Vibration Decoupled Modeling and Robust Control of Redundant Cable-Driven Parallel Robots

Abstract

Trajectory tracking and vibration control of redundant cable-driven parallel robots (CDPR) attracted the attention of different researchers; however, the effects of the CDPRs end-effectors disturbing force/moment on the undesired vibrations and minimization of such effects has received few attention. A new general dynamic modeling and robust control structure for redundant CDPR is proposed in this paper, which evaluates such factors and tries to minimize their effects on the performance of CDPRs. Considering the effects of redundant cables on the CDPRs’ stiffness improvement, we neglect the second and higher order terms of motion errors that helps to separate the moving platform's undesired vibration equation from its desired (nominal) equation of motion. The obtained vibration model forms a linear parametric variable (LPV) dynamic system that lets us investigate the effects of external disturbances on the undesired vibration in different directions, and use a wide class of well-established robust and optimal vibration control techniques. Consequently, in order to minimize the effect of disturbances on the moving platform trajectory tracking performance, a robust and optimal vibration compensator is designed using the $LPV-H_\infty$ control design techniques. Based on the platform's desired trajectory, the proposed control scheme calculates the cables’ nominal tension required for trajectory tracking and further generates the auxiliary signals to augment these tensions to counteract the undesirable vibrations. Based on the obtained dynamic model, the developed approach is simplified for kinematically-constrained redundant CDPRs as a new actuation method with restricted rotational degrees of freedom. Via numerical analysis and experimental tests of a planar kinematically-constrained CDPR, the proposed modeling and robust control design approach are examined and compared with other common control design methodologies. Moreover, the effectiveness of kinematically-constrained actuation method in vibration elimination and control design simplification of CDPRs is demonstrated.