template<typename T >
FrameVector	operator* (const T scale, FrameVector v1)

Matrix63	operator* (const RigidBodyInertia &I, const Matrix63 &m)
	Operator for multiplying a Math::RigidBodyInertia by a Math::Matrix63. More...

template<typename T >
FrameVectorPair	operator* (FrameVectorPair pair, const T scalar)

template<typename T >
FrameVectorPair	operator* (const T scalar, FrameVectorPair pair)

template<typename T >
FrameVector	operator* (const T scale, FramePoint p)

template<typename T >
FrameVector	operator* (FramePoint p, const T scale)

MotionVector	operator* (const SpatialTransform &X, MotionVector v)
	Operator for transforming a MotionVector. More...

template<typename T >
Point3d	operator* (Point3d p, const T scale)

template<typename T >
Point3d	operator* (const T scale, Point3d p)

SpatialAcceleration	operator+ (SpatialAcceleration v1, const SpatialAcceleration &v2)
	Add two SpatialAccelerations. Frame check will be performed to ensure frame rules are abided by. More...

SpatialInertia	operator+ (SpatialInertia inertia_a, const SpatialInertia &inertia_b)
	Adds two Math::SpatialInertia together. Performs frame checks. More...

SpatialForce	operator+ (SpatialForce f1, const SpatialForce &f2)
	Overloaded + operator to add two SpatialForce vectors and return the result in a new SpatialForce. Frame checks are performed. More...

RigidBodyInertia	operator+ (RigidBodyInertia rbi_in, const RigidBodyInertia &rbi)
	Add two Math::RigidBodyInertia objects together. More...

EIGEN_STRONG_INLINE SpatialMotion	operator+ (SpatialMotion v1, const SpatialMotion &v2)

FrameVector	operator+ (FrameVector v1, const Vector3d v2)

FrameVector	operator+ (FrameVector v1, const FrameVector v2)
	Add two FrameVectors together. More...

FrameVectorPair	operator+ (FrameVectorPair v1, const FrameVectorPair v2)

FramePoint	operator+ (FramePoint p, const FrameVector &v)

Point3d	operator+ (Point3d p, const Vector3d &v)

SpatialAcceleration	operator- (SpatialAcceleration v1, const SpatialAcceleration &v2)
	Subtract two SpatialAccelerations. Frame check will be performed to ensure frame rules are abided by. More...

static Momentum	operator- (Momentum m1, const Momentum &m2)
	Add two momentums. More...

SpatialForce	operator- (SpatialForce f1, const SpatialForce &f2)
	Overloaded - operator to add two SpatialForce vectors and return the result in a new SpatialForce. Frame checks are performed. More...

EIGEN_STRONG_INLINE SpatialMotion	operator- (SpatialMotion v1, const SpatialMotion &v2)

FrameVector	operator- (FrameVector v1, const Vector3d v2)

FrameVector	operator- (FrameVector v1, const FrameVector v2)
	Add two FrameVectors together. More...

FrameVectorPair	operator- (FrameVectorPair v1, const FrameVectorPair v2)

FramePoint	operator- (FramePoint p, const FrameVector &v)

Point3d	operator- (Point3d p, const Vector3d &v)

FrameVector	operator- (FramePoint p1, const FramePoint &p2)
	Subtract two FramePoints and return result in newly created FramePoint. More...

Vector3d	operator- (Point3d p1, const Point3d &p2)

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

std::ostream &	operator<< (std::ostream &os, const Point3d &point)

std::ostream &	operator<< (std::ostream &output, const FramePoint &framePoint)

bool	operator== (const FramePoint &lhs, const FramePoint &rhs)
	Check if two FramePoints are equal. More...

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

Quaternion	QuaternionIdentity (0., 0., 0., 1)

Matrix3d	rotx (const double &xrot)

Matrix3d	rotxdot (const double &x, const double &xdot)

Matrix3d	roty (const double &yrot)

Matrix3d	rotydot (const double &y, const double &ydot)

Matrix3d	rotz (const double &zrot)

Matrix3d	rotzdot (const double &z, const double &zdot)

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

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

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

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

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

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

SpatialMatrix	SpatialMatrixIdentity (1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1.)

SpatialMatrix	SpatialMatrixZero (0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.)

