Optimal Control on Crowd Evacuation with Leader-Follower Model
Tianhe Jiang, Ziheng Shangguan · 2018
An MILP-in-MPC algorithm is presented for solving crowd evacuation problems. Crowd evacuation discussed in this paper is simplified as a task to transfer a crowd of followers from their initial states to a target set of states by controlling a set of leader agents while satisfying some constraints. Within minimum time, a solution which the outside controller only gives order to the leaders is proposed. The algorithm works by separating leaders which are fire-fighters in our case and followers which are the crowd into two systems. The leaders form a system which the followers take control input while the followers form a system which impose crowd constraints on the system. Model Predictive Control framework is applied to manage feedback property of the problem, taking both dynamic obstacle constraints and stochastic behavior of followers into account. For time-minimizing trajectory optimization with collision avoidance within a finite horizon, Mixed-Integer Linear Programming method is used. The results show that the MILP-in-MPC algorithm can naturally solve logical constraints and integrate both open-loop and closed-loop property of this problem. Robust control is generated for crowd evacuation applications, which successfully controls the followers within the safe range created by the leaders throughout time period of evacuation.