IK_GN - Gauss-Newton Numerical IK
- class roboticstoolbox.robot.IK.IK_GN(name='IK Solver', 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)
Gauss-Newton Numerical Inverse Kinematics Solver
A class which provides functionality to perform numerical inverse kinematics (IK) using the Gauss-Newton method. See
stepmethod for mathematical description.
When using this class with redundant robots (>6 DoF),
pinvmust be set to
str) – The name of the IK algorithm
int) – How many iterations are allowed within a search before a new search is started
int) – How many searches are allowed before being deemed unsuccessful
float) – Maximum allowed residual error E
bool) – Reject solutions with joint limit violations
float) – The gain for joint limit avoidance. Setting to 0.0 will remove this completely from the solution
float) – The gain for maximisation. Setting to 0.0 will remove this completely from the solution
float) – The minimum angle/distance (in radians or metres) in which the joint is allowed to approach to its limit
The following example gets the
pandarobot object, instantiates the
IK_GNsolver class using default parameters, makes a goal pose
Tep, and then solves for the joint coordinates which result in the pose
>>> import roboticstoolbox as rtb >>> panda = rtb.models.Panda().ets() >>> solver = rtb.IK_GN(pinv=True) >>> Tep = panda.fkine([0, -0.3, 0, -2.2, 0, 2, 0.7854]) >>> solver.solve(panda, Tep) IKSolution(q=array([ 2.0624, -1.7323, -0.7973, -2.0608, -1.4287, 0.8733, 1.728 ]), success=True, iterations=14, searches=1, residual=1.2677181445000686e-12, reason='Success')
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. When the the problem is solvable, it converges very quickly.
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.
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).
Changed in version 1.0.3: Added the Gauss-Newton IK solver class
Performs a single iteration of the Gauss-Newton optimisation method
Solves the IK problem
Calculates the error between Te and Tep
Generate a random valid joint configuration using a private RNG
Checks if the joints are within their respective limits