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

TL;DR

This paper introduces a Semi-Lagrangian method to find the minimal exposure path in wireless sensor networks, effectively handling various sensor models and obstacles, and outperforming existing approaches in accuracy and efficiency.

Contribution

It models the minimal exposure path as an optimal control problem and applies a Semi-Lagrangian approach, providing guaranteed convergence and improved performance over prior methods.

Findings

Achieves approximately 10% better results than state-of-the-art methods.

Handles diverse sensor models and obstacles within the framework.

Reduces computation time compared to existing solutions.

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 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.