Multi-Robot-Guided Crowd Evacuation: Two-Scale Modeling and Control

TL;DR

This work presents a two-scale hydrodynamic framework for robot-guided crowd evacuation, coupling microscopic social-force interactions among humans and robots with macroscopic density and velocity PDEs. The control design separates exploration (position control) from density stabilization (direction control), employing density feedback, backstepping, and an adaptive neural-network to compensate for unknown environmental forces. The authors establish stability guarantees and demonstrate the approach via extensive agent-based simulations across various crowd sizes, robot counts, and obstacle scenarios, showing robust evacuation performance when robot influence covers the crowd. The framework offers a scalable pathway for real-time robot-guided evacuation, with potential extensions to unstructured environments and decentralized implementations.

Abstract

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 use 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 hydrodynamic models, which consist of a family of microscopic social force models that describe how human movements are locally affected by other humans, the environment, and 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 macrostates of the crowd to guide the crowd to a safe location. We prove the stability of the proposed evacuation algorithm and conduct extensive simulations to investigate the performance of the algorithm with different combinations of human numbers, robot numbers, and obstacle settings.

Figures (8)

• Figure 1: All the social forces applied to the red person: a navigation force $F$ from the robot, a repulsive force $G$ from the obstacle, and two repulsive forces from the other two humans.
• Figure 2: The navigation force field with round support generated by a robot.
• Figure 3: The target density $\rho_*(x)$.
• Figure 4: The density convergence errors $\|\tilde{\rho}(\cdot,t)\|_{L^2(\Omega)}^2$.
• Figure 5: Illustration of the evacuation process when the environment was free of obstacles. Each column of subfigures represented the same instant. Each row of subfigures represented the time evaluation of certain variables. Row 1: Human positions $\{x_j(t)\}_{j=1}^N$ (red dots), human velocities $\{v_j(t)\}_{j=1}^N$ (red arrows attached to the red dots), robot positions $\{r_i(t)\}_{i=1}^n$ (black dots), and the navigation force fields $\{F_i(x,t)\}_{i=1}^n$ with round supports generated by the robots (black arrows surrounding the black dots). Row 2: Estimation of the real-time crowd density $\rho(x,t)$ using kernel density estimation. Row 3: Estimation of the real-time crowd velocity field $u(x,t)$ using linear interpolation.

Theorems & Definitions (6)

• Remark 1
• Theorem 1
• proof
• Theorem 2
• proof
• Remark 2