# Robot.ik_NR

Robot.ik_NR(Tep, end=None, start=None, q0=None, ilimit=30, slimit=100, tol=1e-06, mask=None, joint_limits=True, pinv=True, pinv_damping=0.0)

Fast numerical inverse kinematics using Newton-Raphson optimization

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.

Note

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

Parameters:
Return type:
Returns:

• sol – tuple (q, success, iterations, searches, residual)

• The return value sol is a tuple with elements

• ============ ========== ===============================================

• Element Type Description

• ============ ========== ===============================================

• q ndarray(n) joint coordinates in units of radians or metres

• success int whether a solution was found

• iterations int total number of iterations

• searches int total number of searches

• residual float final value of cost function

• ============ ========== ===============================================

• 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.

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_GN method.

>>> import roboticstoolbox as rtb
>>> panda = rtb.models.Panda()
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> panda.ik_NR(Tep)
(array([-1.0805, -0.5328,  0.9086, -2.1781,  0.4612,  1.9018,  0.4239]), 1, 489, 32, 2.8033063270234757e-09)


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.

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_LM
ik_GN