A comparative study of methods to solve the watchman route problem in a photon mapping-illuminated 3D virtual environment

Abstract

Understanding where to place static sensors such that the amount of information gained is maximized while the number of sensors used to obtain that information is minimized is an instance of solving the NP-hard art gallery problem (AGP). A closely-related problem is the watchman route problem (WRP) which seeks to plan an optimal route by an unmanned vehicle (UV) or multiple UVs such that the amount of information gained is maximized while the distance traveled to gain that information is minimized. In order to solve the WRP, we present the Photon-mapping-informed active-Contour Route Designator (PICRD) algorithm. PICRD heuristically solves the WRP by selecting AGP-solving vertices and connecting them with vertices provided by a 3D mesh generated by a photon-mapping informed segmentation algorithm using some shortest-route path-finding algorithm. Since we are using photon-mapping as our foundation for determining UV-sensor coverage by the PICRD algorithm, we can then take into account the behavior of photons as they propagate through the various environmental conditions that might be encountered by a single or multiple UVs. Furthermore, since we are being agnostic with regard to the segmentation algorithm used to create our WRP-solving mesh, we can adjust the segmentation algorithm used in order to accommodate different environmental and computational circumstances. In this paper, we demonstrate how to adapt our methods to solve the WRP for single and multiple UVs using PICRD using two different segmentation algorithms under varying virtual environmental conditions.