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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.
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Optimal navigation over spatiotemporally varying hazardous fields
This paper considers the optimal navigation problem wherein the agent has to traverse a spatiotemporally varying hazardous field that has severely lethal effects on the agent. The accumulated effects of the value of the spatiotemporally varying field along the path, represented by the line integral of the spatial field along the chosen trajectory, constitutes the destructive effects of the hazardous field. When this accumulated amount exceeds a prescribed threshold, the agent is incapacitated and can no longer move. We formulate the navigation problem as an optimal control problem in which the agent has to traverse a 2D enclosed domain and reach its goal destination at a free final time while minimizing the cumulative exposure to the hazardous field. Due to practical considerations, the solution to the optimal control problem is admissible only if the accumulated exposure of the agent when it reaches the final destination is well below the deadly threshold. The evolution of the spatiotemporally varying field is described by a 2D advection-diffusion PDE with a moving source that realistically captures rapidly evolving hazardous fields. Extensive numerical studies are included to highlight the various aspects of the proposed constrained navigation problem.
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- Award ID(s):
- 1825546
- PAR ID:
- 10385850
- Date Published:
- Journal Name:
- 2021 60th IEEE Conference on Decision and Control
- Page Range / eLocation ID:
- 2607 to 2612
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC45484.2021.9682802
