Robot Dynamics Library: RobotDynamics::Math::Quaternion Class Reference

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

#include <rdl_eigenmath.hpp>

Inheritance diagram for RobotDynamics::Math::Quaternion:

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Collaboration diagram for RobotDynamics::Math::Quaternion:

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Public Member Functions
	Quaternion ()
	Constructor. More...

	Quaternion (const Eigen::Quaterniond &q)

	Quaternion (const RobotDynamics::Math::Quaternion &q)

	Quaternion (const Eigen::Product< Eigen::Matrix< double, 3, 3 >, Eigen::Matrix< double, 3, 3 >, 0 > E)

	Quaternion (const Eigen::Matrix3d &E)

	Quaternion (const Eigen::Matrix3d::ConstTransposeReturnType &E)

	Quaternion (Eigen::Transpose< Eigen::Matrix< double, 3, 3 > > E)

	Quaternion (const Vector4d &v)

	Quaternion (const AxisAngle &axis_angle)

	Quaternion (Vector3d axis, double angle)

	Quaternion (double x, double y, double z, double w)
	Constructor. More...

AxisAngle	toAxisAngle () const

bool	isApprox (Quaternion o, double eps) const

bool	isApprox (Matrix3d E, double eps) const

EIGEN_STRONG_INLINE double &	x ()

EIGEN_STRONG_INLINE double	x () const

EIGEN_STRONG_INLINE double &	y ()

EIGEN_STRONG_INLINE double	y () const

EIGEN_STRONG_INLINE double &	z ()

EIGEN_STRONG_INLINE double	z () const

EIGEN_STRONG_INLINE double &	w ()

EIGEN_STRONG_INLINE double	w () const

EIGEN_STRONG_INLINE Vector3d	vec () const
	Get vector part. More...

Quaternion &	operator= (const Eigen::Quaterniond &q)

void	sanitize ()
	sanitize the quaternion by negating each element if the w element is less than zero More...

Quaternion &	operator= (const RobotDynamics::Math::Quaternion &q)

Quaternion &	operator= (const Vector4d &q)

Quaternion &	operator= (const Matrix3d &E)

Quaternion &	operator= (const AxisAngle &axis_angle)

Quaternion	operator* (const double &s) const
	Method to scale the elements of a quaternion by a constant. Normalization is NOT performed. More...

Quaternion	operator* (const Quaternion &q) const
	Quaternion multiplication. More...

Quaternion &	operator*= (const Quaternion &q)
	Overloaded *= operator for quaternion multiplication. More...

void	transform (const RobotDynamics::Math::SpatialTransform &X)
	Pure virtual object. This object forces objects that inherit from it to have a method that tells how that object is transformed. More...

Quaternion	slerp (double alpha, const Quaternion &quat) const
	From Wikipedia: In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1. More...

Quaternion	conjugate () const

Quaternion	timeStep (const Vector3d &omega, double dt)

Vector3d	rotate (const Vector3d &vec) const

void	swingTwistDecomposition (const Vector3d &twist_axis, Quaternion &swing, Quaternion &twist)
	Decompose a quaternion into a swing then twist quaternion where the twist is about the given axis. More...

Vector3d	toIntrinsicZYXAngles (double yaw_at_pitch_singularity=0.) const
	Convert to intrinsic ZYX euler angles. More...

Public Member Functions inherited from RobotDynamics::Math::Vector4d
template<typename OtherDerived >
	Vector4d (const Eigen::MatrixBase< OtherDerived > &other)

template<typename OtherDerived >
Vector4d &	operator= (const Eigen::MatrixBase< OtherDerived > &other)

EIGEN_STRONG_INLINE	Vector4d ()

EIGEN_STRONG_INLINE	Vector4d (const double &v0, const double &v1, const double &v2, const double &v3)

void	set (const double &v0, const double &v1, const double &v2, const double &v3)

Additional Inherited Members
Public Types inherited from RobotDynamics::Math::Vector4d
typedef Eigen::Vector4d	Base

Detailed Description

Quaternion that are used for singularity free joints.

order: x,y,z,w

Constructor & Destructor Documentation

◆ Quaternion() [1/11]

RobotDynamics::Math::Quaternion::Quaternion ( )

inline

Constructor.

