As a novel comprehensive economic paradigm, “low-altitude economy” has permeated various fields such as inspection, logistics, rescue, and communications. This paper focuses on a novel collaborative delivery mode involving drones and trucks, where drones are allowed to dynamically take off and land at arbitrary points along the truck’s route to reduce waiting time. Multiple drones are introduced into the delivery system to enhance overall efficiency. Specifically, the study addresses the truck--multi-drone collaborative delivery routing problem with dynamic synchronization, aiming to minimize the weighted total cost. A path optimization model is developed for this purpose. An adaptive large neighborhood search algorithm is designed to solve the model, with detailed descriptions of the initial solution construction method and the functions of various operators. The Metropolis criterion from simulated annealing algorithm is used to prevent the algorithm from converging to local optima. Experiments using instances of different scales verify the feasibility of the algorithm. Comparisons are made between scenarios where drones take off and land only at truck delivery points and those where drones dynamically operate along the truck’s route. Analyses are conducted on the weighting relationships among different cost components in the model and the impact of varying the number of drones in the system. The results show that the dynamic takeoff and landing strategy for drones along the truck path reduces the weighted total cost by 0.80% to 2.96%, and the dynamic synchronization mechanism is highly sensitive to changes in waiting costs. As the weight of waiting costs increases, the optimized weighted total cost gradually decreases, and increasing the waiting cost can improve the degree of optimization achieved through dynamic synchronization to some extent. The highest level of dynamic synchronization optimization is observed when two drones are deployed in the system. The proposed truck-drone dynamic synchronization scheme can optimize delivery routes for both trucks and drones, offering a new perspective for reducing last-mile logistics costs in urban areas.

Autonomous driving based on single-vehicle perception still cannot avoid the negative impacts caused by traffic oscillations when traveling in mixed-vehicle platoons. In this scenario, real-time and accurate prediction of the future trajectories of the vehicle platoon ahead of the autonomous vehicle is key to addressing this issue. However, in mixed platoons dominated by heterogeneous and uncertain human-driven vehicles (HDVs), this remains a significant challenge. Existing model-driven, data-driven, and hybrid approaches often suffer from poor interpretability, weak physical constraints, and insufficient accuracy in dynamic environments. To overcome these limitations, this study proposes a Causal Physical Information Deep Learning Model (CPIDLM) for high-fidelity platoon trajectory prediction. First, CPIDLM constructs a novel causal graph attention mechanism that explicitly captures behavioral heterogeneity and causal interactions among vehicles. Second, a physics-informed enhancement architecture is developed to embed prior knowledge from physical models into the deep learning network. Additionally, a dynamic adaptive weighting module is designed to achieve a dynamic balance between contributions from physical laws and data-driven patterns. Extensive validation based on real-world trajectory datasets shows that, compared to existing models, CPIDLM reduces gap prediction error by 16.7%, significantly outperforming current state-of-the-art methods in accuracy. This study establishes a powerful new paradigm for vehicle platoon trajectory prediction under traffic oscillation scenarios.