# Robot.ikine_NR

Robot.ikine_NR(Tep, end=None, start=None, q0=None, 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)

Newton-Raphson Numerical Inverse Kinematics Solver

A method which provides functionality to perform numerical inverse kinematics (IK) using the Newton-Raphson method.

See the Inverse Kinematics Docs Page for more details and for a tutorial on numerical IK, see here.

Note

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

Parameters:

Synopsis

Each iteration uses the Newton-Raphson optimisation method

$\vec{q}_{k+1} = \vec{q}_k + {^0\mat{J}(\vec{q}_k)}^{-1} \vec{e}_k$

Examples

The following example gets a panda robot object, makes a goal pose Tep, and then solves for the joint coordinates which result in the pose Tep using the ikine_NR method.

>>> import roboticstoolbox as rtb
>>> panda = rtb.models.Panda()
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> panda.ikine_NR(Tep)
IKSolution(q=array([-2.5448,  0.0635, -0.6093, -2.5018, -1.2853,  1.3894, -0.2102]), success=False, iterations=100, searches=100, residual=0.0, reason='iteration and search limit reached, 100 numpy.LinAlgError encountered')


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.

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).

IK_NR

An IK Solver class which implements the Newton-Raphson optimisation technique

ikine_LM

Implements the IK_LM class as a method within the ETS class

ikine_GN

Implements the IK_GN class as a method within the ETS class

ikine_QP

Implements the IK_QP class as a method within the ETS class

Changed in version 1.0.4: Added the Newton-Raphson IK solver method on the Robot class