Solver for the inverse position kinematics that uses Levenberg-Marquardt. More...

#include <chainiksolverpos_lma.hpp>

Inheritance diagram for KDL::ChainIkSolverPos_LMA:

Public Member Functions
virtual int	CartToJnt (const KDL::JntArray &q_init, const KDL::Frame &T_base_goal, KDL::JntArray &q_out)
	computes the inverse position kinematics.
	ChainIkSolverPos_LMA (const KDL::Chain &_chain, const Eigen::Matrix< double, 6, 1 > &_L, double _eps=1E-5, int _maxiter=500, double _eps_joints=1E-15)
	constructs an ChainIkSolverPos_LMA solver.
	ChainIkSolverPos_LMA (const KDL::Chain &_chain, double _eps=1E-5, int _maxiter=500, double _eps_joints=1E-15)
	identical the full constructor for ChainIkSolverPos_LMA, but provides for a default weight matrix.
void	compute_fwdpos (const VectorXq &q)
	for internal use only.
void	compute_jacobian (const VectorXq &q)
	for internal use only. Only exposed for test and diagnostic purposes. compute_fwdpos(q) should always have been called before.
void	display_jac (const KDL::JntArray &jval)
	for internal use only. Only exposed for test and diagnostic purposes.
virtual	~ChainIkSolverPos_LMA ()
	destructor.
Public Attributes
bool	display_information
	display information on each iteration step to the console.
VectorXq	grad
	for internal use only.
MatrixXq	jac
	for internal use only.
double	lastDifference
	contains the last value for after an execution of CartToJnt.
int	lastNrOfIter
	contains the last number of iterations for an execution of CartToJnt.
double	lastRotDiff
	contains the last value for the (unweighted) rotational difference after an execution of CartToJnt.
VectorXq	lastSV
	contains the last values for the singular values of the weighted Jacobian after an execution of CartToJnt.
double	lastTransDiff
	contains the last value for the (unweighted) translational difference after an execution of CartToJnt.
KDL::Frame	T_base_head
	for internal use only.
Private Types
typedef Eigen::Matrix < ScalarType, Eigen::Dynamic, Eigen::Dynamic >	MatrixXq
typedef double	ScalarType
typedef Eigen::Matrix < ScalarType, Eigen::Dynamic, 1 >	VectorXq
Private Attributes
MatrixXq	A
const KDL::Chain &	chain
VectorXq	diffq
double	eps
double	eps_joints
Eigen::Matrix< ScalarType, 6, 1 >	L
Eigen::LDLT< MatrixXq >	ldlt
unsigned int	maxiter
VectorXq	original_Aii
VectorXq	q
VectorXq	q_new
Eigen::JacobiSVD< MatrixXq >	svd
std::vector< KDL::Frame >	T_base_jointroot
std::vector< KDL::Frame >	T_base_jointtip
VectorXq	tmp

Detailed Description

Solver for the inverse position kinematics that uses Levenberg-Marquardt.

The robustness and speed of this solver is improved in several ways:

by using a Levenberg-Marquardt method that automatically adapts the damping when computing the inverse damped least squares inverse velocity kinematics.
by using an internal implementation of forward position kinematics and the Jacobian kinematics. This implementation is more numerically robust, is able to cache previous computations, and implements an $\mathcal{O}(N)$ algorithm for the computation of the Jacobian (with , the number of joints, and for a fixed size task space).
by providing a way to specify the weights in task space, you can weigh rotations wrt translations. This is important e.g. to specify that rotations do not matter for the problem at hand, or to specify how important you judge rotations w.r.t. translations, typically in S.I.-units, ([m],[rad]), the rotations are over-specified, this can be avoided using the weight matrix. Weights also make the solver more robust .
only the constructors call memory allocation.

De general principles behind the optimisation is inspired on: Jorge Nocedal, Stephen J. Wright, Numerical Optimization,Springer-Verlag New York, 1999.

Definition at line 64 of file chainiksolverpos_lma.hpp.

