Decentralized Social Navigation with Non-Cooperative Robots via Bi-Level Optimization

This paper presents a fully decentralized approach for realtime non-cooperative multi-robot navigation in social mini-games, such as navigating through a narrow doorway or negotiating right of way at a corridor intersection. Our contribution is a new realtime bi-level optimization algorithm, in which the top-level optimization consists of computing a fair and collision-free ordering followed by the bottom-level optimization which plans optimal trajectories conditioned on the ordering. We show that, given such a priority order, we can impose simple kinodynamic constraints on each robot that are sufficient for it to plan collision-free trajectories with minimal deviation from their preferred velocities, similar to how humans navigate in these scenarios. We successfully deploy the proposed algorithm in the real world using F1/10 robots, a Clearpath Jackal, and a Boston Dynamics Spot as well as in simulation using the SocialGym 2.0 multi-agent social navigation simulator, in the doorway and corridor intersection scenarios. We compare with state-of-the-art social navigation methods using multi-agent reinforcement learning, collision avoidance algorithms, and crowd simulation models. We show that (i) classical navigation performs 44% better than the state-of-the-art learning-based social navigation algorithms, (ii) without a scheduling protocol, our approach results in collisions in social mini-games (iii) our approach yields 2× and 5× fewer velocity changes than CADRL in doorways and intersections, and finally (iv) bi-level navigation in doorways at a flow rate of 2.8 - 3.3 (ms)-1 is comparable to flow rate in human navigation at a flow rate of 4 (ms)-1.