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A critical metric of the coverage quality in Wireless Sensor Networks (WSNs)is the Minimal Exposure Path (MEP), a path through the environment that leastexposes an intruder to the sensor detecting nodes. Many approaches have beenproposed in the last decades to solve this optimization problem, ranging fromclassic (grid-based and Voronoi-based) planners to genetic meta-heuristics.However, most of them are limited to specific sensing models and obstacle-freespaces. Still, none of them guarantee an optimal solution, and thestate-of-the-art is expensive in terms of run-time. Therefore, in this paper,we propose a novel method that models the MEP as an Optimal Control problem andsolves it by using a Semi-Lagrangian approach. This framework is shown toconverge to the optimal MEP while also incorporates different homogeneous andheterogeneous sensor models and geometric constraints (obstacles). Experimentsshow that our method dominates the state-of-the-art, improving the results byapproximately 10% with a relatively lower execution time.

A Semi-Lagrangian Approach for the Minimal Exposure Path Problem in Wireless Sensor Networks