[Paper Review] Deadlock-free, Safe, and Decentralized Multi-Robot Navigation in Social Mini-Games via Discrete-Time Control Barrier Functions

Rohan Chandra, Vrushabh Zinage+3 more|arXiv (Cornell University)|Aug 21, 2023

Robotic Path Planning Algorithms4 citations

TL;DR

This paper proposes a decentralized, safe, and deadlock-free multi-robot navigation framework for constrained environments using game-theoretic control barrier functions (CBFs). By formulating deadlock resolution as a Nash equilibrium in a modified Chicken game and integrating it with model predictive control and CBFs, the method ensures liveness and safety with minimal state perturbations, outperforming baselines in simulation and real-world tests on F1/10 robots and a Boston Dynamics Spot.

ABSTRACT

We present an approach to ensure safe and deadlock-free navigation for decentralized multi-robot systems operating in constrained environments, including doorways and intersections. Although many solutions have been proposed that ensure safety and resolve deadlocks, optimally preventing deadlocks in a minimally invasive and decentralized fashion remains an open problem. We first formalize the objective as a non-cooperative, non-communicative, partially observable multi-robot navigation problem in constrained spaces with multiple conflicting agents, which we term as social mini-games. Formally, we solve a discrete-time optimal receding horizon control problem leveraging control barrier functions for safe long-horizon planning. Our approach to ensuring liveness rests on the insight that extit{there exists barrier certificates that allow each robot to preemptively perturb their state in a minimally-invasive fashion onto liveness sets i.e. states where robots are deadlock-free}. We evaluate our approach in simulation as well on physical robots using F$1/10$ robots, a Clearpath Jackal, as well as a Boston Dynamics Spot in a doorway, hallway, and corridor intersection scenario. Compared to both fully decentralized and centralized approaches with and without deadlock resolution capabilities, we demonstrate that our approach results in safer, more efficient, and smoother navigation, based on a comprehensive set of metrics including success rate, collision rate, stop time, change in velocity, path deviation, time-to-goal, and flow rate.

Motivation & Objective

• To address the challenge of safe, deadlock-free navigation in decentralized multi-robot systems operating in constrained environments such as doorways and hallways.
• To formalize multi-robot navigation in these settings as 'social mini-games' involving non-cooperative, partially observable agents with conflicting goals.
• To develop a controller that ensures both safety (via CBFs) and liveness (via barrier certificates for deadlock-free states) in a decentralized, minimally invasive manner.
• To enable robots to emulate human-like behavior—modulating velocity slightly to avoid collisions and deadlocks—while adhering to kinodynamic constraints.
• To evaluate the method in simulation and on physical robots, demonstrating superior performance in success rate, collision avoidance, and trajectory smoothness compared to state-of-the-art baselines.

Proposed method

• The approach combines model predictive control (MPC) with control barrier functions (CBFs) for long-horizon, optimal, and safe trajectory planning.
• It introduces a novel class of barrier certificates that allow each robot to preemptively perturb its state onto 'liveness sets'—states where deadlock is avoided—using minimal, decentralized interventions.
• The liveness mechanism is grounded in a game-theoretic formulation where deadlock resolution is modeled as a Nash equilibrium in an N-player Chicken game.
• The method ensures forward invariance of liveness sets using principles analogous to how CBFs guarantee forward invariance of safety sets.
• The controller is implemented in a decentralized fashion, requiring only local sensing and no communication between robots.
• The framework is validated on F1/10 robots and a Boston Dynamics Spot in real-world scenarios involving doorways, hallways, and corridor intersections.

Figure 1 : Examples/Non-examples of social mini-games: Arrows indicate the direction of motion for two agents $1$ and $2$ toward their goals marked by the corresponding cross. The first scenario is a social mini-game since both the preferred trajectories of agents $1$ and $2$ are in conflict from so

Experimental results

Research questions

• RQ1 Can a decentralized multi-robot system achieve deadlock-free navigation in constrained environments without centralized coordination or communication?
• RQ2 Can a game-theoretic equilibrium be used to enable robots to resolve deadlocks by making minimal, coordinated perturbations to their trajectories?
• RQ3 How can control barrier functions be extended to ensure liveness (i.e., deadlock freedom) in addition to safety?
• RQ4 To what extent does the proposed method outperform existing decentralized and centralized baselines in terms of safety, efficiency, and trajectory smoothness?
• RQ5 Can the approach be deployed on real-world robots while maintaining performance under kinodynamic constraints?

Key findings

• The proposed method achieved 100% success rate in all tested scenarios (doorway, hallway, intersection), outperforming baselines like MPC-CBF, NH-ORCA, and NH-TTC, which failed due to collisions or deadlocks.
• In terms of path deviation, the game-theoretic approach achieved the lowest average deviation (0.12 m) in the doorway setting, indicating smoother, more human-like trajectories.
• The average change in velocity was minimized (0.15 m/s) compared to other methods, demonstrating effective, minimal perturbations to preferred velocities.
• The method achieved a higher flow rate (1.8 agents per second) in the intersection scenario, indicating better throughput and coordination.
• In the hallway scenario, the approach reduced stop time by 40% compared to ORCA-MAPF and 60% compared to CADRL, indicating improved motion continuity.
• Visual comparisons in Figure 8 confirmed that only the proposed method consistently resolved deadlocks without collisions, while baselines like MPC-CBF and NH-ORCA entered deadlocks due to symmetric environments and empty feasible sets.

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