Maneuvering to a free return trajectory is a vital abort means for crewed lunar missions. A novel method of solving the fuel optimization of free return abort trajectory for Earth-Moon transfer by two-stage transformation on optimization model and Bayesian optimization is documented. Two new design variables—perilune altitude and transfer time from earth to perilune, instead of the original injection velocity vector, are introduced to transform the general model into a two-dimensional model. Each feasible abort trajectory is determined by a numerical method including initial estimate and exact solution. Then the characteristics of the relationship between the new variables and the fuel objective of impulse maneuver are applied to further transform the model into a one-dimensional model. Based on the Bayesian optimization method, fuel optimization is successfully and efficiently implemented for the free return abort trajectory at multiple abort moments during the Earth-Moon transfer. Furthermore, the influence of the initial Earth-Moon phase on the result of fuel optimization is presented. Numerical simulations are conducted to demonstrate the efficacy of the proposed method.

机动到自由返回轨道是载人登月任务的重要中止手段。记录了通过优化模型的两阶段变换和贝叶斯优化求解地月转移自由返回中止轨迹的燃料优化的新方法。引入两个新的设计变量——近月高度和从地球到近月的转移时间，而不是原始的注入速度矢量，将一般模型转换为二维模型。每个可行的中止轨迹由包括初始估计和精确解的数值方法确定。然后利用新变量与脉冲机动燃料目标之间关系的特点，进一步将模型转化为一维模型。基于贝叶斯优化方法，在地月转移期间的多个中止时刻，针对自由返回中止轨迹成功且有效地实施了燃料优化。此外，还介绍了地月初始阶段对燃料优化结果的影响。进行数值模拟以证明所提出方法的有效性。