Mixed-Strategy Nash Equilibrium for Crowd Navigation

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.