# IK_GN - Gauss-Newton Numerical IK

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

Bases: IKSolver

Gauss-Newton Numerical Inverse Kinematics Solver

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

Note

When using this class with redundant robots (>6 DoF), pinv must be set to True

Parameters:

Examples

The following example gets the ets of a panda robot object, instantiates the IK_GN 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_GN(pinv=True)
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> solver.solve(panda, Tep)
IKSolution(q=array([ 1.2886,  1.4862, -2.1934, -2.0771,  1.244 ,  1.1468, -0.096 ]), success=True, iterations=53, searches=4, residual=9.796561164911834e-10, reason='Success')


Notes

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. When the the problem is solvable, it converges very quickly.

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).

IKSolver

An abstract super class for numerical IK solvers

IK_NR

Implements IKSolver using the Newton-Raphson method

IK_LM

Implements IKSolver using the Levemberg-Marquadt method

IK_QP

Implements IKSolver using a quadratic programming approach

Changed in version 1.0.3: Added the Gauss-Newton IK solver class

Methods

 step(ets, Tep, q) Performs a single iteration of the Gauss-Newton optimisation method 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