Savkin Andrey V, Huang Hailong
School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney 2052, Australia.
Sensors (Basel). 2019 May 3;19(9):2068. doi: 10.3390/s19092068.
This paper studies the problem of placing a set of drones for surveillance of a ground region. The main goal is to determine the minimum number of drones necessary to be deployed at a given altitude to monitor the region. An easily implementable algorithm to estimate the minimum number of drones and determine their locations is developed. Moreover, it is proved that this algorithm is asymptotically optimal in the sense that the ratio of the number of drones required by this algorithm and the minimum number of drones converges to one as the area of the ground region tends to infinity. The proof is based on Kershner's theorem from combinatorial geometry. Illustrative examples and comparisons with other existing methods show the efficiency of the developed algorithm.
本文研究了布置一组无人机对地面区域进行监视的问题。主要目标是确定在给定高度部署以监测该区域所需的无人机的最小数量。开发了一种易于实现的算法来估计无人机的最小数量并确定它们的位置。此外，还证明了该算法在渐近意义上是最优的，即随着地面区域面积趋于无穷大，该算法所需的无人机数量与无人机最小数量的比值收敛于1。该证明基于组合几何中的克什纳定理。示例说明以及与其他现有方法的比较展示了所开发算法的有效性。
