Changzheng Qian

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.

The minimum fuel transfer problem in low-thrust trajectory optimization remains a major challenge and is typically addressed using bang-bang control. A novel methodology integrating Adaptive Multiresolution Collocation (AMRC) and Sequential Convex Programming (SCP) to solve the minimum-fuel low-thrust trajectory optimization problem is proposed. First, the approach employs the cubic spline wavelet-like transform for mesh refinement, where wavelet coefficients serve as error indicators to dynamically concentrate nodes in regions of rapid state variation. Then, the nonlinear programming problem is convexified via control variable relaxation and small-perturbation linearization, reformulated as a second-order cone programming (SOCP) problem, and efficiently solved using convex optimization tools. Subsequently, progressive selection of the location points ensures rapid and accurate convergence to the optimal trajectory. Finally, numerical simulations of Earth–Mars and Earth–Venus transfer validate the effectiveness and accuracy of the AMRC-based method. Compared with conventional approaches, the proposed method achieves comparable optimality while markedly improving computational efficiency, precisely localizing switching times, and improving numerical precision, requiring only 29.7% of the nodes and 14.7% of the computation time of uniform-grid convex optimization, achieving fuel-optimal deviations within 0.07% of the indirect method and demonstrating accuracy improvements of 2–3 orders of magnitude over GPOPS.