2024/03/03 by Muchen Sun, Sun, Max Muchen, Francesca Baldini +6 · 2 citations
Computer Science · Engineering · Social Sciences · #Computer Science and Game Theory (cs.GT) #Evacuation and Crowd Dynamics #FOS: Computer and information sciences #Machine Learning (cs.LG) #Mobile Crowdsensing and Crowdsourcing #Robotics (cs.RO) #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2403.01537
openalex publication_date 2024/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Robots navigating in crowded areas should negotiate free space with humans rather than fully controlling collision avoidance, as this can lead to freezing behavior. Game theory provides a framework for the robot to reason about potential cooperation from humans for collision avoidance during path planning. In particular, the mixed strategy Nash equilibrium captures the negotiation behavior under uncertainty, making it well suited for crowd navigation. However, computing the mixed strategy Nash equilibrium is often prohibitively expensive for real-time decision-making. In this paper, we propose an iterative Bayesian update scheme over probability distributions of trajectories. The algorithm simultaneously generates a stochastic plan for the robot and probabilistic predictions of other pedestrians' paths. We prove that the proposed algorithm is equivalent to solving a mixed strategy game for crowd navigation, and the algorithm guarantees the recovery of the global Nash equilibrium of the game. We name our algorithm Bayesian Recursive Nash Equilibrium (BRNE) and develop a real-time model prediction crowd navigation framework. Since BRNE is not solving a general-purpose mixed strategy Nash equilibrium but a tailored formula specifically for crowd navigation, it can compute the solution in real-time on a low-power embedded computer. We evaluate BRNE in both simulated environments and real-world pedestrian datasets. BRNE consistently outperforms non-learning and learning-based methods regarding safety and navigation efficiency. It also reaches human-level crowd navigation performance in the pedestrian dataset benchmark. Lastly, we demonstrate the practicality of our algorithm with real humans on an untethered quadruped robot with fully onboard perception and computation.