Time-Optimal Control of Robotic Manipulators Along Specified Paths

TLDR

The authors present a minimum‑time control algorithm that computes optimal open‑loop torques for a specified path while respecting arbitrary torque limits expressed as functions of joint angles and velocities, and is applicable to any rigid‑link manipulator with known dynamics. They demonstrate that the resulting torques can be implemented using a conventional linear feedback controller, yielding the optimal trajectory.

Abstract

The minimum-time manipulator control problem is solved for the case when the path is specified and the actuator torque limitations are known. The optimal open-loop torques are found, and a method is given for implementing these torques with a conventional linear feedback control system. The algorithm allows bounds on the torques that may be arbitrary functions of the joint angles and angular velocities. This method is valid for any path and orientation of the end- effector that is specified. The algorithm can be used for any manipulator that has rigid links, known dynamic equations of motion, and joint angles that can be determined at a given position on the path.