On singular behaviors of impedance‐based repeatable control for redundant robots

Abstract

Abstract This article addresses the association between the unstiffening phenomena in structural mechanics and the algorithmic singularities encountered in the impedance‐based repeatable control algorithms used to command redundant manipulators. It is well known that velocity control schemes such as the pseudoinverse control schemes do not guarantee repeatability for redundant manipulators. In other words, for a closed end‐effector trajectory, the joints do not, in general, exhibit a closed trajectory. One way to overcome this problem is to model each joint with compliance and incorporate a second‐order correction term for the pseudoinverse. With this model, the joint configuration adopted by the manipulator at a given point in task space is one which minimizes the artificial potential energy of the system and is locally unique. In terms of statics, this is equivalent to saying that the elastic structure reaches its static equilibrium under external load. Keep this analogy in mind. We know that the impedance control commands the manipulator to mimic the behavior of an elastic articulated chain. For any phenomena observable on a real elastic structure, we should be able to find its counterpart embedded in the impedance control. In this article, we analyze the performance of such repeatable control algorithms from the point of view of structure mechanics. Singularities in the algorithm are examined and their significance in mechanics are also discussed. © 2001 John Wiley & Sons, Inc.