Robust Route–Speed Optimization for UAV Inspection Missions Under Wind Uncertainty

Unmanned aerial vehicles (UAVs) are widely used for inspection and monitoring tasks, where mission efficiency is strongly influenced by environmental conditions such as wind. In this work, we study a joint route–speed optimization problem for UAV inspection missions under uncertain wind conditions. The objective is to determine both the visiting sequence of inspection targets and the flight speeds along route segments in order to minimize worst-case energy consumption while satisfying mission duration constraints. We formulate the problem using a robust optimization framework that accounts for uncertainty in both wind speed and wind direction. The resulting model involves coupled discrete routing decisions and continuous speed control variables, which makes the problem computationally challenging. To address this difficulty, we propose a robust route–speed decomposition (RRSD) framework that alternates between route improvement and nonlinear speed optimization. Computational experiments on randomly generated instances, evaluated over eight random seeds per setting and compared against five baselines, including a simulated-annealing metaheuristic, demonstrate that RRSD consistently reduces worst-case energy consumption. A sensitivity analysis over the wind-uncertainty half-widths further shows that this advantage widens as the uncertainty set grows, and comparisons with exact enumeration on small instances confirm near-optimal solution quality at reasonable computational cost. These results highlight the importance of jointly optimizing routing decisions and speed control for energy-efficient UAV mission planning under uncertain environmental conditions.