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

static AxisAngle	toAxisAngle (Quaternion q)
	Get axis angle representation of a quaternion. More...

static Vector3d	toIntrinsicZYXAngles (const Quaternion &q, double yaw_at_pitch_singularity=0.)
	Converte quaternion to intrinsic ZYX euler angles. More...

static Vector3d	toIntrinsicZYXAngles (const Matrix3d &m, double yaw_at_pitch_singularity=0.)
	Convert rotation matrix to intrinsic ZYX euler angles. More...

static Matrix3d	toMatrix (const Quaternion &q)
	Convert quaternion to rotation matrix. More...

static Quaternion	toQuaternion (const Vector3d &axis, double angle_rad)
	Get quaternion representation of axis and angle. More...

static Quaternion	toQuaternion (const AxisAngle &axisAngle)
	Convert axis angle to quaternion. More...

static Quaternion	toQuaternion (const Matrix3d &mat)
	convert rotation matrix to quaternion More...

static Matrix3d	toTildeForm (const Vector3d &vector)
	Create a skew symmetric matrix, m, from a 3d vector such that, given two vectors and , a 3rd vector which is the cross product of the first two is given by, $v_3=\tilde{v_1}v_2$ . The $\sim$ operator is referred to in Featherstones RBDA as the 3d vector cross( $\times$ ) operator. More...

static Matrix3d	toTildeForm (const double x, const double y, const double z)

static Matrix3d	toTildeForm (const Point3d &p)

Vector3d	Vector3dZero (0., 0., 0.)

VectorNd	vectorFromPtr (unsigned int n, double *ptr)

SpatialTransform	XeulerXYZ (double roll, double pitch, double yaw)
	Get transform with zero translation and intrinsic euler x/y/z rotation. More...

SpatialTransform	XeulerXYZ (const Vector3d &xyz_angles)
	Get transform with zero translation and euler x/y/z rotation. More...

SpatialTransform	XeulerZYX (double yaw, double pitch, double roll)
	Get transform with zero translation and intrinsic euler z/y/x rotation. More...

SpatialTransform	XeulerZYX (const Vector3d &ypr)
	Get transform defined by intrinsic YPR(yaw->pitch->roll) euler angles. More...

SpatialTransform	Xrot (double angle_rad, const Vector3d &axis)
	Get spatial transform from angle and axis. More...

SpatialTransform	XrotQuat (double x, double y, double z, double w)

SpatialTransform	XrotQuat (const Quaternion &orientation)

SpatialTransform	Xrotx (const double &xrot)
	Get transform with zero translation and pure rotation about x axis. More...

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

SpatialTransform	Xroty (const double &yrot)
	Get transform with zero translation and pure rotation about y axis. More...

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

SpatialTransform	Xrotz (const double &zrot)
	Get transform with zero translation and pure rotation about z axis. More...

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

SpatialTransform	Xtrans (const Vector3d &r)
	Get pure translation transform. More...

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

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

Variables
Matrix3d	Matrix3dIdentity

Matrix3d	Matrix3dZero

Quaternion	QuaternionIdentity

SpatialMatrix	SpatialMatrixIdentity

SpatialMatrix	SpatialMatrixZero

SpatialVector	SpatialVectorZero

Vector3d	Vector3dZero

Detailed Description

Math types such as vectors and matrices and utility functions.

Typedef Documentation

typedef Eigen::AngleAxisd RobotDynamics::Math::AxisAngle

Definition at line 27 of file rdl_eigenmath.h.

typedef std::vector<ForceVector, Eigen::aligned_allocator<ForceVector> > RobotDynamics::Math::ForceVectorV

Definition at line 261 of file ForceVector.hpp.

typedef std::vector<FramePoint, Eigen::aligned_allocator<FramePoint> > RobotDynamics::Math::FramePointV

Definition at line 381 of file FramePoint.hpp.

typedef std::vector<FrameVector, Eigen::aligned_allocator<FrameVector> > RobotDynamics::Math::FrameVectorV

Definition at line 300 of file FrameVector.hpp.

typedef Eigen::Matrix<double, 6, 3> RobotDynamics::Math::Matrix63

Definition at line 24 of file rdl_eigenmath.h.

typedef Eigen::MatrixXd RobotDynamics::Math::MatrixNd

Definition at line 26 of file rdl_eigenmath.h.

typedef std::vector<MotionVector, Eigen::aligned_allocator<MotionVector> > RobotDynamics::Math::MotionVectorV

Definition at line 350 of file MotionVector.hpp.

typedef std::vector<Point3d, Eigen::aligned_allocator<Point3d> > RobotDynamics::Math::Point3V

Definition at line 374 of file Point3.hpp.

typedef std::vector<RigidBodyInertia, Eigen::aligned_allocator<RigidBodyInertia> > RobotDynamics::Math::RigidBodyInertiaV

