Passivity-Based Control Allocation of a Redundantly-Actuated Parallel Robotic Manipulator with a Point-Mass Payload

This paper examines the effect of control allocation on the passive input-output properties of a redundantly-actuated parallel robotic manipulator with a point-mass payload. In particular, it is shown that the mapping matrix used for control allocation is to satisfy a forward velocity kinematic constraint in order to preserve the manipulator's passive inputoutput mapping from modified control torques in task space to the velocity tracking error of the payload. A method to generate the control allocation matrix using load-sharing parameters is proposed, and is shown to have a physically intuitive relationship to the control effort of the individual actuators. A numerical example of a cable-driven parallel robot is presented, which illustrates the intuitive nature of the proposed control allocation method compared to a pseudoinverse method in the literature.