Multi-Robot-Guided Crowd Evacuation: Two-Scale Modeling and Control Based on Mean-Field Hydrodynamic Models

Emergency evacuation describes a complex situation involving time-critical decision-making by evacuees. Mobile robots are being actively explored as a potential solution to provide timely guidance. In this work, we study a robot-guided crowd evacuation problem where a small group of robots is used to guide a large human crowd to safe locations. The challenge lies in how to utilize micro-level human-robot interactions to indirectly influence a population that significantly outnumbers the robots to achieve the collective evacuation objective. To address the challenge, we follow a two-scale modeling strategy and explore mean-field hydrodynamic models which consist of a family of microscopic social-force models that explicitly describe how human movements are locally affected by other humans, the environment, and the robots, and associated macroscopic equations for the temporal and spatial evolution of the crowd density and flow velocity. We design controllers for the robots such that they not only automatically explore the environment (with unknown dynamic obstacles) to cover it as much as possible but also dynamically adjust the directions of their local navigation force fields based on the real-time macro-states of the crowd to guide the crowd to a safe location. We prove the stability of the proposed evacuation algorithm and conduct a series of simulations (involving unknown dynamic obstacles) to validate the performance of the algorithm.