Identification and resolution of structural and algorithmic singularity in redundancy control of serial manipulations

Abstract

Abstract A major difficulty that has haunted most researchers in the process of optimal redundancy resolution of robotic manipulators is the instability observed in even very simple numerical simulations. This numerical instability is not related to the structurally singular configurations of the manipulators, and in the literature has been referred to as “algorithmic singularity,” “artificial singularity,” or “unavoidable singularity.” In this work, conditions on both structural and algorithmic singularities are studied based on the Singular Value Decomposition of the Jacobian matrix, and, hence, a singularity‐free control algorithm for redundant manipulators is developed and resolved as the Lagrange problem of optimal control. It is shown that many well‐known methods for optimal redundant manipulation in the literature, including the Extended Jacobian Technique, most of constraint function‐based methods, and most of the previously reported methods on global optimization techniques, are all special cases of the formulation provided here. Further, the necessary conditions of the global optimality for this general formulation are derived in explicit form and the source of “algorithmic singularity” is rigorously identified and resolved. © 2995 John Wiley & Sons, Inc.