Structure of the Minimum-Time Control Law for Multiple Robot Arms Handling a Common Object

In this paper, the problem of the existence and structure of the minimum-time control for multiple robot arms cooperatively handling a common object is addressed. The dynamical system is modeled by considering the arms as closed kinematic chains. The conditions of the existence of the time-optimal solution are verified by emloying a Lyapunov approach and the concept of feedback equivalence to linear systems. Furthermore, it is shown that the structure of the minimum-time control law for individual joint actuators requires that at least one of the actuators is always saturated on any finite time subinterval, while the rest of them are either saturated or singular depending upon the motion configurations and robot parameters Thus, it is suggested that the totally-singular optimal control does not exist in this problem while a partially-singular control may occur. The theoretical result should be able to provide insight into the dynamic characteristic of the multiple robot system which can be valuable in the path planning and design specifications of the system.