Nonzero-sum game-based decentralized approximate optimal control of modular robot manipulators with coordinate operation tasks using value iteration

Abstract Accurate trajectory tracking and appropriate contact force are crucial for the coordinated operation-oriented control of modular robot manipulators (MRMs). Considering the practical need for precision in system control, resource optimization, and disturbance compensation within the context of the coordinated operation tasks (COTs) of MRMs, this paper employs a value iteration (VI) technique to devise a decentralized approximate optimal control strategy grounded in nonzero-sum game (NZSG) theory. To obtain more accurate, reliable, and safe control, a dynamic model of the MRM is established using joint torque feedback technology; then, the problem of optimal control for MRM systems focused on coordinated operation-oriented control is reformulated as an NZSG involving multiple subsystems. The present study, grounded in the theoretical framework of the adaptive dynamic programming (ADP) algorithm, employs an event-triggered NZSG strategy, utilizing VI to resolve the coupled Hamilton–Jacobian equations, culminating in the derivation of the Nash equilibrium solutions. Through stringent stability analysis, it is established that the trajectory tracking error for the closed-loop MRM system engaged in COTs is uniformly ultimately bounded. The proposed method’s efficacy is subsequently corroborated through experimental validation.