We present a study of the low-thrust transfer problem near the secondary body in the Earth–Moon circular restricted three-body problem (CRTBP). Based on the Pontryagin maximum principle, the time-optimal, energy-optimal and fuel-optimal transfers between the planar Lyapunov orbits around the L2 point of the Earth–Moon system are constructed as a two-point boundary value problem (TPBVP). A criterion for identifying the best trajectory is also described. The Lyapunov orbit structure is used to deal with the potential difficulties of initial guess. As a result, the final transfer trajectory follows a multi-revolution structure, which takes a long time of flight. The homoclinic connection configuration is investigated by introducing the relevant invariant manifolds, allowing for faster transfer and less fuel consumption in the same case. It is designed a linear time-varying model predictive control (MPC) algorithm to perform trajectory tracking in the presence of initial orbit error and deviations in engine operation. Numerical simulations show the efficiency and practicability of the optimal transfer trajectory design strategy and trajectory tracking controller proposed in this paper for future lunar exploration missions.

我们对地月圆形受限三体问题（CRTBP）中次级体附近的低推力传递问题进行了研究。基于庞特里亚金极大值原理，将围绕地月系统L2点的平面Lyapunov轨道之间的时间最优、能量最优和燃料最优转移构造为两点边值问题（TPBVP）。还描述了用于识别最佳轨迹的标准。Lyapunov 轨道结构用于处理初始猜测的潜在困难。结果，最终的转移轨迹遵循多圈结构，需要很长时间的飞行。通过引入相关的不变歧管来研究同宿连接配置，从而在相同情况下实现更快的传输和更少的燃料消耗。它设计了一种线性时变模型预测控制（MPC）算法，用于在存在初始轨道误差和发动机运行偏差的情况下进行轨迹跟踪。数值模拟表明本文提出的最优转移轨迹设计策略和轨迹跟踪控制器对未来探月任务的有效性和实用性。