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, tool=None)

Fast numerical inverse kinematics using Newton-Raphson optimization

Parameters:

Tep (ndarray | SE3) – The desired end-effector pose (a single pose only, for a trajectory use ikine_NR())
end (str | Link | Gripper | None) – the link considered as the end-effector
start (str | Link | Gripper | None) – the link considered as the base frame, defaults to the robots’s base frame
q0 (ndarray | None) – initial joint configuration (default to random valid joint configuration constrained by the joint limits of the robot)
ilimit (int) – maximum number of iterations per search
slimit (int) – maximum number of search attempts
tol (float) – final error tolerance
mask (ndarray | None) – a mask vector which weights the end-effector error priority. Corresponds to translation in X, Y and Z and rotation about X, Y and Z respectively
joint_limits (bool) – constrain the solution to being within the joint limits of the robot (reject solution with invalid joint configurations and perform another search up to the slimit)
pinv (int) – Use the pseudo-inverse instead of the normal matrix inverse
pinv_damping (float) – Damping factor for the pseudo-inverse
tool (ndarray | SE3 | None) – a static tool transformation matrix to apply to the end of end; defaults to the robot’s own self.tool if not given

Returns:

an IKSolution containing joint coordinates q, success flag, iterations, searches and residual error value (reason is always empty – this fast C++ solver doesn’t produce a granular failure reason string, unlike ikine_NR())

Return type:

IKSolution

Warning

This method needs the compiled C++ extension. It raises RuntimeError if the extension is unavailable, for example in a pure-Python wheel or under Pyodide/JupyterLite, and if the sequence has a SymPy parameter, even a numeric one such as sympy.pi/2, or a joint with an offset, which the compiled code cannot use. In all of these cases use ikine_NR(), which has none of these limits.

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

The return value sol is an IKSolution with fields:

Field	Type	Description
`q`	ndarray(n)	joint coordinates in units of radians or metres
`success`	bool	whether a solution was found
`iterations`	int	total number of iterations
`searches`	int	total number of searches
`residual`	float	final value of cost function
`reason`	str	always empty for this C++ solver

If success == False 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 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()
>>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854])
>>> panda.ik_NR(Tep)
IKSolution: q=[-1.523, -0.9951, 1.071, -2.125, 0.8918, 1.593, 0.1073], success=True, iterations=223, searches=16, residual=3.55e-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).