Event-Triggered Mixed Nonzero-Sum Game Optimal Control for Modular Robotic Manipulator Performing Coordinated Operation Tasks

Taking advantage of high-performance intelligent robots to solve the coordination control problem such as assembly, handling, and installation, transportation is gradually becoming a kind of frontier subject with great scientific research value in the field of robotics. However, due to possible conflicts and inconsistencies between the manipulator and the operating object, it is challenging to design the optimal coordination control scheme between human and robot. This article presents an event-triggered mixed nonzero-sum game optimal control method, which considers both nonzero-sum game and cooperative game cases, for modular robotic manipulator (MRM) systems performing coordinated operation tasks. First, the joint torque feedback technique and joint task assignment method are employed to establish the dynamic model of MRM subsystem, and then, the global state-space description is deduced. For the unknown information containing interconnected dynamic coupling (IDC) terms and friction modeling errors, an adaptive neural network (NN) identifier is established by utilizing the measured input-output data of each joint module. The adaptive updating law guarantees that the NN weight error finally converged to a minimum neighborhood of zero. To ensure the optimality of system overall performance, the corresponding value functions reflecting the interconnectedness among each joint subsystem and manipulated object are constructed. Based on the idea of differential game, the coordination control problem of MRM system is transformed into a mixed nonzero-sum game problem among each joint module and the operated object. Next, by constructing a single critic NN with learning structure, the optimal value function is approximated to solve the event-based Hamiltonian equations, and then, the optimal control strategy of each player is obtained. Finally, the Lyapunov theory is used to analyze system stability, and the effectiveness of the presented method is reinforced by experimental results.