IK_NR  NewtonRaphson Numerical IK
 class roboticstoolbox.robot.IK.IK_NR(name='IK Solver', ilimit=30, slimit=100, tol=1e06, mask=None, joint_limits=True, seed=None, pinv=False, kq=0.0, km=0.0, ps=0.0, pi=0.3, **kwargs)[source]
Bases:
IKSolver
NewtonRaphson Numerical Inverse Kinematics Solver
A class which provides functionality to perform numerical inverse kinematics (IK) using the NewtonRaphson method. See
step
method for mathematical description.Note
When using this class with redundant robots (>6 DoF),
pinv
must be set toTrue
 Parameters:
name (
str
) – The name of the IK algorithmilimit (
int
) – How many iterations are allowed within a search before a new search is startedslimit (
int
) – How many searches are allowed before being deemed unsuccessfultol (
float
) – Maximum allowed residual error Emask (
Union
[ndarray
,List
[float
],Tuple
[float
],Set
[float
],None
]) – A 6 vector which assigns weights to Cartesian degreesoffreedom error priorityjoint_limits (
bool
) – Reject solutions with joint limit violationsseed (
Optional
[int
]) – A seed for the private RNG used to generate random joint coordinate vectorspinv (
bool
) – If True, will use the psuedoinverse in thestep
method instead of the normal inversekq (
float
) – The gain for joint limit avoidance. Setting to 0.0 will remove this completely from the solutionkm (
float
) – The gain for maximisation. Setting to 0.0 will remove this completely from the solutionps (
float
) – The minimum angle/distance (in radians or metres) in which the joint is allowed to approach to its limitpi (
Union
[ndarray
,float
]) – The influence angle/distance (in radians or metres) in null space motion becomes active
Examples
The following example gets the
ets
of apanda
robot object, instantiates the IK_NR solver class using default parameters, makes a goal poseTep
, and then solves for the joint coordinates which result in the poseTep
using thesolve
method.>>> import roboticstoolbox as rtb >>> panda = rtb.models.Panda().ets() >>> solver = rtb.IK_NR(pinv=True) >>> Tep = panda.fkine([0, 0.3, 0, 2.2, 0, 2, 0.7854]) >>> solver.solve(panda, Tep) IKSolution(q=array([2.3853, 0.3909, 2.4784, 2.1923, 0.27 , 1.9673, 0.9981]), success=True, iterations=188, searches=12, residual=2.42191743196601e10, reason='Success')
Notes
When using the NR method, the initial joint coordinates \(q_0\), should correspond to a nonsingular manipulator pose, since it uses the manipulator Jacobian. When the the problem is solvable, it converges very quickly. However, this method frequently fails to converge on the goal.
This class supports nullspace motion to assist with maximising manipulability and avoiding joint limits. These are enabled by setting kq and km to nonzero 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).
See also
Changed in version 1.0.3: Added the NewtonRaphson IK solver class
Methods

Performs a single iteration of the NewtonRaphson optimisation method 

Solves the IK problem 

Calculates the error between Te and Tep 
Private Methods

Generate a random valid joint configuration using a private RNG 

Checks if the joints are within their respective limits 