Analytically Informed Inverse Kinematics Solution at Singularities

TL;DR

This paper introduces an analytically informed inverse kinematics method that effectively handles singularities in robotic manipulators by combining explicit analytic descriptions with iterative numerical solutions.

Contribution

The proposed AI-IK method uniquely integrates analytic tangent descriptions of singular motions with iterative algorithms to improve IK solutions at singularities.

Findings

AI-IK successfully resolves IK near singularities for a 7-DOF robot.

The method outperforms traditional pseudoinverse approaches in singular configurations.

Numerical results demonstrate improved stability and accuracy of the proposed approach.

Abstract

Near kinematic singularities of a serial manipulator, the inverse kinematics (IK) problem becomes ill-conditioned, which poses computational problems for the numerical solution. Computational methods to tackle this issue are based on various forms of a pseudoinverse (PI) solution to the velocity IK problem. The damped least squares (DLS) method provides a robust solution with controllable convergence rate. However, at singularities, it may not even be possible to solve the IK problem using any PI solution when certain end-effector motions are prescribed. To overcome this problem, an analytically informed inverse kinematics (AI-IK) method is proposed. The key step of the method is an explicit description of the tangent aspect of singular motions (the analytic part) to deduce a perturbation that yields a regular configuration. The latter serves as start configuration for the iterative solution (the numeric part). Numerical results are reported for a 7-DOF Kuka iiwa.