Inverse Kinematic Solutions With Singularity Robustness for Robot Manipulator Control

TLDR

The singularity problem is an inherent issue in controlling articulated robot manipulators. The paper proposes determining joint motion for a requested end‑effector trajectory by evaluating feasibility and introduces the singularity‑robust inverse (SR‑inverse) as an alternative to the Jacobian pseudoinverse. The SR‑inverse is defined as a Jacobian‑based method that yields a feasible joint motion approximating the desired Cartesian trajectory even near singularities, and its computational complexity is analyzed for implementability. Comparisons with the inverse and pseudoinverse reveal the SR‑inverse’s properties, and simulations demonstrate its effectiveness in handling singularities.

Abstract

The singularity problem is an inherent problem in controlling robot manipulators with articulated configuration. In this paper, we propose to determine the joint motion for the requested motion of the endeffector by evaluating the feasibility of the joint motion. The determined joint motion is called an inverse kinematic solution with singularity robustness, because it denotes feasible solution even at or in the neighborhood of singular points. The singularity robust inverse (SR-inverse) is introduced as an alternative to the pseudoinverse of the Jacobian matrix. The SR-inverse of the Jacobian matrix provides us with an approximating motion close to the desired Cartesian trajectory of the endeffector, even when the inverse kinematic solution by the inverse or the pseudoinverse of the Jacobian matrix is not feasible at or in the neighborhood of singular points. The properties of the SR-inverse are clarified by comparing it with the inverse and the pseudoinverse. The computational complexity of the SR-inverse is considered to discuss its implementability. Several simulation results are also shown to illustrate the singularity problem and the effectiveness of the inverse kinematic solution with singularity robustness.