Learning heuristics with Vision Transformers for risk-aware drone last-mile delivery

Abstract

Last-mile delivery by Uncrewed Aerial Vehicles (UAVs) has gained increasing attention as a promising solution for urban parcel transport, offering a sustainable and cost-effective alternative to traditional ground-based logistics. Such operations, however, introduce significant risks, requiring effective mitigation strategies and efficient path-planning tools. Risk-aware path planning in complex urban environments remains computationally demanding, as it involves a highly combinatorial sequential decision-making problem while requiring efficient online replanning to ensure reactivity. Efficient planners often rely on graph-based search methods, in which the heuristic used to guide the search plays a crucial role. However, in risk-aware path planning, heuristic estimation is particularly challenging, as risk evaluation forms part of the cost estimation and differs significantly from classical line-of-sight or Euclidean approaches. To address this limitation, this study presents a novel Deep Learning framework for estimating accurate and admissible heuristic functions in risk-aware UAV path planning. To this end, a comprehensive database of cost-to-go maps was generated using realistic 3D urban scenarios and a graph-based optimisation framework. This dataset was used to train a Vision Transformer (ViT) network capable of providing accurate cost-to-go estimates for various objective-function configurations. The proposed architecture incorporates an admissibility correction mechanism that regulates the trade-off between heuristic accuracy and admissibility, promoting either solution optimality or search efficiency. The method was benchmarked against conventional heuristics in terms of computation time and cost-to-go. Results show speed-ups of up to 20 times compared to traditional approaches while maintaining near-optimal solutions, with marginal increases in average path cost of the order of 0.1%.