A Path Planning Algorithm for Human Evacuations with an Environment Dependent Motion

Abstract

This work proposes an algorithm for the optimal guidance of evacuees in indoor environments. The proposed work examines the path-dependent accumulation of hazardous substances inhaled, such as carbon monoxide, and provides an optimal path that ensures that evacuees can survive to emergency exits by guaranteeing the accumulated inhalation of carbon monoxide is below life-threatening levels. The spatiotemporal variation of the hazardous and toxic field, as described by either Poisson or advection-diffusion partial differential equation, is used to compute the accumulated amount of carbon monoxide inhaled. The accumulated amount is given in terms of the line integral of the hazardous field along the escape paths. The effects of carbon monoxide on evacuee speed are considered. To ensure a path with lower carbon monoxide inhalation levels as well as reduced flight times, level sets are used to generate the set of angles for each path. This is done using a coefficient that changes the direction of motion based on the instantaneous carbon monoxide concentration. This coefficient varies based on the level set with a specific critical level set declared such that it is never crossed. The optimization scheme provides the optimal path among all admissible paths having the smallest value below the tolerance levels of the substance. Simulation studies considering both spatially and spatiotemporally varying functions of carbon monoxide in an indoor environment representing a floor of an office building, are provided to further demonstrate evacuation policies in contaminated indoor environments.