Risk-Field Visualization and Path Planning for UAV Air Refueling Considering Wake Vortex Effects

Autonomous aerial refueling is a key technology for enhancing the endurance of unmanned aerial vehicles; however, the wingtip vortices generated by the tanker create a strong three-dimensional wake-vortex flow field, whose downwash and lateral airflow can impose significant rolling moments on the follower Unmanned Aerial Vehicle (UAV), posing a serious threat to flight safety. To address this issue, this study proposes an integrated framework that combines wake-vortex risk-field modeling with optimal path planning. The classical Hallock–Burnham (HB) model is first employed to predict vortex descent and lateral transport, while a two-phase model is used to characterize the temporal decay of vortex circulation. The predicted vortex parameters are then coupled with the UAV’s aerodynamic characteristics, and the rolling-moment coefficient (RMC) is introduced as a risk metric to compute its spatiotemporal distribution in three dimensions, thereby transforming the invisible wake-vortex disturbance into a visualizable and quantifiable dynamic three-dimensional risk map. On this basis, a wake-vortex-aware path-planning algorithm based on particle swarm optimization (PSO) is developed, incorporating adaptive weighting and elitist mutation strategies. A multi-objective cost function considering path length, safety, and smoothness is further constructed to search for an optimal safe path under wake-vortex influence. Simulation results indicate that, compared with the classical A* and Rapidly-Exploring Random Tree (RRT) algorithms, the proposed method reduces cumulative risk exposure by approximately 90% and 75%, respectively, while limiting the increase in path length to about 8% (significantly lower than the increases of 40% for A* and 44% for RRT). In addition, the maximum turning angle is constrained within 10°, and the computation time remains around 0.052 s, satisfying real-time requirements. These results demonstrate that the proposed method can generate safe, efficient, and dynamically feasible paths for UAV aerial refueling and provide a valuable reference for wake-vortex avoidance in similar aerospace missions.