#include <chainiksolvervel_wdls.hpp>

Inheritance diagram for KDL::ChainIkSolverVel_wdls:

Public Member Functions
virtual int	CartToJnt (const JntArray &q_in, const Twist &v_in, JntArray &qdot_out)
virtual int	CartToJnt (const JntArray &q_init, const FrameVel &v_in, JntArrayVel &q_out)
	ChainIkSolverVel_wdls (const Chain &chain, double eps=0.00001, int maxiter=150)
double	getLambda () const
double	getLambdaScaled () const
unsigned int	getNrZeroSigmas () const
double	getSigmaMin () const
int	getSVDResult () const
void	setEps (const double eps_in)
void	setLambda (const double lambda)
void	setMaxIter (const int maxiter_in)
void	setWeightJS (const Eigen::MatrixXd &Mq)
void	setWeightTS (const Eigen::MatrixXd &Mx)
virtual const char *	strError (const int error) const
	~ChainIkSolverVel_wdls ()
Static Public Attributes
static const int	E_CONVERGE_PINV_SINGULAR = +100
	solution converged but (pseudo)inverse is singular
static const int	E_SVD_FAILED = -100
Private Attributes
const Chain	chain
double	eps
Jacobian	jac
ChainJntToJacSolver	jnt2jac
double	lambda
double	lambda_scaled
int	maxiter
unsigned int	nrZeroSigmas
Eigen::VectorXd	S
double	sigmaMin
int	svdResult
Eigen::VectorXd	tmp
Eigen::MatrixXd	tmp_jac
Eigen::MatrixXd	tmp_jac_weight1
Eigen::MatrixXd	tmp_jac_weight2
Eigen::MatrixXd	tmp_js
Eigen::MatrixXd	tmp_ts
Eigen::MatrixXd	U
Eigen::MatrixXd	V
Eigen::MatrixXd	weight_js
Eigen::MatrixXd	weight_ts

Detailed Description

Implementation of a inverse velocity kinematics algorithm based on the weighted pseudo inverse with damped least-square to calculate the velocity transformation from Cartesian to joint space of a general KDL::Chain. It uses a svd-calculation based on householders rotations.

J# = M_q*Vb*pinv_dls(Db)*Ub'*M_x

where B = Mx*J*Mq

and B = Ub*Db*Vb' is the SVD decomposition of B

Mq and Mx represent, respectively, the joint-space and task-space weighting matrices. Please refer to the documentation of setWeightJS(const Eigen::MatrixXd& Mq) and setWeightTS(const Eigen::MatrixXd& Mx) for details on the effects of these matrices.

For more details on Weighted Pseudo Inverse, see : 1) [Ben Israel 03] A. Ben Israel & T.N.E. Greville. Generalized Inverses : Theory and Applications, second edition. Springer, 2003. ISBN 0-387-00293-6.

2) [Doty 93] K. L. Doty, C. Melchiorri & C. Boniveto. A theory of generalized inverses applied to Robotics. The International Journal of Robotics Research, vol. 12, no. 1, pages 1-19, february 1993.

Definition at line 63 of file chainiksolvervel_wdls.hpp.

Constructor & Destructor Documentation

KDL::ChainIkSolverVel_wdls::ChainIkSolverVel_wdls	(	const Chain &	chain,
		double	eps = `0.00001`,
		int	maxiter = `150`
	)		`[explicit]`

Constructor of the solver

Parameters:

chain	the chain to calculate the inverse velocity kinematics for
eps	if a singular value is below this value, its inverse is set to zero, default: 0.00001
maxiter	maximum iterations for the svd calculation, default: 150

Definition at line 28 of file chainiksolvervel_wdls.cpp.

KDL::ChainIkSolverVel_wdls::~ChainIkSolverVel_wdls ( )

Definition at line 53 of file chainiksolvervel_wdls.cpp.

Member Function Documentation

int KDL::ChainIkSolverVel_wdls::CartToJnt	(	const JntArray &	q_in,
		const Twist &	v_in,
		JntArray &	qdot_out
	)		`[virtual]`

Find an output joint velocity qdot_out, given a starting joint pose q_init and a desired cartesian velocity v_in

Returns:: E_NOERROR=svd solution converged in maxiter E_SVD_FAILED=svd solution failed E_CONVERGE_PINV_SINGULAR=svd solution converged but (pseudo)inverse singular

Note:: if E_CONVERGE_PINV_SINGULAR returned then converged and can continue motion, but have degraded solution; If E_SVD_FAILED returned, then getSvdResult() returns the error code from the SVD algorithm.

