关键词: 航班化模式, Halo轨道, 轨迹优化, 不变流形, 列生成, 动态规划

Abstract: To meet the large-scale material transfer requirements in the context of normalized operations of Earth-Moon space service stations, a trajectory optimization algorithm for airline flight mode round-trip scheduling considering phasing constraints was proposed. First, a solution space search strategy based on the manifold method and homotopy continuation was designed to achieve bounded traversal of the time-of-flight (TOF), and the LEO-Halo round-trip transfer trajectory solution space was constructed. Subsequently, the scheduling task was modeled as a combinatorial optimization problem on a space-time directed acyclic graph (DAG). A bilevel optimization algorithm based on column generation and dynamic programming was utilized to address the curse of dimensionality in multi-spacecraft, multi-voyage mission scheduling.Numerical examples demonstrate that distinct phasing windows exist for LEO-to-Halo transfer trajectories. Although the Halo target phasing constraints lead to increased velocity increment consumption, the associated Pareto front remains extremely flat along the TOF dimension, which provides sufficient scheduling margins for phasing alignment. Regarding the optimization performance, the algorithm adjusts scheduling strategies adaptively when facing conflicts between velocity increment costs and spatiotemporal windows. The total velocity increment consumption is approximately 10.7% lower than that of the Depth-First Search (DFS) algorithm. These findings reveal the characteristics of the LEO-Halo transfer trajectory solution space and establish an optimization paradigm for airline flight mode scheduling, which provides theoretical support for the future normalized operation of Earth-Moon space infrastructure.

Key words: airline flight mode, Halo orbit, trajectory optimization, invariant manifolds, column generation, dynamic programming