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.

翻译：机器人在拥挤区域导航时，应与人类协商共享空间而非完全控制避碰行为，否则可能导致运动冻结问题。博弈论为机器人在路径规划中推断人类潜在协作避碰行为提供了理论框架。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场景。然而，混合策略纳什均衡的计算复杂度通常过高，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。该算法能同时生成机器人的随机路径规划及其他行人轨迹的概率预测。我们证明该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递归纳什均衡（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计算形式，其可在低功耗嵌入式计算机上实现实时求解。我们在仿真环境与真实行人数据集上评估BRNE算法。实验表明，BRNE在安全性与导航效率方面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，我们在搭载全自主感知计算系统的无缆四足机器人上，通过真实人机交互实验验证了算法的实用性。