Optimal design of adaptive robust control for a planar two-DOF redundantly actuated parallel robot

An adaptive robust control combined with a multi-objective parameter optimization method for a parallel robot under unknown uncertainty is proposed. In the active joint space, the model of the parallel robot can be obtained by combining the closed-chain constraint force and the open-chain system’s dynamic equation. Based on the Udwadia–Kalaba theory, the closed-chain constraint force imposed by the end effector can be calculated if no uncertainty. If there is uncertainty, we propose an adaptive robust control, based on a set of feasible design parameters, which guarantees deterministic performances, including uniform boundedness and uniform ultimate boundedness. To seek the optimal choice of the design parameters, among the feasible pool. We examine the system performance, which includes the transient performance, the steady state performance, and the control cost. By a fuzzy-theoretic D -operation, a performance index is formulated. The problem of choosing the optimal control parameters is equivalent to the problem of finding the minimum value of the performance index. An illustrative example demonstrates the superiority of the adaptive robust control. Mass uncertainty and external disturbance torque are introduced to test the effectiveness of the proposed control strategy.