A Convex Optimization Approach to Time-Optimal Path Tracking Problem for Cooperative Manipulators

Abstract

This paper studies the time-optimal path tracking problem for a cooperative robotic system. The considered system is composed of two two-link planar manipulators with non-actuated end-effectors rigidly grasping a bar. Given a predefined geometric path, the objective is to cooperatively move the bar along the path in minimum time subject to inequality constraints on the joint torques. We show that this problem can be cast as a convex optimization problem by using the existing results for a single manipulator, and also the fact that the desired motion of the bar can be achieved by incorporating its dynamics into the manipulators' dynamics. We illustrate our results in simulation.