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.

用简单的迭代贝叶斯更新方案证明了混合策略纳什均衡模型收敛于混合策略社交导航游戏的纳什均衡，并提出了一个基于数据驱动的框架，该框架通过将代理策略初始化为从人类数据集中学得的高斯过程来构建游戏。基于提出的混合策略纳什均衡模型，我们开发了一个基于采样的群体导航框架，可以集成到现有的导航方法中，在笔记本电脑的 CPU 上实时运行。我们在模拟环境和非结构化环境中的真实人类数据集上评估了我们的框架，其在安全性和导航效率方面始终优于非学习和基于学习的方法，并在元规划之上达到了人类水平的群体导航性能。