A projection method for the elimination of contradicting control forces in redundantly actuated PKM

While redundantly actuated PKM (RA-PKM) possess desirable kinematic and dynamic properties, their control is impeded by the occurrence of antagonistic control forces. Such forces are observed in non-linear model-based as well as in decentralized control schemes. In this paper it is outlined that such antagonistic forces are inherent to the decentralized control of RA-PKM, and also that calibration errors and finite encoder resolutions cause antagonistic control forces and excited vibrations, hence energy loss and instabilities. The effect of measurement errors and the stability of individual PD and computed torque control is analyzed. They are shown to yield asymptotically stable setpoint control. A central result of this paper is a projection method for the elimination of contradicting control commands. This method is valid independently of the actual control scheme. Experimental results are presented for a 2RRR/RR implementation. The results confirm that the proposed scheme reduces antagonistic control forces up to measurement errors and model uncertainties.