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:

Tep (Union[ndarray, SE3]) – The desired end-effector pose
end (Union[str, Link, Gripper, None]) – the link considered as the end-effector
start (Union[str, Link, Gripper, None]) – the link considered as the base frame, defaults to the robots’s base frame
q0 (Union[ndarray, List[float], Tuple[float], Set[float], None]) – The initial joint coordinate vector
ilimit (int) – How many iterations are allowed within a search before a new search is started
slimit (int) – How many searches are allowed before being deemed unsuccessful
tol (float) – Maximum allowed residual error E
mask (Union[ndarray, List[float], Tuple[float], Set[float], None]) – A 6 vector which assigns weights to Cartesian degrees-of-freedom error priority
joint_limits (bool) – Reject solutions with joint limit violations
seed (Optional[int]) – A seed for the private RNG used to generate random joint coordinate vectors
pinv (bool) – If True, will use the psuedoinverse in the step method instead of the normal inverse
kq (float) – The gain for joint limit avoidance. Setting to 0.0 will remove this completely from the solution
km (float) – The gain for maximisation. Setting to 0.0 will remove this completely from the solution
ps (float) – The minimum angle/distance (in radians or metres) in which the joint is allowed to approach to its limit
pi (Union[ndarray, float]) – The influence angle/distance (in radians or metres) in null space motion becomes active

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([-1.8231, -1.294 , -2.0631, -2.5124,  1.427 ,  0.9265, -0.2425]), 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).