We address the problem of finding mixed-strategy Nash equilibrium for crowd navigation. Mixed-strategy Nash equilibrium provides a rigorous model for the robot to anticipate uncertain yet cooperative human behavior in crowds, but the computation cost is often too high for scalable and real-time decision-making. Here we prove that a simple iterative Bayesian updating scheme converges to the Nash equilibrium of a mixed-strategy social navigation game. Furthermore, we propose a data-driven framework to construct the game by initializing agent strategies as Gaussian processes learned from human datasets. Based on the proposed mixed-strategy Nash equilibrium model, we develop a sampling-based crowd navigation framework that can be integrated into existing navigation methods and runs in real-time on a laptop CPU. We evaluate our framework in both simulated environments and real-world human datasets in unstructured environments. Our framework consistently outperforms both non-learning and learning-based methods on both safety and navigation efficiency and reaches human-level crowd navigation performance on top of a meta-planner.

翻译：本文针对人群导航中的混合策略纳什均衡求解问题展开研究。混合策略纳什均衡为机器人预测人群中不确定但具备合作性的人类行为提供了严谨模型，但其计算成本过高，难以实现可扩展的实时决策。我们证明，一种简单的迭代贝叶斯更新过程能够收敛至混合策略社会导航博弈的纳什均衡。此外，我们提出了一种数据驱动框架，通过将智能体策略初始化为从人类数据集中学习到的高斯过程来构建博弈。基于所提出的混合策略纳什均衡模型，我们开发了一种基于采样的群体导航框架，该框架可集成至现有导航方法中，并在笔记本电脑CPU上实现实时运行。我们在非结构化环境的仿真环境与真实人类数据集上对框架进行了评估。实验结果表明，我们的框架在安全性与导航效率两方面均持续优于非学习方法与基于学习的方法，并在元规划器之上达到了人类水平的群体导航性能。