Distributed Formation Control of Multi-Agent Systems: A Novel Fast-Optimal Balanced Differential Game Approach

• Published in: Unmanned systems (Singapore) pp. 1 - 21
• Main Authors: Xue, Wenyan, Huang, Jie, Chen, Nan, Chen, Yutao, Lin, Dingci
• Format: Journal Article
• Language: English
• Published: 04.11.2023
• ISSN: 2301-3850; 2301-3869
• DOI: 10.1142/S230138502550013X

This paper proposes an efficient fast-optimal balanced differential game (DG) approach to address the formation control problem in dynamic environments for networked multi-agent systems (MASs). Compared to existing receding horizon distributed differential game (RH-DDG) approaches, the proposed approach employs a two-layer game structure to balance optimality and real-time performance, with a focus on formation control, collision avoidance and obstacle avoidance. In the offline layer, the problem is converted into a distributed differential game (DDG) where each agent computes strategies using distributed information from locally neighboring agents. The strategy of each agent self-enforces a unique global Nash equilibrium (G-NE) with a strongly connected communication topology, providing an optimal reference trajectory for the online game. In the online layer, a receding horizon differential game with an event-trigger mechanism (RH-DGET) is presented to track the G-NE trajectory. Ego players are triggered to update online Nash strategies only when the event-triggering condition is satisfied, ensuring the real-time safety certificate. Rigorous proofs demonstrate that the online Nash strategies converge to the offline G-NE until the trigger ends, and a certain dwell time condition is given to prevent the Zeno behavior. Simulation results validate the effectiveness of the proposed approach.