◆ Quaternion() [2/11]

RobotDynamics::Math::Quaternion::Quaternion ( const Eigen::Quaterniond & q )

inline

◆ Quaternion() [3/11]

RobotDynamics::Math::Quaternion::Quaternion ( const RobotDynamics::Math::Quaternion & q )

inline

◆ Quaternion() [4/11]

RobotDynamics::Math::Quaternion::Quaternion ( const Eigen::Product< Eigen::Matrix< double, 3, 3 >, Eigen::Matrix< double, 3, 3 >, 0 > E )

inline

◆ Quaternion() [5/11]

RobotDynamics::Math::Quaternion::Quaternion ( const Eigen::Matrix3d & E )

◆ Quaternion() [6/11]

RobotDynamics::Math::Quaternion::Quaternion ( const Eigen::Matrix3d::ConstTransposeReturnType & E )

inline

◆ Quaternion() [7/11]

RobotDynamics::Math::Quaternion::Quaternion ( Eigen::Transpose< Eigen::Matrix< double, 3, 3 > > E )

inline

◆ Quaternion() [8/11]

RobotDynamics::Math::Quaternion::Quaternion ( const Vector4d & v )

inline

◆ Quaternion() [9/11]

RobotDynamics::Math::Quaternion::Quaternion ( const AxisAngle & axis_angle )

inline

◆ Quaternion() [10/11]

RobotDynamics::Math::Quaternion::Quaternion	(	Vector3d	axis,
		double	angle
	)

inline

◆ Quaternion() [11/11]

RobotDynamics::Math::Quaternion::Quaternion	(	double	x,
		double	y,
		double	z,
		double	w
	)

inline

Constructor.

Parameters

x
y
z
w

Member Function Documentation

◆ conjugate()

Quaternion RobotDynamics::Math::Quaternion::conjugate ( ) const

inline

◆ isApprox() [1/2]

bool RobotDynamics::Math::Quaternion::isApprox	(	Matrix3d	E,
		double	eps
	)		const

inline

◆ isApprox() [2/2]

bool RobotDynamics::Math::Quaternion::isApprox	(	Quaternion	o,
		double	eps
	)		const

inline

◆ operator*() [1/2]

Quaternion RobotDynamics::Math::Quaternion::operator* ( const double & s ) const

inline

Method to scale the elements of a quaternion by a constant. Normalization is NOT performed.

Parameters

Returns: Scaled quaternion

◆ operator*() [2/2]

Quaternion RobotDynamics::Math::Quaternion::operator* ( const Quaternion & q ) const

inline

Quaternion multiplication.

Parameters

q	Quaternion to multiply by

Returns: New multiplied quaternion result

◆ operator*=()

Quaternion& RobotDynamics::Math::Quaternion::operator*= ( const Quaternion & q )

inline

Overloaded *= operator for quaternion multiplication.

Parameters

q	Quaternion to multiply by

Returns: Modified result of the multiplication

◆ operator=() [1/5]

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const AxisAngle & axis_angle )

inline

◆ operator=() [2/5]

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Eigen::Quaterniond & q )

inline

◆ operator=() [3/5]

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Matrix3d & E )

inline

◆ operator=() [4/5]

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const RobotDynamics::Math::Quaternion & q )

inline

◆ operator=() [5/5]

Quaternion& RobotDynamics::Math::Quaternion::operator= ( const Vector4d & q )

inline

◆ rotate()

Vector3d RobotDynamics::Math::Quaternion::rotate ( const Vector3d & vec ) const

inline

◆ sanitize()

void RobotDynamics::Math::Quaternion::sanitize ( )

inline

sanitize the quaternion by negating each element if the w element is less than zero

◆ slerp()

Quaternion RobotDynamics::Math::Quaternion::slerp	(	double	alpha,
		const Quaternion &	quat
	)		const

From Wikipedia: In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1.

