Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of fieedom increase the orientation and reach of the robot. The load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion. In a usual robotic task, only the end-effector position trajectory is specified The joint position trajectory will therefore be unknown, for a redundant multirobot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. We show that the adaptive conuol of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived it ensures bounded parameter convergence, exponential convergence to zero of the load position error, the internal force error and the reference velocity error. The individual robot joint motions is shown to be stable by decomposing the joint coordinates into two variables one which is homeomorphic to the load coordinated, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold is directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold results. The overall stability of the joint angle is established from the stability of two cascaded dynamic systems involving the two decomposed co0rdlIliltes.