Definition at line 290 of file RigidBodyInertia.hpp.

typedef std::vector<SpatialAcceleration, Eigen::aligned_allocator<SpatialAcceleration> > RobotDynamics::Math::SpatialAccelerationV

Definition at line 148 of file SpatialAcceleration.hpp.

typedef std::vector<SpatialForce, Eigen::aligned_allocator<SpatialForce> > RobotDynamics::Math::SpatialForceV

Definition at line 248 of file SpatialForce.hpp.

typedef std::vector<SpatialInertia, Eigen::aligned_allocator<SpatialInertia> > RobotDynamics::Math::SpatialInertiaV

Definition at line 139 of file SpatialRigidBodyInertia.hpp.

typedef std::vector<SpatialMomentum, Eigen::aligned_allocator<SpatialMomentum> > RobotDynamics::Math::SpatialMomentumV

Definition at line 174 of file SpatialMomentum.hpp.

typedef std::vector<SpatialMotion, Eigen::aligned_allocator<SpatialMotion> > RobotDynamics::Math::SpatialMotionV

Definition at line 260 of file SpatialMotion.hpp.

typedef Eigen::VectorXd RobotDynamics::Math::VectorNd

Definition at line 25 of file rdl_eigenmath.h.

Enumeration Type Documentation

enum RobotDynamics::Math::LinearSolver

Available solver methods for the linear systems.

Enumerator
LinearSolverUnknown
LinearSolverPartialPivLU
LinearSolverColPivHouseholderQR
LinearSolverHouseholderQR
LinearSolverLLT
LinearSolverLast

Definition at line 34 of file rdl_mathutils.h.

Function Documentation

Vector3d RobotDynamics::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 223 of file rdl_mathutils.h.

Vector3d RobotDynamics::Math::angular_velocity_from_angle_rates	(	const Vector3d &	zyx_angles,
		const Vector3d &	zyx_angle_rates
	)

inline

Definition at line 204 of file rdl_mathutils.h.

static RigidBodyInertia RobotDynamics::Math::createFromMassComInertiaC	(	double	mass,
		const Vector3d &	com,
		const Matrix3d &	inertia_C
	)

inlinestatic

Creates a RigidBodyInertia from a body's mass, center of mass location, and 3x3 inertia matrix

Parameters

mass	Body mass
com	Center of mass location in body frame
inertia_C	3x3 inertia tensor about from located at center of mass and aligned with body frame

Returns: RigidBodyInertia

Definition at line 273 of file RigidBodyInertia.hpp.

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

inline

Get the spatial force cross matrix.

Parameters

v

Returns: $v\times*$

Definition at line 403 of file SpatialAlgebraOperators.h.

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

inline

Spatial motion cross spatial force.

Parameters

v1	Spatial motion
v2	Spatial force

Returns: $v1\times* v2$

Definition at line 415 of file SpatialAlgebraOperators.h.

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

inline

Get the spatial motion cross matrix.

Parameters

v

Returns: $v\times$

Definition at line 379 of file SpatialAlgebraOperators.h.

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

inline

Spatial motion cross times spatial motion.

Parameters

v1
v2

Returns: $v1\times v2$

Definition at line 391 of file SpatialAlgebraOperators.h.

Vector3d RobotDynamics::Math::getLinearPartTransformed	(	const SpatialVector &	v,
		const SpatialTransform &	X
	)

inline

Get the rotated linear portion of the spatial vector.

Parameters

v	Spatial vector
X	Spatial transform

Returns: Rotated linear portion of the spatial vector argument

Definition at line 428 of file SpatialAlgebraOperators.h.

Vector3d RobotDynamics::Math::global_angular_velocity_from_rates	(	const Vector3d &	zyx_angles,
		const Vector3d &	zyx_rates
	)

inline

Definition at line 215 of file rdl_mathutils.h.

static Quaternion RobotDynamics::Math::intrinsicXYZAnglesToQuaternion	(	double	roll,
		double	pitch,
		double	yaw
	)

inlinestatic

Convert RPY angles to quaternion.

Definition at line 114 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::intrinsicXYZAnglesToQuaternion ( const Vector3d & xyz_angles )

inlinestatic

Convert RPY angles to quaternion.

Definition at line 122 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::intrinsicYXZAnglesToQuaternion	(	double	pitch,
		double	roll,
		double	yaw
	)

inlinestatic

Convert PRY angles to quaternion.

Definition at line 98 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::intrinsicYXZAnglesToQuaternion ( const Vector3d & yxz_angles )

inlinestatic

Convert PRY angles to quaternion.

