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, Eigen::Dynamic, Eigen::Dynamic >	tinyrobotics::null (const Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &A)
	Computes an orthonormal basis for the null space of a matrix.
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.

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_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.

null()

template<typename Scalar >

Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > tinyrobotics::null

(

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

A

)

Computes an orthonormal basis for the null space of a matrix.

Parameters

A	Input matrix.

Template Parameters

Scalar

Scalar type.

Returns

The orthonormal basis for the null space of A.

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