GameChat: Multi-LLM Dialogue for Safe, Agile, and Socially Optimal Multi-Agent Navigation in Constrained Environments

Safe, agile, and socially compliant multi-robot navigation in cluttered and constrained environments remains a critical challenge. This is especially difficult with self-interested agents in decentralized settings, where there is no central authority to resolve conflicts induced by spatial symmetry. We address this challenge by proposing a novel approach, GameChat, which facilitates safe, agile, and deadlock-free navigation for both cooperative and self-interested agents. Key to our approach is the use of natural language communication to resolve conflicts, enabling agents to prioritize more urgent tasks and break spatial symmetry in a socially optimal manner. Our algorithm ensures subgame perfect equilibrium, preventing agents from deviating from agreed-upon behaviors and supporting cooperation. Furthermore, we guarantee safety through control barrier functions and preserve agility by minimizing disruptions to agents' planned trajectories. We evaluate GameChat in simulated environments with doorways and intersections. The results show that even in the worst case, GameChat reduces the time for all agents to reach their goals by over 35% from a naive baseline and by over 20% from SMG-CBF in the intersection scenario, while doubling the rate of ensuring the agent with a higher priority task reaches the goal first, from 50% (equivalent to random chance) to a 100% perfect performance at maximizing social welfare.