UAV–Rider Collaborative Dispatching Under Stochastic Wind Conditions Considering Nonlinear Energy Dynamics

To mitigate UAV (unmanned aerial vehicle) range limitation risks and scheduling disruptions caused by complex wind fields in urban instant delivery, this paper proposes a UAV–rider collaborative dispatching framework. By incorporating aerodynamic-based nonlinear energy dynamics, the model accurately characterizes power variations under stochastic wind conditions, significantly enhancing the operational reliability of urban delivery missions. First, an aerodynamic-based nonlinear energy function is constructed, coupling payload, airspeed, and random wind vectors to accurately characterize power variations. Second, a scenario-based two-stage stochastic programming framework is adopted, where the rider’s deterministic path is optimized in the first-stage decision to ensure stability, and the UAV’s scenario-dependent flight plan is resolved in the second stage to adapt to wind uncertainty. An improved branch-and-price (IBP) algorithm is designed to solve this large-scale model, where nonlinear energy is evaluated during label extension in the pricing sub-problem, effectively avoiding linearization errors. The numerical results demonstrate that the proposed framework improves the mission success probability (the likelihood of completing delivery routes without battery exhaustion across all considered wind scenarios) by 25% under strong-wind conditions by effectively avoiding power failure risks. Furthermore, the IBP algorithm outperforms traditional exact solvers by over 40% in solution efficiency for large-scale cases. These findings demonstrate that energy-aware stochastic dispatching significantly improves the reliability and robustness of UAV-assisted last-mile delivery in windy urban environments, thereby providing an effective operational solution for real-world drone delivery logistics.