A semi-Lagrangian approach for the Minimal Exposure Path Problem in Wireless Sensor Networks

Abstract

A critical metric of the coverage quality in Wireless Sensor Networks (WSNs) is the Minimal Exposure Path (MEP), a path through the environment that least exposes a mobile target to the sensor nodes detection. Many approaches have been proposed in the last decades to solve this optimization problem, ranging from classic grid-based and Voronoi-based planners to meta-heuristics. However, most of them are limited to specific sensing models and obstacle-free spaces. Still, none of them guarantee an optimal solution, and the state-of-the-art is expensive in terms of execution time. Therefore, in this paper, we propose a novel method, called SL-MEP, that models the MEP as an optimal control problem and solves it by using a semi-Lagrangian (SL) scheme. This framework is shown to converge to the optimal MEP while it incorporates different homogeneous and heterogeneous sensor models and geometric constraints (obstacles). Experiments show that our method dominates the state-of-the-art, improving the results by approximately 10% with a relatively lower execution time.