Implements KDL::ChainIkSolverVel.

Definition at line 80 of file chainiksolvervel_wdls.cpp.

virtual int KDL::ChainIkSolverVel_wdls::CartToJnt	(	const JntArray &	q_init,
		const FrameVel &	v_in,
		JntArrayVel &	q_out
	)		`[inline, virtual]`

not (yet) implemented.

Implements KDL::ChainIkSolverVel.

Definition at line 106 of file chainiksolvervel_wdls.hpp.

double KDL::ChainIkSolverVel_wdls::getLambda ( ) const [inline]

Request the value of lambda for the minimum

Definition at line 185 of file chainiksolvervel_wdls.hpp.

double KDL::ChainIkSolverVel_wdls::getLambdaScaled ( ) const [inline]

Request the scaled value of lambda for the minimum singular value 1-6

Definition at line 191 of file chainiksolvervel_wdls.hpp.

unsigned int KDL::ChainIkSolverVel_wdls::getNrZeroSigmas ( ) const [inline]

Request the number of singular values of the jacobian that are < eps; if the number of near zero singular values is > jac.col()-jac.row(), then the jacobian pseudoinverse is singular

Definition at line 175 of file chainiksolvervel_wdls.hpp.

double KDL::ChainIkSolverVel_wdls::getSigmaMin ( ) const [inline]

Request the minimum of the first six singular values

Definition at line 180 of file chainiksolvervel_wdls.hpp.

int KDL::ChainIkSolverVel_wdls::getSVDResult ( ) const [inline]

Retrieve the latest return code from the SVD algorithm

Returns:: 0 if CartToJnt() not yet called, otherwise latest SVD result code.

Definition at line 197 of file chainiksolvervel_wdls.hpp.

void KDL::ChainIkSolverVel_wdls::setEps ( const double eps_in )

Set eps

Definition at line 70 of file chainiksolvervel_wdls.cpp.

void KDL::ChainIkSolverVel_wdls::setLambda ( const double lambda )

Set lambda

Definition at line 65 of file chainiksolvervel_wdls.cpp.

void KDL::ChainIkSolverVel_wdls::setMaxIter ( const int maxiter_in )

Set maxIter

Definition at line 75 of file chainiksolvervel_wdls.cpp.

void KDL::ChainIkSolverVel_wdls::setWeightJS ( const Eigen::MatrixXd & Mq )

Set the joint space weighting matrix

Parameters:

weight_js joint space weighting symetric matrix, default : identity. M_q : This matrix being used as a weight for the norm of the joint space speed it HAS TO BE symmetric and positive definite. We can actually deal with matrices containing a symmetric and positive definite block and 0s otherwise. Taking a diagonal matrix as an example, a 0 on the diagonal means that the corresponding joints will not contribute to the motion of the system. On the other hand, the bigger the value, the most the corresponding joint will contribute to the overall motion. The obtained solution q_dot will actually minimize the weighted norm sqrt(q_dot'*(M_q^-2)*q_dot). In the special case we deal with, it does not make sense to invert M_q but what is important is the physical meaning of all this : a joint that has a zero weight in M_q will not contribute to the motion of the system and this is equivalent to saying that it gets an infinite weight in the norm computation. For more detailed explanation : vincent.padois@upmc.fr

Definition at line 57 of file chainiksolvervel_wdls.cpp.

void KDL::ChainIkSolverVel_wdls::setWeightTS ( const Eigen::MatrixXd & Mx )

Set the task space weighting matrix

Parameters:

weight_ts task space weighting symetric matrix, default: identity M_x : This matrix being used as a weight for the norm of the error (in terms of task space speed) it HAS TO BE symmetric and positive definite. We can actually deal with matrices containing a symmetric and positive definite block and 0s otherwise. Taking a diagonal matrix as an example, a 0 on the diagonal means that the corresponding task coordinate will not be taken into account (ie the corresponding error can be really big). If the rank of the jacobian is equal to the number of task space coordinates which do not have a 0 weight in M_x, the weighting will actually not impact the results (ie there is an exact solution to the velocity inverse kinematics problem). In cases without an exact solution, the bigger the value, the most the corresponding task coordinate will be taken into account (ie the more the corresponding error will be reduced). The obtained solution will minimize the weighted norm sqrt(|x_dot-Jq_dot|'*(M_x^2)*|x_dot-Jq_dot|). For more detailed explanation : vincent.padois@upmc.fr

Definition at line 61 of file chainiksolvervel_wdls.cpp.

const char * KDL::ChainIkSolverVel_wdls::strError ( const int error ) const [virtual]

Return a description of the latest error