在线无人机对线状目标的覆盖
Online Drone Coverage of Targets on a Line
AI总结：
研究无人机在线覆盖线状目标的问题，提出三种算法，针对不同视角角度α优化轨迹长度，证明竞争比上界，并给出α=π/4时的下界。
摘要：
我们研究了一种由无人机或传感器（配备固定半角视野α的摄像头或天线）在线覆盖目标的问题。待监控的目标在一条线状屏障上任意位置出现。当新目标出现时，无人机必须移动到覆盖新出现目标及已存在目标的位置。目标是设计一个覆盖算法，优化无人机轨迹的总长度。我们的结果以算法的竞争比报告，即在所有输入情况下，算法成本与最优离线算法成本的最坏情况比率。在上界方面，我们提出了三种在线算法，并为每个α∈[0, π/2]证明了它们的竞争比的上界。其中最佳的算法\FA在π/6 < α < π/3时显著优于其他两个。特别是对于α=π/4，其最坏情况竞争比为1.25，而其他两个为√2。最后，我们证明了对于半角为α∈[0, π/4]的无人机，在线算法的竞争比下界是一个关于α的函数，在α=π/4时达到最大值(1+√2)/2≈1.207。
英文摘要：
We study a problem of online targets coverage by a drone or a sensor that is equipped with a camera or an antenna of fixed half-angle of view $α$. The targets to be monitored appear at arbitrary positions on a line barrier in an online manner. When a new target appears, the drone has to move to a location that covers the newly arrived target, as well as already existing targets. The objective is to design a coverage algorithm that optimizes the total length of the drone's trajectory. Our results are reported in terms of an algorithm's competitive ratio, i.e., the worst-case ratio (over all inputs) of its cost to that of an optimal offline algorithm. In terms of upper bounds, we present three online algorithms and prove bounds on their competitive ratios for every $α\in [0, π/2]$. The best of them, called \FA is significantly better than the other two for $π/6 < α< π/3$. In particular, for $α=π/4$, its worst case, \FA has competitive ratio $1.25$, while the other two have competitive ratio $\sqrt{2}$. Finally, we prove a lower bound on the competitive ratio of online algorithms for a drone with half-angle $α\in [0, π/4]$; this bound is a function of $α$ that achieves its maximum value at $α= π/4$ equal to $(1+\sqrt{2})/2 \approx 1.207$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
