In this paper, an optimal motion/force hybrid control strategy based on adaptive reinforcement learning (ARL) is proposed for cooperating manipulator systems. The optimal trajectory control and constraint force factor control, by using the Moore–Penrose pseudoinverse, are addressed to design the controller corresponding to the manipulator dynamic model. In addition, a frame of a different auxiliary term and an appropriate state-variable vector are presented to address the non-autonomous closed system with a time-varying desired trajectory. The simultaneous actor/critic algorithm is implemented by optimizing the squared Bellman difference to be computed from the error of control policy and optimal control input. Moreover, the constraint force factor controller is discussed by a nonlinear technique after achieving the result of the constraint force factor. The tracking and convergence of ARL-based optimal motion/force hybrid control strategy are validated in closed-loop systems by a proposed Lyapunov function candidate. Finally, simulation results are implemented on a constrained system using three manipulators to verify the physical implementation of the presented optimal motion/force hybrid-tracking control strategy.
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