math.hpp File Reference

Contains various math related functions. More...

#include <Eigen/Core>
#include <Eigen/Geometry>

Go to the source code of this file.

Functions
template<typename Scalar >
Eigen::Matrix< Scalar, 3, 3 >	tinyrobotics::skew (const Eigen::Matrix< Scalar, 3, 3 > &input)
	Computes the skew of a 3x3 vector.
template<typename Scalar >
Eigen::Matrix< Scalar, 3, 3 >	tinyrobotics::skew (const Eigen::Matrix< Scalar, 3, 1 > &input)
	Computes the skew matrix for a 3x1 vector.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::cross_spatial (const Eigen::Matrix< Scalar, 6, 1 > &v)
	Computes the 6x6 cross-product matrix for a 6D spatial vector.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::cross_motion (const Eigen::Matrix< Scalar, 6, 1 > &v)
	Computes the 6x6 cross-product matrix for a motion vector and a force vector.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::translation_to_spatial (const Eigen::Matrix< Scalar, 3, 1 > &xyz)
	Spatial coordinate transform from a xyz translation.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::rpy_to_spatial (const Eigen::Matrix< Scalar, 3, 1 > &rpy)
	Spatial coordinate transform from roll-pitch-yaw angles.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::homogeneous_to_spatial (const Eigen::Transform< Scalar, 3, Eigen::Isometry > &H)
	Spatial coordinate transform from homogeneous transformation matrix.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 6 >	tinyrobotics::inertia_to_spatial (const Scalar m, const Eigen::Matrix< Scalar, 3, 1 > &c, const Eigen::Matrix< Scalar, 3, 3 > &I)
	Spatial inertia matrix from inertia parameters.
template<typename Scalar >
Eigen::Matrix< Scalar, 6, 1 >	tinyrobotics::homogeneous_error (const Eigen::Transform< Scalar, 3, Eigen::Isometry > &H1, const Eigen::Transform< Scalar, 3, Eigen::Isometry > &H2)
	Computes the error between two homogeneous transformation matrices.

Detailed Description

Contains various math related functions.

Function Documentation

cross_motion()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::cross_motion

(

const Eigen::Matrix< Scalar, 6, 1 > &

v

)

Computes the 6x6 cross-product matrix for a motion vector and a force vector.

Parameters

v	The motion and force vector.

Template Parameters

Scalar

Scalar type.

Returns

6x6 cross-product matrix.

cross_spatial()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::cross_spatial

(

const Eigen::Matrix< Scalar, 6, 1 > &

v

)

Computes the 6x6 cross-product matrix for a 6D spatial vector.

Parameters

v	The 6D spatial vector.

Template Parameters

Scalar

Scalar type.

Returns

6x6 cross-product matrix.

homogeneous_error()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 1 > tinyrobotics::homogeneous_error	(	const Eigen::Transform< Scalar, 3, Eigen::Isometry > &	H1,
		const Eigen::Transform< Scalar, 3, Eigen::Isometry > &	H2
	)

Computes the error between two homogeneous transformation matrices.

Parameters

H1	The first homogeneous transformation matrix.
H2	The second homogeneous transformation matrix.

Template Parameters

Scalar

Scalar type.

Returns

6x1 error vector.

homogeneous_to_spatial()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::homogeneous_to_spatial

(

const Eigen::Transform< Scalar, 3, Eigen::Isometry > &

H

)

Spatial coordinate transform from homogeneous transformation matrix.

Parameters

H	The homogeneous transformation matrix.

Template Parameters

Scalar

Scalar type.

Returns

Spatial coordinate transform matrix.

inertia_to_spatial()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::inertia_to_spatial	(	const Scalar	m,
		const Eigen::Matrix< Scalar, 3, 1 > &	c,
		const Eigen::Matrix< Scalar, 3, 3 > &	I
	)

Spatial inertia matrix from inertia parameters.

Parameters

m	Mass of link.
C	Vector from the origin of the link to the center of mass.
I	Inertia of link.

Template Parameters

Scalar

Scalar type.

Returns

Spatial inertia matrix.

rpy_to_spatial()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::rpy_to_spatial

(

const Eigen::Matrix< Scalar, 3, 1 > &

rpy

)

Spatial coordinate transform from roll-pitch-yaw angles.

Parameters

rpy	The roll-pitch-yaw angles.

Template Parameters

Scalar

Scalar type.

Returns

Spatial coordinate transform matrix.

skew() [1/2]

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 3 > tinyrobotics::skew

(

const Eigen::Matrix< Scalar, 3, 1 > &

input

)

Computes the skew matrix for a 3x1 vector.

Parameters

input

The 3x1 vector.

Template Parameters

Scalar

Scalar type.

Returns

The skew of input.

skew() [2/2]

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 3 > tinyrobotics::skew

(

const Eigen::Matrix< Scalar, 3, 3 > &

input

)

Computes the skew of a 3x3 vector.

Parameters

input

The 3x3 vector.

Template Parameters

Scalar

Scalar type.

Returns

The skew of input.

translation_to_spatial()

template<typename Scalar >

Eigen::Matrix< Scalar, 6, 6 > tinyrobotics::translation_to_spatial

(

const Eigen::Matrix< Scalar, 3, 1 > &

xyz

)

Spatial coordinate transform from a xyz translation.

Parameters

v	The spatial vector

Returns

Spatial coordinate transform matrix