[Paper Review] Decentralized Social Navigation with Non-Cooperative Robots via Bi-Level Optimization

Rohan Chandra, Rahul Menon+3 more|arXiv (Cornell University)|Jun 15, 2023

Evacuation and Crowd Dynamics4 citations

TL;DR

This paper proposes a fully decentralized bi-level optimization framework for non-cooperative multi-robot navigation in social mini-games like doorways and corridor intersections. It first determines a fair, collision-free priority order via decentralized bidding, then plans kinodynamically feasible trajectories that minimize velocity deviation—achieving 44% better performance than state-of-the-art learning-based methods and 2×–5× fewer velocity changes than CADRL.

ABSTRACT

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 F$1/10$ 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 $2 imes$ and $5 imes$ 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)$^{-1}$.

Motivation & Objective

• To address the challenge of safe, efficient, and socially compliant navigation in non-cooperative multi-robot systems navigating constrained environments like doorways and corridors.
• To overcome limitations of existing methods—such as deep reinforcement learning (MARL) and crowd simulation models—that suffer from sim-to-real gaps, poor real-world deployment, or assume cooperative behavior.
• To develop a decentralized, real-time solution that enables robots to autonomously determine priority order and plan trajectories without centralized coordination.
• To achieve human-like navigation behavior characterized by minimal velocity deviation and smooth, cooperative-like maneuvers despite non-cooperative objectives.

Proposed method

• Uses a bi-level optimization framework: the top-level solves for a fair, collision-free priority order via decentralized auction-based bidding, where each robot independently submits a bid based on its own objective.
• The bottom-level optimization plans kinodynamically feasible trajectories conditioned on the assigned priority order, ensuring collision avoidance while minimizing deviation from each robot’s preferred velocity.
• Imposes simple, local kinodynamic constraints on each robot that are sufficient to guarantee collision-free navigation under the priority schedule, without requiring global state knowledge.
• Employs a decentralized implementation where each robot computes its own priority and trajectory independently, enabling real-time operation on physical robots.
• Leverages real-world hardware (F1/10 cars, Jackal, Spot) and simulation (SocialGym 2.0) to validate the approach across diverse scenarios.
• Uses handcrafted priority rules for simplicity, with future work aiming to learn cost functions via inverse optimal control for better generalization.

(a) No scheduling, initial time.

Experimental results

Research questions

• RQ1 Can a bi-level optimization framework effectively decouple priority ordering and trajectory planning in decentralized, non-cooperative multi-robot navigation?
• RQ2 Does a decentralized auction-based priority protocol lead to collision-free and efficient navigation in social mini-games like doorways and corridor intersections?
• RQ3 Can simple kinodynamic constraints, when combined with a priority order, produce socially compliant trajectories with minimal velocity deviation?
• RQ4 How does the proposed method compare quantitatively to state-of-the-art MARL, RVO, and Social Forces baselines in real-world and simulation settings?
• RQ5 To what extent does the absence of a scheduling protocol lead to collisions or deadlocks in non-cooperative navigation?

Key findings

• Classical navigation with the proposed bi-level optimization outperformed state-of-the-art MARL-based social navigation algorithms by 44% in success rate on the doorway task.
• Without a scheduling protocol, the system resulted in collisions in social mini-games, demonstrating the necessity of priority ordering for safe navigation.
• The proposed method achieved 2× and 5× fewer velocity changes than CADRL in doorway and intersection scenarios, respectively, indicating higher social compliance.
• In doorway navigation at a flow rate of 2.8–3.3 m/s, the bi-level approach matched the performance of human navigation at 4 m/s, indicating strong social compliance.
• The Only Local baseline (no high-level policy) failed nearly 100% of the time in the doorway scenario, confirming that local-only navigation fails without a global coordination mechanism.
• Many MARL baselines reported low collision rates not due to effective navigation, but because of frequent deadlocks and timeouts, as evidenced by abysmal success rates.

(b) No schedule results in collision.