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

TL;DR

R3R addresses the lack of infinite-horizon safety guarantees in decentralized multi-agent motion planning under distance-based communications by introducing R-Boundedness, which confines an agent’s future trajectory to an $R$-ball, and integrating it with the gatekeeper safety framework. The key insight is that if $R^{\text{comm}} = 3R^{\text{plan}} + \delta$, local safety checks suffice to ensure global, time-invariant safety for nonlinear agents, even with asynchronous joining and replanning. The approach is validated through simulations with up to 128 Dubins vehicles, demonstrating scalable, collision-free operation in dense, obstacle-rich environments, albeit with occasional deadlocks at extreme densities. These results show that scalability and formal safety can be achieved together in decentralized settings, enabling practical deployment in large teams of agents. Mathematical rigor is maintained by explicitly tying planning and communication radii and by proving forward-invariant safety under local validity checks.

Abstract

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.

Figures (4)

• Figure 1: Constructing a Safe, Committed Trajectory. An agent at the anchor point plans a nominal trajectory (orange) toward its goal. To ensure safety, it must find a candidate trajectory that remains entirely within its planning radius $R^\text{plan}$ (red circle). An unsafe candidate that exits this radius (red) is rejected. A safe candidate that stays within the radius (green) is verified and becomes the committed trajectory for the agent to follow.
• Figure 2: Demonstration of R3R over time for two Dubins agents. The timeline indicates when each agent (Red: Agent 1, Blue: Agent 2) plans or replans. Committed trajectories (solid lines) are certified to be safe for all time, and remain within a planning radius $R^\text{plan}$ (filled circles), around where they are constructed. Agents first plan goal-oriented nominal trajectories (dashed lines). A portion of this nominal is combined with a backup trajectory, to form a candidate. If this candidate is deemed safe, it becomes a committed trajectory. At times $t_{0,1} \neq t_{0,2}$ agents $1$ and $2$ wish to join the network. Each agent independently constructs a valid committed trajectory, which is then simultaneously committed and broadcast as the agent enters the network. (a.) The initial committed trajectories of both agents remain within the planning radius. The agents could not communicate at the time of planning, so we see their nominal trajectories, which may be unsafe, intersect. (b.) Both agents have continued to track their initial committed trajectories, and are now within communication range. Both agents are near their backup sets, and thus should soon replan to continue making progress. (c.) Agent $1$'s logic dictated performing a replan first, so at time $t_{1_1}$, it constructs a new nominal trajectory to its goal, which attempts to avoid agent $2$. It then constructs a new committed trajectory, which it certifies as safe with respect to the committed trajectory of agent $2$. At some time $t_{1_2} > t_{1_1}$, agent $2$ constructs a new committed trajectory which must avoid the recently committed trajectory of agent $1$. This reflects the asynchronous nature of the algorithm, where agents replan independently and assume a low priority with respect to all neighbors. (d-f.) The process continues throughout the encounter. We see that agent $2$ replans again at time $t_{2_2}$, but as agent $1$ has not yet reached its backup set, its internal logic does not necessitate a replan.
• Figure 3: 64 Dubins vehicles initialized with random start and goal positions in a city-like environment.
• Figure 4: Runtime performance of R3R as a function of agent density for $N$ agents in a variable-sized environment over 20 randomized trials. (Top) The average time per replanning attempt increases with density due to a higher number of neighboring agents to consider in collision checks. (Bottom) The rate of replanning failures (no valid candidates found) also increases with density as it becomes more difficult to find a valid trajectory.

Theorems & Definitions (21)

• Definition 1: Agent
• Definition 2: Trajectory
• Definition 3
• Definition 4: $\operatorname{dist}$
• Definition 5: Backup Set
• Definition 6: Nominal Trajectory
• Definition 7: Backup Trajectory
• Definition 8: Candidate Trajectory
• Definition 9: $R-$Bounded
• Lemma 1: Collision of Bounded Trajectories