提出无人机群在同步换电需求下的可靠编队规模方法
Robust Fleet Sizing for Multi-UAV Inspection Missions under Synchronized Replacement Demand
- 基于同步耗电结构设计，给出闭式舰队规模公式
- 实测任务成功率99.8%，远超传统方法的69.9%
- 适合高可靠性巡检场景，尤其风电/电网应用
多无人机巡检任务需备用机在充电周期中替换已用无人机。现有方法常假设稳态条件，或视替换请求为独立事件，导致单次请求阻塞率虽低，但集群需求下任务整体失败。本文揭示一种结构性失效模式：高效路径分配使各无人机负载相似，导致电池同步耗尽，引发替换高峰，耗尽备用机池即使平均容量充足。本文推导出闭式足够舰队规模规则：k = m(ceil(R) + 1)，其中m为活跃无人机数，R为恢复时间与活跃时间比。该规则通过额外m台备用机吸收最坏情况下的同步替换需求，确保任务级可靠性。五组蒙特卡洛测试（m ∈ [2,10]，R ∈ [0.87,3.39]，每组1000次）显示，采用Erlang-B模型且目标阻塞率ε=0.01时，在R=3.39下任务成功率降至69.9%，95%的备用耗尽事件集中于前10%的5分钟需求窗口。相比之下，本文方法在所有条件下均保持99.8%成功率（威尔逊95%置信下界99.3%），即使风速变异系数达CV=0.30，最恶劣情况下仅需增加4台无人机。
原文摘要 · Abstract (English)
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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