Note: Only unit quaternions are valid rotations, so make sure to normalize

Parameters

alpha	Interpolation parameter. Should be between 0 and 1
quat	Quaternion to interpolate between

Returns: Interpolated quaternion

◆ swingTwistDecomposition()

void RobotDynamics::Math::Quaternion::swingTwistDecomposition	(	const Vector3d &	twist_axis,
		Quaternion &	swing,
		Quaternion &	twist
	)

inline

Decompose a quaternion into a swing then twist quaternion where the twist is about the given axis.

twist_axis Unit vector for the axis of the twist, e.g. (0., 0., 1.) for the z-axis
swing Modified. Location for the resulting swing quaternion to be stored
twist Modified. Location for the resulting twist quaternion to be stored

Note: This implementation can be found in PRZEMYSLAW DOBROWOLSKI's thesis titled, "SWING-TWIST DECOMPOSITION IN CLIFFORD ALGEBRA"

◆ timeStep()

Quaternion RobotDynamics::Math::Quaternion::timeStep	(	const Vector3d &	omega,
		double	dt
	)

inline

◆ toAxisAngle()

AxisAngle RobotDynamics::Math::Quaternion::toAxisAngle ( ) const

inline

◆ toIntrinsicZYXAngles()

Vector3d RobotDynamics::Math::Quaternion::toIntrinsicZYXAngles ( double yaw_at_pitch_singularity = 0. ) const

Convert to intrinsic ZYX euler angles.

Parameters

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

◆ transform()

void RobotDynamics::Math::Quaternion::transform ( const RobotDynamics::Math::SpatialTransform & X )

inlinevirtual

Pure virtual object. This object forces objects that inherit from it to have a method that tells how that object is transformed.

Parameters

X	SpatialTransform

Implements RobotDynamics::Math::TransformableGeometricObject.

◆ vec()

EIGEN_STRONG_INLINE Vector3d RobotDynamics::Math::Quaternion::vec ( ) const

inline

Get vector part.

Returns: Vector part

◆ w() [1/2]

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::w ( )

inline

◆ w() [2/2]

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::w ( ) const

inline

◆ x() [1/2]

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::x ( )

inline

◆ x() [2/2]

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::x ( ) const

inline

◆ y() [1/2]

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::y ( )

inline

◆ y() [2/2]

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::y ( ) const

inline

◆ z() [1/2]

EIGEN_STRONG_INLINE double& RobotDynamics::Math::Quaternion::z ( )

inline

◆ z() [2/2]

EIGEN_STRONG_INLINE double RobotDynamics::Math::Quaternion::z ( ) const

inline

The documentation for this class was generated from the following files:

rdl_dynamics/include/rdl_dynamics/rdl_eigenmath.hpp
rdl_dynamics/src/rdl_eigenmath.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/11]

◆ Quaternion() [2/11]

◆ Quaternion() [3/11]

◆ Quaternion() [4/11]

◆ Quaternion() [5/11]

◆ Quaternion() [6/11]

◆ Quaternion() [7/11]

◆ Quaternion() [8/11]

◆ Quaternion() [9/11]

◆ Quaternion() [10/11]

◆ Quaternion() [11/11]

Member Function Documentation

◆ conjugate()

◆ isApprox() [1/2]

◆ isApprox() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator=() [1/5]

◆ operator=() [2/5]

◆ operator=() [3/5]

◆ operator=() [4/5]

◆ operator=() [5/5]

◆ rotate()

◆ sanitize()

◆ slerp()

◆ swingTwistDecomposition()

◆ timeStep()

◆ toAxisAngle()

◆ toIntrinsicZYXAngles()

◆ transform()

◆ vec()

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]