A stochastic reachability approach to emergency building evacuation

In this paper we introduce a framework for real-time path planning for emergency building evacuation based on the theory of stochastic reachability with random sets. We consider the problem of a single human in a building escaping from a propagating dangerous contamination. We model the human and the hazard as stochastic processes. We formulate the task as a finite horizon stochastic reach-avoid problem in which the objective is to maximise the probability of the human leaving the building while avoiding contact with the hazard within a certain time. We apply dynamic programming to solve the reach-avoid problem and obtain an optimal control policy for the human and a corresponding value for the probability of success. We finally test the results in simulation.