Singularity Analysis for Redundant Manipulators of Arbitrary Kinematic Structure

Abstract

This paper presents a technique to identify singularities of any rank for a robot of any kinematic structure. The technique is based on computing the gradient of singular values of the robot Jacobian. The algorithm deals with the situations when two or more singular values become nearly equal and their corresponding singular vectors are ill-defined. Also, an algorithm is developed to identify the physically meaningful singular directions from the high dimensional singular subspaces of high-rank singularities. The suggested technique is applied to a 4-DoF and a 7-DoF robot to show its efficacy at identifying robot singularities of all ranks and dealing with the ill-defined singular directions.