Manipulability Optimization for Redundant Manipulators Using Singular Value Analysis: A Convex Approach

It is imperative for a redundant manipulator to avoid singular configurations in order to successfully accomplish a task. The manipulability describes the distance between the current configuration of a redundant manipulator and singular configurations to a certain extent. The probability of a redundant manipulator entering singular configurations can be reduced by maximizing the manipulability. However, the manipulability is a nonconvex function of the joint angle, making it difficult to be optimized directly at the joint-angle level. In this article, we propose a singular value analysis-based manipulability optimization scheme. In this scheme, the redundant manipulator is driven from a low manipulability state to a high one by optimizing the derivative of the manipulability with respect to time. Specifically, we take singular values as the intermediate variable for derivation, which avoids the pseudoinverse calculation and the introduction of auxiliary variables in these existing methods. In addition, the orientation control is considered in this scheme to assist the redundant manipulator in completing challenging tasks. This article illustrates that the proposed scheme outperforms existing methods in a variety of simulations and experiments and demonstrates its performance in the real world.