Event-triggered-based Cooperative Game Optimal Tracking Control for Modular Robot Manipulator with Constrained Input

In this paper, a cooperative game optimal tracking control method based on event-triggered mechanism for constrained input modular robot manipulators (MRMs) system is introduced. According to the joint torque feedback (JTF) technique, the dynamics model of the constrained input subsystem is established and the global state space equation is derived. The control inputs of $n$ joints in the MRM system with constrained input are taken as $n$ participants of cooperative game, the tracking control problem of the manipulator system is transformed into the optimal control problem based on the cooperative game. Next, a fusion function containing position and velocity errors is defined to construct the performance index function. In order to improve the control performance and robustness of the manipulator system, part of the known model information is used to devise controller, the model uncertainty is dealt by the neural network (NN) observer, and the optimal compensation control strategy is used to deal with internal disturbance such as sensor measurement error and transmission ripple due to power fluctuations, electromagnetic effects, noise and vibration. Based on the adaptive dynamic programming (ADP) algorithm and event-triggered mechanism, the optimal tracking control strategy is obtained by approximately solving the event-triggered Hamilton-Jacobi-Bellman (HJB) equation with the critic NN. The Lyapunov theory proves that trajectory tracking error of MRM system with constrained input is uniformly ultimately bounded (UUB). Finally, the experimental results demonstrate the effectiveness of the proposed control method.