๐ค AI Summary
This study addresses the problem of multi-UAV target tracking with known trajectories by dynamically adjusting the sensing radii of fixed monitoring stations to minimize the systemโs peak power consumption, formulated as a min-max optimization. The work presents the first real-time optimal algorithm tailored for scenarios with known target trajectories and establishes that the problem admits no polynomial-time optimal solution in the general case. By integrating computational geometry with resource allocation strategies, the authors devise an efficient geometry-based solution method. Experimental results demonstrate that the proposed algorithm computes solutions within seconds for large-scale instances involving 500 targets and 25 monitoring stations, thereby meeting the requirement for minute-level real-time control.
๐ Abstract
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations, each with a sensing region of adjustable range; how should we adjust the individual sensor ranges in order to optimize energy consumption? We provide both negative theoretical and positive practical results for this important and natural challenge. On the theoretical side, we show that even if all objects move at constant speed along straight lines, no polynomial-time algorithm can guarantee optimal coverage for a given starting solution. On the practical side, we present an algorithm based on geometric insights that is able to find optimal solutions for the $\min \max$ variant of the problem, which aims at minimizing peak power consumption. Runtimes for instances with 500 moving objects and 25 stations are in the order of seconds for scenarios that take minutes to play out in the real world, demonstrating real-time capability of our methods.