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 Bayes' Rule 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.

翻译：机器人在拥挤区域导航时，应与人类协商自由空间而非完全控制避碰，否则可能导致冻结行为。博弈论为机器人在路径规划中推断人类潜在协作避碰提供了框架。特别地，混合策略纳什均衡能够捕捉不确定性下的协商行为，使其非常适合人群导航。然而，计算混合策略纳什均衡的计算成本通常过高，难以满足实时决策需求。本文提出一种基于轨迹概率分布的迭代贝叶斯更新方案。该算法同时生成机器人的随机规划行径与其他行人路径的概率预测。我们证明所提算法等价于求解人群导航的混合策略博弈，且能保证恢复博弈的全局纳什均衡。我们将该算法命名为贝叶斯规则纳什均衡（BRNE），并开发了实时模型预测人群导航框架。由于BRNE并非求解通用混合策略纳什均衡，而是针对人群导航特化的公式，其可在低功耗嵌入式计算机上实时求解。我们在仿真环境与真实行人数据集中评估BRNE。在安全性与导航效率方面，BRNE持续优于非学习方法与基于学习的方法，并在行人数据集基准测试中达到人类水平的人群导航性能。最后，我们在搭载全机载感知与计算系统的无缆四足机器人上，通过真实人类交互验证了算法的实用性。