Maximizing the Size of Self-Motion Manifolds to Improve Robot Fault Tolerance

Abstract

One measure of a robot's fault tolerance is the size of its self-motion manifold. This letter presents a new methodology for finding the largest self-motion manifold(s) of kinematically redundant robots, that consists of two algorithms. Because large self-motion manifolds occur near singular configurations, the first algorithm is designed to identify singularities of all ranks, including high-rank singularities. One unique feature of this algorithm is its ability to deal with the ill conditioned nature of singular vectors when there are multiple nearly equal singular values. The second algorithm is constructed to compute the self-motion manifolds that contain these singular configurations by iteratively moving along the null space of the robot's Jacobian. An important aspect of this computation is to deal with singularities along the manifold, where the null space is high dimensional. These two algorithms are applied to the well-known Mitsubishi PA-10 to illustrate their effectiveness at identifying singularities and computing the largest self-motion manifold(s).