Definition at line 106 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::intrinsicZYXAnglesToQuaternion	(	double	yaw,
		double	pitch,
		double	roll
	)

inlinestatic

Convert YPR angles to quaternion.

Definition at line 82 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::intrinsicZYXAnglesToQuaternion ( const Vector3d & zyx_angles )

inlinestatic

Convert YPR angles to quaternion.

Definition at line 90 of file SpatialAlgebraOperators.h.

bool RobotDynamics::Math::linSolveGaussElimPivot	(	MatrixNd	A,
		VectorNd	b,
		VectorNd &	x
	)

Solves a linear system using gaussian elimination with pivoting.

Definition at line 36 of file rdl_mathutils.cc.

Matrix3d RobotDynamics::Math::Matrix3dIdentity	(	1.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		1
	)

Matrix3d RobotDynamics::Math::Matrix3dZero	(	0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.
	)

MatrixNd RobotDynamics::Math::matrixFromPtr	(	unsigned int	rows,
		unsigned int	cols,
		double *	ptr,
		bool	row_major = `true`
	)

inline

Definition at line 66 of file rdl_mathutils.h.

bool RobotDynamics::Math::operator!=	(	const FramePoint &	lhs,
		const FramePoint &	rhs
	)

inline

Check if two FramePoints are not equal.

Parameters

lhs
rhs

Exceptions

ReferenceFrameException If the two FramePoint arguments are not expressed in the same ReferenceFrame

Returns: bool false if equal, true if not equal

Definition at line 370 of file FramePoint.hpp.

EIGEN_STRONG_INLINE SpatialMotion RobotDynamics::Math::operator%	(	SpatialMotion	v1,
		const SpatialMotion &	v2
	)

Definition at line 255 of file SpatialMotion.hpp.

MotionVector RobotDynamics::Math::operator%	(	MotionVector	v,
		const MotionVector &	v2
	)

inline

Operator for performing the spatial vector $\times$ operator.

Parameters

v
v2

Returns: Returns $ret = (v \times)v2$

Definition at line 335 of file MotionVector.hpp.

ForceVector RobotDynamics::Math::operator%	(	MotionVector	v,
		const ForceVector &	v2
	)

inline

Operator for performing the spatial vector $\times*$ operator

Parameters

v
v2

Returns: Returns $ret = (v\times*)v2$

Definition at line 346 of file MotionVector.hpp.

SpatialMomentum RobotDynamics::Math::operator*	(	const SpatialInertia &	inertia,
		const SpatialMotion &	vector
	)

inline

Overloaded * operator for computing a SpatialMomentum from a SpatialInertia and SpatialMotion. Frame checks will be performed.

Parameters

inertia
vector

Returns: The resulting SpatialMomentum

Definition at line 167 of file SpatialMomentum.hpp.

static Momentum RobotDynamics::Math::operator*	(	const RigidBodyInertia &	I,
		const MotionVector &	v
	)

inlinestatic

Multiplying a Math::RigidBodyInertia by a Math::MotionVector returns a Momentum.

Parameters

I
v

Returns: I*V

Definition at line 195 of file Momentum.hpp.

SpatialForce RobotDynamics::Math::operator*	(	SpatialForce	f1,
		double	scale
	)

inline

Overloaded * operator to scale a spatial force by a scalar value.

Parameters

f1
scale

Returns

Definition at line 244 of file SpatialForce.hpp.

template<typename T >

FrameVector RobotDynamics::Math::operator*	(	FrameVector	v1,
		const T	scale
	)

inline

Definition at line 250 of file FrameVector.hpp.

SpatialVector RobotDynamics::Math::operator*	(	const RigidBodyInertia &	I,
		const SpatialVector &	v
	)

inline

Operator for multiplying a Math::RigidBodyInertia by a Math::SpatialVector.

Parameters

I
v

Returns: Math::RigidBodyInertia times Math::SpatialVector

Definition at line 250 of file RigidBodyInertia.hpp.

ForceVector RobotDynamics::Math::operator*	(	const SpatialTransform &	X,
		ForceVector	f
	)

inline

Operator for transforming a ForceVector. Calls the ForceVector::transform method.

Parameters

X	SpatialTransform
f	ForceVector to be transformed

Returns: Transformed ForceVector

Definition at line 256 of file ForceVector.hpp.

template<typename T >

FrameVector RobotDynamics::Math::operator*	(	const T	scale,
		FrameVector	v1
	)

inline

Definition at line 257 of file FrameVector.hpp.

