Event-triggered bilayer game-based coordination control of multiple modular robot manipulators with input constraints

This paper presents an event-triggered bilayer game-based coordination control framework for multiple Modular Robot Manipulators (MRMs) operating under stringent resource and actuator saturation constraints. To alleviate the computational and communication burdens characteristic of extreme environments, we introduce an event-triggering mechanism built on Neural Dynamic Programming (NDP) and differential-game theory, while casting intra-MRM subsystem interactions and inter-MRM collaborative transport as a bilayer nonzero-sum differential game. Coupled Hamilton-Jacobi equations are approximately solved via adaptive critic networks, yielding near-optimal control policies that explicitly enforce input constraints. A Lyapunov-based analysis proves that the subsystem trajectory tracking errors are Ultimately Uniformly Bounded (UUB), and the multi-MRM system under the collaborative handling task is asymptotically stable. Experiments conducted on both a 7-DOF MRM, which is used to validate high-dimensional joint coordination, and a 2-DOF MRM platform, which provides a simplified setting for cooperative manipulation tasks, demonstrate the proposed method’s efficacy and highlight its performance advantages over existing approaches.