Robust Fleet Sizing for Multi-UAV Inspection Missions under Synchronized Replacement Demand

2026-04-17

AI Summary

This study addresses the challenge in multi-UAV inspection missions where efficient path planning often leads to synchronized battery depletion, causing concentrated replacement demands and task interruptions. To mitigate this structural failure mode, the work proposes a robust fleet-sizing strategy grounded in a closed-form rule \( k = m(\lceil R \rceil + 1) \), which ensures mission-level reliability. By integrating queueing theory, worst-case analysis, and Monte Carlo simulations, the approach models synchronization peaks within the charge-and-operate cycles. Experimental results demonstrate that under diverse wind conditions and mission parameters, the proposed method achieves a task success rate of up to 99.8% (with a 95% confidence lower bound of 99.3%), substantially outperforming the conventional Erlang-B approach, whose success rate drops as low as 69.9%.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Humans and AI: Planning and Decision Support for Human-Machine Teams
• Intelligent Robots: Motion and Path Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Fleet Sizing
• Multi-UAV Inspection
• Synchronized Replacement
• Mission Reliability
• Spare Drone Allocation

Innovation

• synchronized replacement
• fleet sizing
• UAV inspection
• mission-level reliability
• closed-form rule