Matrix63 RobotDynamics::Math::operator*	(	const RigidBodyInertia &	I,
		const Matrix63 &	m
	)

inline

Operator for multiplying a Math::RigidBodyInertia by a Math::Matrix63.

Parameters

I
m

Returns: The result of multiplying a Math::RigidBodyInertia by a Math::Matrix63

Definition at line 261 of file RigidBodyInertia.hpp.

template<typename T >

FrameVectorPair RobotDynamics::Math::operator*	(	FrameVectorPair	pair,
		const T	scalar
	)

inline

Definition at line 279 of file FrameVectorPair.hpp.

template<typename T >

FrameVectorPair RobotDynamics::Math::operator*	(	const T	scalar,
		FrameVectorPair	pair
	)

inline

Definition at line 286 of file FrameVectorPair.hpp.

template<typename T >

FrameVector RobotDynamics::Math::operator*	(	const T	scale,
		FramePoint	p
	)

inline

Definition at line 308 of file FramePoint.hpp.

template<typename T >

FrameVector RobotDynamics::Math::operator*	(	FramePoint	p,
		const T	scale
	)

inline

Definition at line 315 of file FramePoint.hpp.

MotionVector RobotDynamics::Math::operator*	(	const SpatialTransform &	X,
		MotionVector	v
	)

inline

Operator for transforming a MotionVector.

Parameters

X	SpatialTransform to the desired frame
v

Returns: Transformed MotionVector

Definition at line 323 of file MotionVector.hpp.

template<typename T >

Point3d RobotDynamics::Math::operator*	(	Point3d	p,
		const T	scale
	)

inline

Definition at line 344 of file Point3.hpp.

template<typename T >

Point3d RobotDynamics::Math::operator*	(	const T	scale,
		Point3d	p
	)

inline

Definition at line 352 of file Point3.hpp.

SpatialAcceleration RobotDynamics::Math::operator+	(	SpatialAcceleration	v1,
		const SpatialAcceleration &	v2
	)

inline

Add two SpatialAccelerations. Frame check will be performed to ensure frame rules are abided by.

Parameters

v1
v2

Returns: A new SpatialAcceleration that is the addition of the two arguments.

Definition at line 131 of file SpatialAcceleration.hpp.

SpatialInertia RobotDynamics::Math::operator+	(	SpatialInertia	inertia_a,
		const SpatialInertia &	inertia_b
	)

inline

Adds two Math::SpatialInertia together. Performs frame checks.

Parameters

inertia_a
inertia_b

Returns: The addition of the two arguments

Definition at line 134 of file SpatialRigidBodyInertia.hpp.

SpatialForce RobotDynamics::Math::operator+	(	SpatialForce	f1,
		const SpatialForce &	f2
	)

inline

Overloaded + operator to add two SpatialForce vectors and return the result in a new SpatialForce. Frame checks are performed.

Parameters

f1
f2

Returns

Definition at line 221 of file SpatialForce.hpp.

RigidBodyInertia RobotDynamics::Math::operator+	(	RigidBodyInertia	rbi_in,
		const RigidBodyInertia &	rbi
	)

inline

Add two Math::RigidBodyInertia objects together.

Parameters

rbi_in	A copy that is modified and returned.
rbi

Returns: A Math::RigidBodyInertia that is the addition of the two arguments

Definition at line 238 of file RigidBodyInertia.hpp.

EIGEN_STRONG_INLINE SpatialMotion RobotDynamics::Math::operator+	(	SpatialMotion	v1,
		const SpatialMotion &	v2
	)

Definition at line 243 of file SpatialMotion.hpp.

FrameVector RobotDynamics::Math::operator+	(	FrameVector	v1,
		const Vector3d	v2
	)

inline

Definition at line 263 of file FrameVector.hpp.

FrameVector RobotDynamics::Math::operator+	(	FrameVector	v1,
		const FrameVector	v2
	)

inline

Add two FrameVectors together.

Parameters

v1
v2

Returns: THe result of

Definition at line 282 of file FrameVector.hpp.

FrameVectorPair RobotDynamics::Math::operator+	(	FrameVectorPair	v1,
		const FrameVectorPair	v2
	)

inline

Definition at line 293 of file FrameVectorPair.hpp.

FramePoint RobotDynamics::Math::operator+	(	FramePoint	p,
		const FrameVector &	v
	)

inline

Definition at line 295 of file FramePoint.hpp.

Point3d RobotDynamics::Math::operator+	(	Point3d	p,
		const Vector3d &	v
	)

inline

Definition at line 331 of file Point3.hpp.

