R3R: Decentralized Multi-Agent Collision Avoidance with Infinite-Horizon Safety

Existing decentralized methods for multi-agent motion planning lack formal, infinite-horizon safety guarantees, especially for communication-constrained systems. We present R3R, to our knowledge the first decentralized and asynchronous framework for multi-agent motion planning under distance-based communication constraints with infinite-horizon safety guarantees for systems of nonlinear agents. R3R's novelty lies in combining our gatekeeper safety framework with a geometric constraint called R-Boundedness, which together establish a formal link between an agent's communication radius and its ability to plan safely. We constrain trajectories to within a fixed planning radius that is a function of the agent's communication radius, which enables trajectories to be shown provably safe for all time, using only local information. Our algorithm is fully asynchronous, and ensures the forward invariance of these guarantees even in time-varying networks where agents asynchronously join, leave, and replan. We validate our approach in simulations of up to 128 Dubins vehicles, demonstrating 100% safety in dense, obstacle rich scenarios. Our results demonstrate that R3R's performance scales with agent density rather than problem size, providing a practical solution for scalable and provably safe multi-agent systems.