Time-optimal control of multiple cooperating manipulators with trajectory and motion program constraints

Abstract

Two types of problems associated with time-optimal control of multiple manipulators moving a commonly held object along specified trajectories are studied. The first problem involves finding the minimum traveling time and the optimal control torques for any desired motion programs of the given trajectory. The second problem involves finding the optimal velocity distribution along the trajectory such that the motion can be completed in the minimum time. To solve these problems, a parametric form of the generalized dynamic equation is derived. An iterative search procedure is developed for solving the first problem. During the search, the lower bound of the traveling time at any point of the given trajectory is determined by using the linear programming technique. The second problem is solved by integrating the parametric dynamic equation along the given trajectory based on the phase-plane switching curve approach. The maximum acceleration and the upper bound of the operation speed at each integration instance are determined from two linear programs. The proposed methods are applicable to various complex multi-robot systems and can handle nonlinear torque-speed characteristics of the joint actuators. © 1996 John Wiley & Sons, Inc.