SpatialAcceleration RobotDynamics::Math::operator-	(	SpatialAcceleration	v1,
		const SpatialAcceleration &	v2
	)

inline

Subtract two SpatialAccelerations. Frame check will be performed to ensure frame rules are abided by.

Parameters

v1
v2

Returns: A new SpatialAcceleration that is the subtraction of the second argument from the first.

Definition at line 143 of file SpatialAcceleration.hpp.

static Momentum RobotDynamics::Math::operator-	(	Momentum	m1,
		const Momentum &	m2
	)

inlinestatic

Add two momentums.

Parameters

m1
m2

Returns: m = m1-m2 /f$

Definition at line 218 of file Momentum.hpp.

SpatialForce RobotDynamics::Math::operator-	(	SpatialForce	f1,
		const SpatialForce &	f2
	)

inline

Overloaded - operator to add two SpatialForce vectors and return the result in a new SpatialForce. Frame checks are performed.

Parameters

f1
f2

Returns

Definition at line 233 of file SpatialForce.hpp.

EIGEN_STRONG_INLINE SpatialMotion RobotDynamics::Math::operator-	(	SpatialMotion	v1,
		const SpatialMotion &	v2
	)

Definition at line 249 of file SpatialMotion.hpp.

FrameVector RobotDynamics::Math::operator-	(	FrameVector	v1,
		const Vector3d	v2
	)

inline

Definition at line 269 of file FrameVector.hpp.

FrameVector RobotDynamics::Math::operator-	(	FrameVector	v1,
		const FrameVector	v2
	)

inline

Add two FrameVectors together.

Parameters

v1
v2

Returns: THe result of

Definition at line 295 of file FrameVector.hpp.

FrameVectorPair RobotDynamics::Math::operator-	(	FrameVectorPair	v1,
		const FrameVectorPair	v2
	)

inline

Definition at line 300 of file FrameVectorPair.hpp.

FramePoint RobotDynamics::Math::operator-	(	FramePoint	p,
		const FrameVector &	v
	)

inline

Definition at line 301 of file FramePoint.hpp.

Point3d RobotDynamics::Math::operator-	(	Point3d	p,
		const Vector3d &	v
	)

inline

Definition at line 337 of file Point3.hpp.

FrameVector RobotDynamics::Math::operator-	(	FramePoint	p1,
		const FramePoint &	p2
	)

inline

Subtract two FramePoints and return result in newly created FramePoint.

Parameters

p1
p2

Exceptions

ReferenceFrameException If the two FramePoint arguments are not expressed in the same ReferenceFrame

Returns: A FramePoint that is the difference of the two argument FramePoints, i.e. p1-=p2

Definition at line 357 of file FramePoint.hpp.

Vector3d RobotDynamics::Math::operator-	(	Point3d	p1,
		const Point3d &	p2
	)

inline

Definition at line 359 of file Point3.hpp.

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

inline

Definition at line 237 of file SpatialAlgebraOperators.h.

std::ostream& RobotDynamics::Math::operator<<	(	std::ostream &	os,
		const Point3d &	point
	)

inline

Definition at line 364 of file Point3.hpp.

std::ostream& RobotDynamics::Math::operator<<	(	std::ostream &	output,
		const FramePoint &	framePoint
	)

inline

Definition at line 375 of file FramePoint.hpp.

bool RobotDynamics::Math::operator==	(	const FramePoint &	lhs,
		const FramePoint &	rhs
	)

inline

Check if two FramePoints are equal.

Parameters

lhs
rhs

Exceptions

ReferenceFrameException If the two FramePoint arguments are not expressed in the same ReferenceFrame

Returns: bool true if equal, false if not equal

Definition at line 328 of file FramePoint.hpp.

Matrix3d RobotDynamics::Math::parallel_axis	(	const Matrix3d &	inertia,
		double	mass,
		const Vector3d &	com
	)

Translates the inertia matrix to a new center.

Definition at line 126 of file rdl_mathutils.cc.

Quaternion RobotDynamics::Math::QuaternionIdentity	(	0.	,
		0.	,
		0.	,
		1
	)

Matrix3d RobotDynamics::Math::rotx ( const double & xrot )

inline

Definition at line 150 of file rdl_mathutils.h.

Matrix3d RobotDynamics::Math::rotxdot	(	const double &	x,
		const double &	xdot
	)

inline

Definition at line 177 of file rdl_mathutils.h.

Matrix3d RobotDynamics::Math::roty ( const double & yrot )

inline

Definition at line 159 of file rdl_mathutils.h.

