Submodular Optimization for Heterogeneous UAV Deployment

Abstract

Unmanned Aerial Vehicles (UAVs) are widely used in environmental monitoring tasks such as forest surveillance, agricultural mapping, and disaster assessment, where their ability to collect dense and high-resolution observations is particularly advantageous. However, many existing approaches implicitly assume that UAV platforms and onboard sensors are homogeneous. This assumption can introduce significant estimation errors in real-world deployments. This work studies the deployment of heterogeneous UAVs equipped with sensors of different accuracies for fire-scene assessment, using a point-of-interest–based model. Research on heterogeneous UAV measurements remains relatively limited. We introduce a weighted frame potential (WFP) that captures the orthogonality structure of sensing matrices under heterogeneous noise. By reformulating the problem as a submodular maximization task, we develop a Random Greedy Algorithm that guarantees a 1/(1+c)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1/(1+c)$$\end{document} approximation of the optimal solution, where c denotes the curvature of the submodular function. A theoretical upper bound on the reconstruction error induced by the selected UAV configuration is also established. Experiments on both small- and large-scale fire monitoring tasks show that the proposed method achieves higher reconstruction accuracy and better computational efficiency than existing algorithms.