Cooperative-theoretic optimal adaptive robust control for fuzzy multiple manipulator systems

Abstract

This article presents the study of the trajectory tracking issue of multiple manipulators from the viewpoint of servo constraint-following. First, on the framework of Udwadia-Kalaba (U-K) theory, the tasks of (holonomic or nonholonomic) trajectory tracking control are transformed into a series of servo constraints, and a nominal control is presented to realize the servo constraint-following for the system without uncertainty. Second, consider that there exists the time-varying uncertainty in the system, which is bounded and characterized by the fuzzy set theory. An adaptive robust control (ARC) is presented to achieve tracking errors uniform boundedness (UB) and uniform ultimate boundedness (UUB). Third, cooperative game theory is employed to obtain the dual optimal control parameters of the presented controller, and the mathematical derivation is performed to verify that there exists the Pareto optimal solution. Finally, simulation results show the effectiveness of the proposed control for the trajectory tracking control of multiple manipulators.