Alternating direction response dynamics for distributed multi-agent interaction and formation coordination

Multi-agent systems have gained prominence in various applications for their scalability, flexibility, and efficiency. However, generating coordinated formation trajectories in a distributed manner remains challenging due to the lack of global information or designated leaders. To address this issue, we propose a fully distributed framework based on dynamic game theory. The problem is formulated as a dynamic trajectory game with a potential structure, jointly optimizing collision avoidance, control effort, formation coordination, and goal-reaching objectives. To compute the corresponding Nash equilibrium (NE), we introduce a distributed algorithm termed ADRD. By leveraging the consensus Alternating Direction Method of Multipliers (ADMM), our approach decouples inter-agent interactions. This enables each agent to independently compute its trajectory with theoretical convergence guarantees. Extensive simulations in obstacle-rich environments demonstrate that ADRD produces safe and coordinated trajectories with superior robustness compared to centralized and distributed baselines. Quantitative comparisons show consistent improvements over the proximal iterative best response scheme in formation accuracy, control cost, and overall cost metrics. Scalability experiments with up to 12 agents further validate the effectiveness of the method in larger teams.