Fast Reachable-Set Estimation for Stratospheric Airships Considering Day–Night Energy Constraints

Stratospheric airships utilize solar energy for station keeping in the near-space environment over extended periods; however, their operational safety is significantly challenged by the strong coupling between time-varying wind fields and the diurnal energy cycle. This paper proposes a framework for fast approximate reachable-set estimation of stratospheric airships by propagating fixed-heading trajectory families under prescribed wind fields and speed strategies. A coupled kinematic and energy model retains the position and battery state of charge (SOC) of each trajectory. Fourth-order Runge–Kutta (RK4) integration propagates the trajectory ensembles. An Alpha-shape algorithm is further employed to reconstruct sampled reachable envelopes as geometric approximations to the reachable sets. Energy-coupled 36 h simulations on four winter and summer dates show that the heuristic energy-aware strategy yields the largest terminal-envelope area among the three tested strategies. In a separate six-hour kinematic benchmark with energy constraints inactive in both methods, the baseline ray calculation takes 0.807 s and has a bidirectional Hausdorff distance of 5.086 km from a level-set reference with 2.5 km grid spacing.