Optimal navigation over spatiotemporally varying hazardous fields
Michael A. Demetriou, Efstathios Bakolas · 2021 60th IEEE Conference on Decision and Control (CDC) · 2021
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.