Minimal Exposure Paths in Time-Varying Fields: A Semi-Lagrangian Approach

In the context of Wireless Sensor Networks (WSNs), the Minimal Exposure Path (MEP) represents an important metric to evaluate the quality of network services. Most of the current literature is concentrated on stationary sensors, while few works have addressed the existence of moving nodes. Mobile Wireless Sensor Networks (MWSNs) present a great potential for detecting invaders compared to static ones, but dealing with dynamic sensors significantly increases the coverage complexity since the overall exposure of the sensor field depends on time. Therefore, in this letter, we propose an approach to compute Minimal Exposure Paths in time-varying fields based on a control optimization method called semi-Lagrangian (SL) scheme, in such a way that an intruder will be able to penetrate the dynamic field with the lowest exposure. The SL has already been proven to reach the optimal Minimal Exposure Path (MEP) on static WSNs, but concerning dynamic nodes, the proof is much more complicated. Then, we propose a heuristics that provides convergence of the SL algorithm to a result we conjecture to be the optimal one. Results with different time-varying sensor models in obstacle-free and cluttered environments have been presented and discussed.