多无人机巡检任务下同步替换需求的鲁棒编队
Robust Fleet Sizing for Multi-UAV Inspection Missions under Synchronized Replacement Demand
AI总结：
本文针对多无人机巡检任务中同步替换需求的鲁棒编队问题，提出一种闭式充分编队规则，通过增加缓冲无人机数量提升任务可靠性。
摘要：
多无人机巡检任务需要备用无人机在充电周期内替换活跃无人机。现有编队方法通常假设稳态运行条件，不适用于有限时间跨度任务，或认为替换请求为独立事件。后者提供每请求阻塞保证，但无法转化为任务级可靠性当需求集中时。本文识别出一种结构性失效模式，高效路线分配相似工作量给每个无人机，导致同步电池耗尽和替换峰值，即使平均容量充足也会耗尽备用池。我们推导出闭式充分编队规则k = m(ceil(R) + 1)，其中m是活跃无人机数量，R是恢复到活跃时间比。该加性缓冲吸收最坏情况同步需求在恢复周期边界，并确保任务级可靠性即使所有无人机同时耗尽。蒙特卡洛验证在五个场景（m在[2, 10]，R在[0.87, 3.39]，每个1000次试验）显示，Erlang-B编队与每请求阻塞目标ε=0.01在R=3.39时任务成功率降至69.9%，95%的备用池耗尽事件集中在前十百分位5分钟需求窗口。相比之下，所提规则在所有测试条件下保持99.8%成功率（Wilson 95%下限界99.3%），包括风变异性高达CV=0.30，同时仅需最严峻场景中额外四架无人机。
英文摘要：
Multi-UAV inspection missions require spare drones to replace active drones during recharging cycles. Existing fleet-sizing approaches often assume steady-state operating conditions that do not apply to finite-horizon missions, or they treat replacement requests as statistically independent events. The latter provides per-request blocking guarantees that fail to translate to mission-level reliability when demands cluster. This paper identifies a structural failure mode where efficient routing assigns similar workloads to each UAV, leading to synchronized battery depletion and replacement bursts that exhaust the spare pool even when average capacity is sufficient. We derive a closed-form sufficient fleet-sizing rule, k = m(ceil(R) + 1), where m is the number of active UAVs and R is the recovery-to-active time ratio. This additive buffer of m spares absorbs worst-case synchronized demand at recovery-cycle boundaries and ensures mission-level reliability even when all UAVs deplete simultaneously. Monte Carlo validation across five scenarios (m in [2, 10], R in [0.87, 3.39], 1000 trials each) shows that Erlang-B sizing with a per-request blocking target epsilon = 0.01 drops to 69.9% mission success at R = 3.39, with 95% of spare exhaustion events concentrated in the top-decile 5-minute demand windows. In contrast, the proposed rule maintains 99.8% success (Wilson 95% lower bound 99.3%) across all tested conditions, including wind variability up to CV = 0.30, while requiring only four additional drones in the most demanding scenario.
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