Nonholonomic control of a three-DOF planar underactuated manipulator

Control of a manipulator with a passive joint which has neither an actuator nor a holding brake is investigated. The manipulator has three degrees of freedom in a horizontal plane, with the third joint being passive. The dynamic constraint on the free link is shown to be second-order nonholonomic. Controllability of the system is proved by constructing examples of the input trajectories from arbitrary initial states to arbitrary desired states, considering the motion of the center of percussion of the link. Trajectories for positioning are composed of simple translational and rotational trajectory segments. The trajectory segments are stabilized by nonlinear feedback control. Simulations and experimental results show the effectiveness of the planned trajectory and the feedback control law.