Optimal Positioning Strategy for Multi-Camera Zooming Drones

In the context of multiple-target tracking and surveillance applications, this paper investigates the challenge of determining the optimal positioning of a single autonomous aerial vehicle or agent equipped with multiple independently-steerable zooming cameras to effectively monitor a set of targets of interest. Each camera is dedicated to tracking a specific target or cluster of targets. The key innovation of this study, in comparison to existing approaches, lies in incorporating the zooming factor for the onboard cameras into the optimization problem. This enhancement offers greater flexibility during mission execution by allowing the autonomous agent to adjust the focal lengths of the on-board cameras, in exchange for varying real-world distances to the corresponding targets, thereby providing additional degrees of freedom to the optimization problem. The proposed optimization framework aims to strike a balance among various factors, including distance to the targets, verticality of viewpoints, and the required focal length for each camera. The primary focus of this paper is to establish the theoretical groundwork for addressing the non-convex nature of the optimization problem arising from these considerations. To this end, we develop an original convex approximation strategy. The paper also includes simulations of diverse scenarios, featuring varying numbers of onboard tracking cameras and target motion profiles, to validate the effectiveness of the proposed approach.