KDL
1.3.0
|
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. More...
#include <src/chainiksolvervel_wdls.hpp>
Public Types | |
enum | { E_DEGRADED = +1, E_NOERROR = 0, E_NO_CONVERGE = -1, E_UNDEFINED = -2 } |
Public Member Functions | |
ChainIkSolverVel_wdls (const Chain &chain, double eps=0.00001, int maxiter=150) | |
Constructor of the solver. More... | |
~ChainIkSolverVel_wdls () | |
virtual int | CartToJnt (const JntArray &q_in, const Twist &v_in, JntArray &qdot_out) |
Find an output joint velocity qdot_out, given a starting joint pose q_init and a desired cartesian velocity v_in. More... | |
virtual int | CartToJnt (const JntArray &q_init, const FrameVel &v_in, JntArrayVel &q_out) |
not (yet) implemented. More... | |
void | setWeightJS (const Eigen::MatrixXd &Mq) |
Set the joint space weighting matrix. More... | |
void | setWeightTS (const Eigen::MatrixXd &Mx) |
Set the task space weighting matrix. More... | |
void | setLambda (const double lambda) |
Set lambda. More... | |
void | setEps (const double eps_in) |
Set eps. More... | |
void | setMaxIter (const int maxiter_in) |
Set maxIter. More... | |
unsigned int | getNrZeroSigmas () const |
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. More... | |
double | getSigmaMin () const |
Request the minimum of the first six singular values. More... | |
double | getLambda () const |
Request the value of lambda for the minimum. More... | |
double | getLambdaScaled () const |
Request the scaled value of lambda for the minimum singular value 1-6. More... | |
int | getSVDResult () const |
Retrieve the latest return code from the SVD algorithm. More... | |
virtual const char * | strError (const int error) const |
Return a description of the latest error. More... | |
virtual int | getError () const |
Return the latest error. More... | |
Static Public Attributes | |
static const int | E_SVD_FAILED = -100 |
static const int | E_CONVERGE_PINV_SINGULAR = +100 |
SVD solver failed. More... | |
Protected Attributes | |
int | error |
Latest error, initialized to E_NOERROR in constructor. More... | |
Private Attributes | |
const Chain | chain |
ChainJntToJacSolver | jnt2jac |
Jacobian | jac |
Eigen::MatrixXd | U |
Eigen::VectorXd | S |
Eigen::MatrixXd | V |
double | eps |
int | maxiter |
Eigen::VectorXd | tmp |
Eigen::MatrixXd | tmp_jac |
Eigen::MatrixXd | tmp_jac_weight1 |
Eigen::MatrixXd | tmp_jac_weight2 |
Eigen::MatrixXd | tmp_ts |
Eigen::MatrixXd | tmp_js |
Eigen::MatrixXd | weight_ts |
Eigen::MatrixXd | weight_js |
double | lambda |
double | lambda_scaled |
unsigned int | nrZeroSigmas |
int | svdResult |
double | sigmaMin |
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.
|
inherited |
|
explicit |
Constructor of the solver.
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 |
KDL::ChainIkSolverVel_wdls::~ChainIkSolverVel_wdls | ( | ) |
|
virtual |
Find an output joint velocity qdot_out, given a starting joint pose q_init and a desired cartesian velocity v_in.
Implements KDL::ChainIkSolverVel.
References KDL::Jacobian::columns(), KDL::Jacobian::data, E_CONVERGE_PINV_SINGULAR, KDL::SolverI::E_NOERROR, E_SVD_FAILED, eps, KDL::SolverI::error, jac, jnt2jac, KDL::ChainJntToJacSolver::JntToJac(), lambda, lambda_scaled, maxiter, nrZeroSigmas, KDL::Jacobian::rows(), S, sigmaMin, svdResult, tmp, tmp_jac_weight1, tmp_jac_weight2, tmp_js, tmp_ts, U, V, weight_js, and weight_ts.
|
inlinevirtual |
not (yet) implemented.
Implements KDL::ChainIkSolverVel.
|
inlinevirtualinherited |
Return the latest error.
References KDL::SolverI::error.
|
inline |
Request the value of lambda for the minimum.
References lambda.
|
inline |
Request the scaled value of lambda for the minimum singular value 1-6.
References lambda_scaled.
|
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.
References nrZeroSigmas.
|
inline |
Request the minimum of the first six singular values.
References sigmaMin.
|
inline |
Retrieve the latest return code from the SVD algorithm.
References svdResult.
void KDL::ChainIkSolverVel_wdls::setEps | ( | const double | eps_in | ) |
Set eps.
References eps.
void KDL::ChainIkSolverVel_wdls::setLambda | ( | const double | lambda | ) |
Set lambda.
References lambda.
void KDL::ChainIkSolverVel_wdls::setMaxIter | ( | const int | maxiter_in | ) |
Set maxIter.
References maxiter.
void KDL::ChainIkSolverVel_wdls::setWeightJS | ( | const Eigen::MatrixXd & | Mq | ) |
Set the joint space weighting matrix.
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 : vince nt.p adois @upm c.fr |
References weight_js.
void KDL::ChainIkSolverVel_wdls::setWeightTS | ( | const Eigen::MatrixXd & | Mx | ) |
Set the task space weighting matrix.
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 : vince nt.p adois @upm c.fr |
References weight_ts.
|
virtual |
Return a description of the latest error.
Reimplemented from KDL::SolverI.
References E_SVD_FAILED, and KDL::SolverI::strError().
|
private |
|
static |
|
static |
Referenced by CartToJnt(), and strError().
|
private |
Referenced by CartToJnt(), and setEps().
|
protectedinherited |
Latest error, initialized to E_NOERROR in constructor.
Referenced by KDL::ChainIkSolverPos_NR::CartToJnt(), KDL::ChainIkSolverVel_pinv::CartToJnt(), CartToJnt(), KDL::SolverI::getError(), and KDL::ChainJntToJacSolver::JntToJac().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt(), getLambda(), and setLambda().
|
private |
Referenced by CartToJnt(), and getLambdaScaled().
|
private |
Referenced by CartToJnt(), and setMaxIter().
|
private |
Referenced by CartToJnt(), and getNrZeroSigmas().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt(), and getSigmaMin().
|
private |
Referenced by CartToJnt(), and getSVDResult().
|
private |
Referenced by CartToJnt().
|
private |
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt().
|
private |
Referenced by CartToJnt(), and setWeightJS().
|
private |
Referenced by CartToJnt(), and setWeightTS().