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.

翻译：无线传感器网络(WSNs)覆盖质量的一个关键衡量标准是最低接触路径(MEP),这是一条穿过环境的路径,最不暴露于传感器探测节点的入侵者。在过去几十年中,为解决这一优化问题提出了许多方法,从经典(基于电网的和基于Voronoi的)规划者到基因超重学,从典型的(基于电网的和基于Voronoi的)规划者到基因超重症学家,到基因超重论的基因超重问题。然而,其中大多数都局限于特定的感应模型和无障碍的空间。然而,它们都无法保证最佳的解决方案,而且最新技术在运行时成本很高。因此,在本文件中,我们提出了一个新颖的方法,将MEP作为最佳控制问题模型,通过使用半Lagrangian的方法加以解决。这个框架显示在与最佳的MEP同时结合了不同的同和混合感应模型和几何限制(缩影塔)。实验表明,我们的方法主宰了最先进的技术,在运行时成本是昂贵的。因此,我们用10%的时间将结果改进了近10%。