Matrix3d RobotDynamics::Math::rotydot	(	const double &	y,
		const double &	ydot
	)

inline

Definition at line 186 of file rdl_mathutils.h.

Matrix3d RobotDynamics::Math::rotz ( const double & zrot )

inline

Definition at line 168 of file rdl_mathutils.h.

Matrix3d RobotDynamics::Math::rotzdot	(	const double &	z,
		const double &	zdot
	)

inline

Definition at line 195 of file rdl_mathutils.h.

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

Definition at line 170 of file rdl_mathutils.cc.

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

Definition at line 204 of file rdl_mathutils.cc.

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

Definition at line 214 of file rdl_mathutils.cc.

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

Definition at line 209 of file rdl_mathutils.cc.

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

Definition at line 233 of file rdl_mathutils.cc.

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

Definition at line 219 of file rdl_mathutils.cc.

SpatialMatrix RobotDynamics::Math::SpatialMatrixIdentity	(	1.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		1.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		1.
	)

SpatialMatrix RobotDynamics::Math::SpatialMatrixZero	(	0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.
	)

SpatialVector RobotDynamics::Math::SpatialVectorZero	(	0.	,
		0.	,
		0.	,
		0.	,
		0.	,
		0.
	)

static AxisAngle RobotDynamics::Math::toAxisAngle ( Quaternion q )

inlinestatic

Get axis angle representation of a quaternion.

Parameters

q

Returns: Axis angle

Definition at line 132 of file SpatialAlgebraOperators.h.

static Vector3d RobotDynamics::Math::toIntrinsicZYXAngles	(	const Quaternion &	q,
		double	yaw_at_pitch_singularity = `0.`
	)

inlinestatic

Converte quaternion to intrinsic ZYX euler angles.

Parameters

q	The quaternion to convert to ZYX angles
yaw_at_pitch_singularity	At Y = +- PI/2 is a singularity in which there are multiple solutions. This will be the yaw value in the output and the roll value is dependent on this. To get the most accurate results at singularity, provide this value as close as possible to desired/reality and the resulting roll value will be near the expected

q can be non-normalised quaternion

Definition at line 34 of file SpatialAlgebraOperators.h.

static Vector3d RobotDynamics::Math::toIntrinsicZYXAngles	(	const Matrix3d &	m,
		double	yaw_at_pitch_singularity = `0.`
	)

inlinestatic

Convert rotation matrix to intrinsic ZYX euler angles.

Parameters

m	Rotation matrix to convert
yaw_at_pitch_singularity	At Y = +- PI/2 is a singularity in which there are multiple solutions. This will be the yaw value in the output and the roll value is dependent on this. To get the most accurate results at singularity, provide this value as close as possible to desired/reality and the resulting roll value will be near the expected

Definition at line 205 of file SpatialAlgebraOperators.h.

static Matrix3d RobotDynamics::Math::toMatrix ( const Quaternion & q )

inlinestatic

Convert quaternion to rotation matrix.

Definition at line 187 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::toQuaternion	(	const Vector3d &	axis,
		double	angle_rad
	)

inlinestatic

Get quaternion representation of axis and angle.

Parameters

axis
angle_rad

Returns: Quaternion

Definition at line 63 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::toQuaternion ( const AxisAngle & axisAngle )

inlinestatic

Convert axis angle to quaternion.

Definition at line 74 of file SpatialAlgebraOperators.h.

static Quaternion RobotDynamics::Math::toQuaternion ( const Matrix3d & mat )

inlinestatic

convert rotation matrix to quaternion

Definition at line 158 of file SpatialAlgebraOperators.h.

static Matrix3d RobotDynamics::Math::toTildeForm ( const Vector3d & vector )

inlinestatic

Create a skew symmetric matrix, m, from a 3d vector such that, given two vectors $v_1$ and $v_2$ , a 3rd vector which is the cross product of the first two is given by, $v_3=\tilde{v_1}v_2$ . The $\sim$ operator is referred to in Featherstones RBDA as the 3d vector cross( $\times$ ) operator.

Parameters

vector

Returns: A skew symmetric matrix

Definition at line 227 of file SpatialAlgebraOperators.h.

static Matrix3d RobotDynamics::Math::toTildeForm	(	const double	x,
		const double	y,
		const double	z
	)

inlinestatic

Definition at line 232 of file SpatialAlgebraOperators.h.

static Matrix3d RobotDynamics::Math::toTildeForm ( const Point3d & p )

inlinestatic

Definition at line 370 of file Point3.hpp.

