Basic optimization methods of redundant manipulators

Abstract

In this article, basic optimization methods of redundant manipulators are surveyed. First, some mathematical tools for redundancy utilization are introduced. Then, two methods for redundancy control, that is, local and global optimization methods, are described in three levels of problem formulation, that is, velocity input formulation, acceleration input formulation, and torque input formulation. As for the local optimization, we introduce the task-decomposition approach in which a total task to be performed by the manipulator is decomposed into two (or more) subtasks with order of priority. Two cases of this approach are explained in detail. One is the case where the second subtask is specified by a desired trajectory for some manipulation variables, and the other is the case where the second subtask is specified by a criterion function. Applications of the method to avoiding obstacles and avoiding singular configurations are also illustrated. As for the global optimization, after formulating the problem as optimal control problems, it is shown that necessary conditions of optimality can be given by using the calculus of variations or the Maximum Principle. © 1996 John Wiley & Sons, Inc.