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This paper presents a decentralized zero-sum optimal control method for MRMs with environmental collisions via an actor-critic-identifier (ACI) structure-based adaptive dynamic programming (ADP) algorithm. The dynamic model of the MRMs is formulated via a novel collision identification method that is deployed for each joint module, in which the local position and torque information are used to design the model compensation controller. A neural network (NN) identifier is developed to compensate the model uncertainties and then, the optimal control problem of the MRMs with environmental collisions can be transformed into a two-player zero-sum optimal control one. Based on the ADP algorithm, the Hamilton-Jacobi-Isaacs (HJI) equation is solved by constructing the actor-critic NNs, thus making the derivation of the approximate optimal control policy feasible. Based on the Lyapunov theory, the closed-loop robotic system is proved to be asymptotically stable. Finally, the experiments are conducted to verify the effectiveness and advantages of the proposed method.

Actor-Critic-Identifier Structure-Based Decentralized Neuro-Optimal Control of Modular Robot Manipulators With Environmental Collisions