Vector3d RobotDynamics::Math::Vector3dZero	(	0.	,
		0.	,
		0.
	)

VectorNd RobotDynamics::Math::vectorFromPtr	(	unsigned int	n,
		double *	ptr
	)

inline

Definition at line 53 of file rdl_mathutils.h.

SpatialTransform RobotDynamics::Math::XeulerXYZ	(	double	roll,
		double	pitch,
		double	yaw
	)

inline

Get transform with zero translation and intrinsic euler x/y/z rotation.

Parameters

roll
pitch
yaw

Returns: Transform with zero translation and x/y/z rotation

Definition at line 339 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::XeulerXYZ ( const Vector3d & xyz_angles )

inline

Get transform with zero translation and euler x/y/z rotation.

Parameters

intrinsic xyz_angles xyz angles where element 0 is roll, 1 is pitch, and 2 is yaw

Returns: Transform with zero translation and x/y/z rotation

Definition at line 349 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::XeulerZYX	(	double	yaw,
		double	pitch,
		double	roll
	)

inline

Get transform with zero translation and intrinsic euler z/y/x rotation.

Parameters

yaw
pitch
roll

Returns: Transform with zero translation and z/y/x rotation

Definition at line 316 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::XeulerZYX ( const Vector3d & ypr )

inline

Get transform defined by intrinsic YPR(yaw->pitch->roll) euler angles.

Parameters

ypr	Vector of euler angles where ypr[0] is yaw, ypr[1] is pitch, and ypr[2] is roll

Returns: spatial transform where rotation component is defined by the YPR rotations

Definition at line 327 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::Xrot	(	double	angle_rad,
		const Vector3d &	axis
	)

inline

Get spatial transform from angle and axis.

Parameters

angle_rad	angle magnitude
axis	normalized 3d vector

Returns: Spatial transform

Definition at line 250 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::XrotQuat	(	double	x,
		double	y,
		double	z,
		double	w
	)

inline

Definition at line 354 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::XrotQuat ( const Quaternion & orientation )

inline

Definition at line 359 of file SpatialAlgebraOperators.h.

SpatialTransform RobotDynamics::Math::Xrotx ( const double & xrot )

inline

Get transform with zero translation and pure rotation about x axis.

Parameters

xrot

Returns: Transform with zero translation and x-rotation

Definition at line 272 of file SpatialAlgebraOperators.h.

SpatialMatrix RobotDynamics::Math::Xrotx_mat ( const double & 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 138 of file rdl_mathutils.cc.

SpatialTransform RobotDynamics::Math::Xroty ( const double & yrot )

inline

Get transform with zero translation and pure rotation about y axis.

Parameters

yrot

Returns: Transform with zero translation and y-rotation

Definition at line 286 of file SpatialAlgebraOperators.h.

SpatialMatrix RobotDynamics::Math::Xroty_mat ( const double & 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 147 of file rdl_mathutils.cc.

SpatialTransform RobotDynamics::Math::Xrotz ( const double & zrot )

inline

Get transform with zero translation and pure rotation about z axis.

Parameters

zrot

Returns: Transform with zero translation and z-rotation

Definition at line 300 of file SpatialAlgebraOperators.h.

SpatialMatrix RobotDynamics::Math::Xrotz_mat ( const double & 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 156 of file rdl_mathutils.cc.

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

inline

Get pure translation transform.

Parameters

r

Returns: Transform with identity rotation and translation

Definition at line 369 of file SpatialAlgebraOperators.h.

SpatialMatrix RobotDynamics::Math::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 133 of file rdl_mathutils.cc.

SpatialMatrix RobotDynamics::Math::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 165 of file rdl_mathutils.cc.

Variable Documentation

Matrix3d RobotDynamics::Math::Matrix3dIdentity(1., 0., 0., 0., 1., 0., 0., 0., 1)

Matrix3d RobotDynamics::Math::Matrix3dZero(0., 0., 0., 0., 0., 0., 0., 0., 0.)

Quaternion RobotDynamics::Math::QuaternionIdentity(0., 0., 0., 1)

SpatialMatrix RobotDynamics::Math::SpatialMatrixIdentity(1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 1.)

SpatialMatrix RobotDynamics::Math::SpatialMatrixZero(0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.)

SpatialVector RobotDynamics::Math::SpatialVectorZero(0., 0., 0., 0., 0., 0.)

Vector3d RobotDynamics::Math::Vector3dZero(0., 0., 0.)

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

Enumeration Type Documentation

Function Documentation

Variable Documentation