Cooperation control of multiple manipulators with passive joints

This paper studies the problem of modeling and control of multiple cooperative underactuated manipulators handling a rigid object. A single underactuated manipulator is a nonholonomic system in most cases, but cooperative underactuated manipulator systems may not. We reveal holonomic property of such a system by presenting a smooth feedback controller subject to two conditions: 1) there are not fewer active joints than the degrees of freedom of the object; 2) the Jacobian matrix with respect to passive joints is not singular. This controller is an extension of the PD plus gravity compensation scheme and its asymptotic stability is guaranteed by LaSalle theorem. Furthermore, we develop a trajectory tracking controller that yields asymptotic convergence of position errors and bounded interaction forces simultaneously. The performance of the proposed controllers has been investigated by simulations on two six-DOF underactuated manipulators and by experiments on the cooperative underactuated manipulator system developed at CMU.