  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 an intruder to the sensor detecting nodes. Many approaches have been
proposed in the last decades to solve this optimization problem, ranging from
classic (grid-based and Voronoi-based) planners to genetic 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 run-time. Therefore, in this paper,
we propose a novel method that models the MEP as an Optimal Control problem and
solves it by using a Semi-Lagrangian approach. This framework is shown to
converge to the optimal MEP while also 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.