Member Typedef Documentation

typedef Eigen::Matrix<ScalarType,Eigen::Dynamic,Eigen::Dynamic> KDL::ChainIkSolverPos_LMA::MatrixXq [private]

Definition at line 68 of file chainiksolverpos_lma.hpp.

typedef double KDL::ChainIkSolverPos_LMA::ScalarType [private]

Definition at line 67 of file chainiksolverpos_lma.hpp.

typedef Eigen::Matrix<ScalarType,Eigen::Dynamic,1> KDL::ChainIkSolverPos_LMA::VectorXq [private]

Definition at line 69 of file chainiksolverpos_lma.hpp.

Constructor & Destructor Documentation

KDL::ChainIkSolverPos_LMA::ChainIkSolverPos_LMA	(	const KDL::Chain &	_chain,
		const Eigen::Matrix< double, 6, 1 > &	_L,
		double	_eps = `1E-5`,
		int	_maxiter = `500`,
		double	_eps_joints = `1E-15`
	)

constructs an ChainIkSolverPos_LMA solver.

The default parameters are choosen to be applicable to industrial-size robots (e.g. 0.5 to 3 meters range in task space), with an accuracy that is more then sufficient for typical industrial applications.

Weights are applied in task space, i.e. the kinematic solver minimizes: $E = \Delta \mathbf{x}^T \mathbf{L} \mathbf{L}^T \Delta \mathbf{x}$ , with $\mathbf{L}$ a diagonal matrix.

Parameters:

_chain	specifies the kinematic chain.
_L	specifies the "square root" of the weight (diagonal) matrix in task space. This diagonal matrix is specified as a vector.
_eps	specifies the desired accuracy in task space; after weighing with the weight matrix, it is applied on .
_maxiter	specifies the maximum number of iterations.
_eps_joints	specifies that the algorithm has to stop when the computed joint angle increments are smaller then _eps_joints. This is to avoid unnecessary computations up to _maxiter when the joint angle increments are so small that they effectively (in floating point) do not change the joint angles any more. The default is a few digits above numerical accuracy.

Definition at line 50 of file chainiksolverpos_lma.cpp.

KDL::ChainIkSolverPos_LMA::ChainIkSolverPos_LMA	(	const KDL::Chain &	_chain,
		double	_eps = `1E-5`,
		int	_maxiter = `500`,
		double	_eps_joints = `1E-15`
	)

identical the full constructor for ChainIkSolverPos_LMA, but provides for a default weight matrix.

$\mathbf{L} = \mathrm{diag}\left( \begin{bmatrix} 1 & 1 & 1 & 0.01 & 0.01 & 0.01 \end{bmatrix} \right)$ .

Definition at line 79 of file chainiksolverpos_lma.cpp.

KDL::ChainIkSolverPos_LMA::~ChainIkSolverPos_LMA ( ) [virtual]

destructor.

Definition at line 112 of file chainiksolverpos_lma.cpp.

Member Function Documentation

int KDL::ChainIkSolverPos_LMA::CartToJnt	(	const KDL::JntArray &	q_init,
		const KDL::Frame &	T_base_goal,
		KDL::JntArray &	q_out
	)		`[virtual]`

computes the inverse position kinematics.

Parameters:

q_init	initial joint position.
T_base_goal	goal position expressed with respect to the robot base.
q_out	joint position that achieves the specified goal position (if successful).

Returns:: 0 if successful, -1 the gradient of towards the joints is to small, -2 if joint position increments are to small, -3 if number of iterations is exceeded.

Implements KDL::ChainIkSolverPos.

Definition at line 160 of file chainiksolverpos_lma.cpp.

void KDL::ChainIkSolverPos_LMA::compute_fwdpos ( const VectorXq & q )

for internal use only.

Only exposed for test and diagnostic purposes.

Definition at line 114 of file chainiksolverpos_lma.cpp.

void KDL::ChainIkSolverPos_LMA::compute_jacobian ( const VectorXq & q )

for internal use only. Only exposed for test and diagnostic purposes. compute_fwdpos(q) should always have been called before.

Definition at line 131 of file chainiksolverpos_lma.cpp.

void KDL::ChainIkSolverPos_LMA::display_jac ( const KDL::JntArray & jval )

for internal use only. Only exposed for test and diagnostic purposes.

Definition at line 150 of file chainiksolverpos_lma.cpp.