ETS.ik_NR

ETS.ik_NR(Tep, q0=None, ilimit=30, slimit=100, tol=1e-06, mask=None, joint_limits=True, pinv=True, pinv_damping=0.0)[source]

Fast numerical inverse kinematics using Newton-Raphson optimisation

Parameters:

  • Tep (ndarray | SE3) – the desired end-effector pose or pose trajectory

  • q0 (ndarray | None) – initial joint configuration (random valid configuration if not supplied)

  • ilimit (int) – maximum number of iterations per search

  • slimit (int) – maximum number of search attempts

  • tol (float) – final error tolerance

  • mask (ndarray | None) – a 6-vector weighting end-effector error priority (XYZ translation, XYZ rotation)

  • joint_limits (bool) – reject solutions with invalid joint configurations

  • pinv (int) – use the pseudo-inverse instead of the normal matrix inverse

  • pinv_damping (float) – damping factor for the pseudo-inverse

Returns:

tuple (q, success, iterations, searches, residual)

Return type:

tuple[ndarray, int, int, int, float]

sol = ets.ik_NR(Tep) are the joint coordinates (n) corresponding to the robot end-effector pose Tep which is an SE3 or ndarray object. This method can be used for robots with any number of degrees of freedom. This is a fast solver implemented in C++.

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.

If success == 0 the q values will be valid numbers, but the solution will be in error. The amount of error is indicated by the residual.

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 ik_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.ik_NR(Tep)
(array([-1.9204,  0.6377,  2.1494, -2.1664, -0.5755,  1.8434,  1.2343]), 1, 74, 7, 1.5663866774043808e-08)

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.

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

ik_LM() ik_GN()