Cooperation of multiple manipulators with passive joints

A single manipulator with passive joints is most likely nonholonomic systems, but multimanipulator systems may not. This paper investigates this issue by presenting a smooth feedback stabilization controller when the number of passive joints is not more than that of motion constraints associated to cooperations. This controller is a variation of the classical PD plus gravity compensation scheme and its asymptotic stability is guaranteed by LaSalle theorem. On the basis of this controller, we further discuss holonomy and nonholonomy conditions of multi-manipulator systems with passive joints. In addition, we propose a trajectory tracking controller which gives rise to asymptotic convergence of position errors and bounded interaction forces. Finally, we demonstrate asymptotic convergences of the proposed controllers with simulation study