IK_LM - Levemberg-Marquadt Numerical IK

class roboticstoolbox.robot.IK.IK_LM(name='IK Solver', ilimit=30, slimit=100, tol=1e-06, mask=None, joint_limits=True, seed=None, k=1.0, method='chan', kq=0.0, km=0.0, ps=0.0, pi=0.3, **kwargs)[source]

Bases: IKSolver

Levemberg-Marquadt Numerical Inverse Kinematics Solver

A class which provides functionality to perform numerical inverse kinematics (IK) using the Levemberg-Marquadt method. See step method for mathematical description.

Parameters:

  • name (str) – The name of the IK algorithm

  • ilimit (int) – How many iterations are allowed within a search before a new search is started

  • slimit (int) – How many searches are allowed before being deemed unsuccessful

  • tol (float) – Maximum allowed residual error E

  • mask (Union[ndarray, List[float], Tuple[float, ...], None]) – A 6 vector which assigns weights to Cartesian degrees-of-freedom error priority

  • joint_limits (bool) – Reject solutions with joint limit violations

  • seed (int | None) – A seed for the private RNG used to generate random joint coordinate vectors

  • k (float) – Sets the gain value for the damping matrix Wn in the step method. See notes

  • method – One of “chan”, “sugihara” or “wampler”. Defines which method is used to calculate the damping matrix Wn in the step method

  • kq (float) – The gain for joint limit avoidance. Setting to 0.0 will remove this completely from the solution

  • km (float) – The gain for maximisation. Setting to 0.0 will remove this completely from the solution

  • ps (float) – The minimum angle/distance (in radians or metres) in which the joint is allowed to approach to its limit

  • pi (ndarray | float) – The influence angle/distance (in radians or metres) in null space motion becomes active

Example:

The following example gets the ``ets`` of a ``panda`` robot object, instantiates
the IK_LM solver class using default parameters, makes a goal pose ``Tep``,
and then solves for the joint coordinates which result in the pose ``Tep``
using the `solve` method.

>>> import roboticstoolbox as rtb
>>> panda = rtb.models.Panda().ets()
>>> solver = rtb.IK_LM()
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> solver.solve(panda, Tep)
IKSolution(q=array([-0.9098, -0.4447,  0.7856, -2.1872,  0.3501,  1.9444,  0.5101]), success=True, iterations=25, searches=1, residual=3.949190575755929e-08, reason='Success')

Notes

The value for the k kwarg will depend on the method chosen and the arm you are using. Use the following as a rough guide chan, k = 1.0 - 0.01, wampler, k = 0.01 - 0.0001, and sugihara, k = 0.1 - 0.0001

When using the this method, the initial joint coordinates \(q_0\), should correspond to a non-singular manipulator pose, since it uses the manipulator Jacobian.

This class supports null-space motion to assist with maximising manipulability and avoiding joint limits. These are enabled by setting kq and km to non-zero values.

References

  • J. Haviland, and P. Corke. “Manipulator Differential Kinematics Part I: Kinematics, Velocity, and Applications.” arXiv preprint arXiv:2207.01796 (2022).

  • J. Haviland, and P. Corke. “Manipulator Differential Kinematics Part II: Acceleration and Advanced Applications.” arXiv preprint arXiv:2207.01794 (2022).

See also

IKSolver An abstract super class for numerical IK solvers

IK_NR Implements the IKSolver class using the Newton-Raphson method

IK_GN Implements the IKSolver class using the Gauss-Newton method

IK_QP Implements the IKSolver class using a quadratic programming approach

Changed in version 1.0.3: Added the Levemberg-Marquadt IK solver class

Methods

step(ets, Tep, q)

Performs a single iteration of the Levenberg-Marquadt optimisation

solve(ets, Tep[, q0])

Solves the IK problem

error(Te, Tep)

Calculates the error between Te and Tep

Private Methods

_random_q(ets[, i])

Generate a random valid joint configuration using a private RNG

_check_jl(ets, q)

Checks if the joints are within their respective limits