Bilayer nonzero-sum differential game-based optimal control of modular robot manipulator for human–robot collaboration - Cui, Yiming; An, Tianjiao; Dong, Bo; Ma, Bing; Zhang, Zhenguo (European journal of control, 2025)
This paper introduces a bilayer nonzero-sum differential game-based optimal control framework for a Modular Robot Manipulator (MRM) in Human–Robot Collaboration (HRC) tasks. The dynamic model of the MRM is obtained with the Joint Torque Feedback (JTF) technique. Consider the N-player nonzero-sum differential game within the MRM subsystems and the 2-player nonzero-sum differential game involving both the MRM and human collaborators in HRC tasks as the inner and outer layers of the bilayer nonzero-sum differential game. The Nash equilibrium solutions for the inner and outer layers of the nonzero-sum differential games are independently determined using the Adaptive Dynamic Programming (ADP) algorithm, which is based on a fuzzy logic system. As a result, optimal control policies for MRM subsystems and the optimal interaction force in HRC tasks are derived. The trajectory tracking error of the MRM system and the outer layer physical Human–Robot Interaction (pHRI) system have both been proven to be Ultimately Uniformly Bounded (UUB) under the bilayer nonzero-sum differential game-based optimal control of MRM for HRC with the application of Lyapunov theory. Finally, experiment results are presented to validate the superiority and effectiveness of the proposed method.