Scalar Field Mapping with Adaptive High-Intensity Region Avoidance

This research is motivated by a scenario where a group of UAVs is assigned to map an unknown scalar field, with the imperative of maintaining a safe distance from the sources of the field to evade detection or damage. The location of the sources is unknown a priori, so the UAVs rely on measurements of the field intensity to gauge safety. The UAVs estimate the unknown scalar field using Gaussian process (GP) regression and use the estimate to generate a map of high-intensity regions using Hough transform (HT), updated online based on the field measurements. A convergence analysis shows the boundedness of the error between the actual scalar field and the learned scalar field. The effectiveness of the method is evaluated through simulations, showcasing its ability to accurately learn scalar fields with multiple high-intensity regions while reducing the number of measurements taken inside the high-intensity regions.