Tools

Collaboration diagram for Tools:

Classes
struct	Eigen::BlockIndex
class	Eigen::MatrixBlockView< _ArgType, _Rows, _Cols, _allRows, _allCols >
class	Eigen::MatrixBlocks< _allRows, _allCols >
class	Eigen::MatrixBlocksBase< Derived >

Typedefs
typedef Eigen::MatrixBlocks< false, true >	Eigen::RowBlockIndices
typedef Eigen::MatrixBlocks< true, false >	Eigen::ColBlockIndices

Functions
template<typename Derived >
std::ostream &	Eigen::operator<< (std::ostream &os, const MatrixBlocksBase< Derived > &mbi)
template<typename Derived >
void	hpp::constraints::logSO3 (const matrix3_t &R, value_type &theta, Eigen::MatrixBase< Derived > const &result)
template<typename Derived >
void	hpp::constraints::JlogSO3 (const value_type &theta, const Eigen::MatrixBase< Derived > &log, matrix3_t &Jlog)
template<typename Derived >
void	hpp::constraints::logSE3 (const Transform3f &M, Eigen::MatrixBase< Derived > &result)
template<typename Derived >
void	hpp::constraints::JlogSE3 (const Transform3f &M, Eigen::MatrixBase< Derived > const &Jlog)
template<typename Derived1 , typename Derived2 >
void	hpp::constraints::matrixToQuat (const Eigen::MatrixBase< Derived1 > &M, Eigen::MatrixBase< Derived2 > const &q)
template<typename Derived >
void	hpp::constraints::se3ToConfig (const Transform3f &M, Eigen::MatrixBase< Derived > const &q)

Detailed Description

Typedef Documentation

ColBlockIndices

typedef Eigen::MatrixBlocks<true, false> Eigen::ColBlockIndices

RowBlockIndices

typedef Eigen::MatrixBlocks<false, true> Eigen::RowBlockIndices

Function Documentation

JlogSE3()

template<typename Derived >

void hpp::constraints::JlogSE3	(	const Transform3f &	M,
		Eigen::MatrixBase< Derived > const &	Jlog
	)

JlogSO3()

template<typename Derived >

void hpp::constraints::JlogSO3	(	const value_type &	theta,
		const Eigen::MatrixBase< Derived > &	log,
		matrix3_t &	Jlog
	)

Compute jacobian of function log of rotation matrix in SO(3)

Let us consider a matrix \(R=\exp \left[\mathbf{r}\right]_{\times}\in SO(3)\). This functions computes the Jacobian of the function from \(SO(3)\) into \(\mathbf{R}^3\) that maps \(R\) to \(\mathbf{r}\). In other words,

\begin{equation*} \dot{\mathbf{r}} = J_{log}(R)\ \omega\,\,\,\mbox{with}\,\,\, \dot {R} = \left[\omega\right]_{\times} R \end{equation*}

Warning

Two representations of the angular velocity \(\omega\) are possible:

• \(\dot{R} = \left[\omega\right]_{\times}R\) or
• \(\dot{R} = R\left[\omega\right]_{\times}\).

The expression below assumes the second representation is used.

Parameters

theta	angle of rotation \(R\), also \(\|r\|\),
log	3d vector \(\mathbf{r}\),

Return values

Jlog	matrix \(J_{log} (R)\).

\begin{align*} J_{log} (R) &=& \frac{\|\mathbf{r}\|\sin\|\mathbf{r}\|}{2(1-\cos\|\mathbf{r}\|)} I_3 - \frac {1}{2}\left[\mathbf{r}\right]_{\times} + (\frac{1}{\|\mathbf{r}\|^2} - \frac{\sin\|\mathbf{r}\|}{2\|\mathbf{r}\|(1-\cos\|\mathbf{r}\|)}) \mathbf{r}\mathbf{r}^T\\ &=& I_3 +\frac{1}{2}\left[\mathbf{r}\right]_{\times} + \left(\frac{2(1-\cos\|\mathbf{r}\|) - \|\mathbf{r}\|\sin\|\mathbf{r}\|}{2\|\mathbf{r}\|^2(1-\cos\|\mathbf{r}\|)}\right)\left[\mathbf{r}\right]_{\times}^2 \end{align*}

Todo:

remove this and use pinocchio::Jlog3

logSE3()

template<typename Derived >

void hpp::constraints::logSE3 ( const Transform3f &  M, Eigen::MatrixBase< Derived > &  result  )

inline

Compute log of rigid-body transform

Parameters

M	rigid body transform,

Return values

theta	angle of rotation,
result	6d vector \((\mathbf{v},\mathbf{r})\) such that the screw motion of linear velocity (of the origin) \(\mathbf{v}\) expressed in the moving frame and of angular velocity \(\mathbf{r}\) expressed in the moving reaches $M$ in unit time.

logSO3()

template<typename Derived >

void hpp::constraints::logSO3 ( const matrix3_t &  R, value_type &  theta, Eigen::MatrixBase< Derived > const &  result  )

inline

Compute log of rotation matrix as a 3d vector

Parameters

R	rotation matrix in SO(3),

Return values

theta	angle of rotation,
result	3d vector \(\mathbf{r}\) such that \(R=\exp [\mathbf{r}]_{\times}\)

matrixToQuat()

template<typename Derived1 , typename Derived2 >

void hpp::constraints::matrixToQuat	(	const Eigen::MatrixBase< Derived1 > &	M,
		Eigen::MatrixBase< Derived2 > const &	q
	)

operator<<()

template<typename Derived >

std::ostream& Eigen::operator<<	(	std::ostream &	os,
		const MatrixBlocksBase< Derived > &	mbi
	)

se3ToConfig()

template<typename Derived >

void hpp::constraints::se3ToConfig	(	const Transform3f &	M,
		Eigen::MatrixBase< Derived > const &	q
	)