A Bidirectional Initialization Framework for Multi-Phase Indirect Shooting in Time-Optimal Low-Thrust GTO-to-DRO Transfers

The distant retrograde orbit (DRO) serves as a strategic staging point for future cislunar missions, and geostationary transfer orbit (GTO) provides a practical departure option for rideshare low-thrust cargo missions. However, time-optimal low-thrust GTO-to-DRO transfers remain computationally demanding. Indirect methods are highly sensitive to boundary conditions and prone to divergence, whereas direct methods face dimensionality issues as the number of variables scales with trajectory duration and revolutions. To address this issue, this paper proposes a bidirectional initialization framework for multi-phase indirect shooting. A forward auxiliary solution is constructed for the GTO-raising phase in planar modified equinoctial elements, while a backward auxiliary solution is generated for the DRO-insertion phase in the planar Earth–Moon circular restricted three-body problem. The two subproblems are connected through an intermediate interface and coordinated by an outer-level stationarity iteration, after which lunar phase continuity and lunar perturbations are reintroduced into a fully coupled indirect shooting problem. The numerical results show that the proposed strategy provides a reliable initial guess for the complete optimization and enables robust convergence to a continuous time-optimal GTO-to-DRO transfer. The method improves the tractability of long-duration multi-phase indirect trajectory optimization for low-thrust cislunar mission design.