ETS.ikine_NR

ETS.ikine_NR(Tep, 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)[source]

Newton-Raphson numerical inverse kinematics solver

Parameters:

Tep (ndarray | SE3) – the desired end-effector pose
q0 (Union[ndarray, List[float], Tuple[float, ...], None]) – the initial joint coordinate vector
ilimit (int) – maximum iterations allowed per search
slimit (int) – maximum search attempts before failure
tol (float) – maximum allowed residual error E
mask (Union[ndarray, List[float], Tuple[float, ...], None]) – a 6-vector weighting Cartesian DoF error priority
joint_limits (bool) – reject solutions with joint limit violations
seed (int | None) – seed for the RNG used to generate random joint configurations
pinv (bool) – use the pseudo-inverse in the step method instead of the normal inverse
kq (float) – gain for joint limit avoidance (0.0 disables)
km (float) – gain for manipulability maximisation (0.0 disables)
ps (float) – minimum joint approach distance to limit (radians or metres)
pi (ndarray | float) – null-space influence distance (radians or metres)

Returns:

IK solution

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.

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

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 the ets of 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().ets()
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> panda.ikine_NR(Tep)
IKSolution(q=array([ 0.4496,  0.9133, -1.9684, -2.9689, -2.5681,  1.8771,  0.0901]), success=False, iterations=100, searches=100, residual=0.0, reason='iteration and search limit reached, 100 numpy.LinAlgError encountered')

Notes

When using 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).