行星际Halo轨道转移的多目标优化设计

研究了星历约束下不同太阳—行星系统Halo轨道间转移的多目标优化设计问题。分析了直接和间接两种转移方式的特点，并引入伪流形技术加快了Halo轨道的逃逸和捕获速度。构建了两种转移机制的多目标优化模型。对于直接转移方式，采用伪流形双向拼接策略实现了转移轨道的构建；对于间接转移方式，通过近拱点庞加莱映射与双曲超速匹配完成了转移轨道的拼接。进一步，采用多项式样条函数对伪流形进行逼近，提高了伪流形的计算效率。两种转移机制的轨道优化设计都可以归结为简单的多变量无约束优化问题，采用非支配快速排序遗传算法NSGA-II求解。对地球—火星Halo轨道间的转移进行了多目标优化设计，校验了本文方法的有效性。

Multi Objective Optimization of Interplanetary Halo to Halo Orbit Transfers

In this paper, the multi-objective optimization of Halo-to-Halo transfer trajectory between different Sun-planet systems is discussed by considering the ephemeris constraints. The direct and indirect transfers that employ the different sets of the invariant manifolds are analyzed, respectively. The pseudo-manifolds, along which the spacecraft can depart and approach Halo orbit quickly, is introduced to replace the traditional invariant manifolds. Then, the multi-objective optimization models are built for two transfer schemes. In the direct transfer scheme, the outer branches of the pseudo-manifolds are connected under the heliocentric two-body model. In the indirect transfer, the inner branches of the pseudo-manifolds and the interplanetary transfer trajectory are connected by combining the periapsis Poincare map with a matching algorithm. Further, a polynomial spline method is utilized to estimate the pseudo-manifolds. The computational efficiency is improved for avoiding the numerical integration. For each transfer scheme, the trajectory design can be considered as a multi-variable unconstrained optimization problem. The NSGA-II (Non-domination Sort Genetic Algorithm) is adopted to solve the problems taking total velocity increment and flying time as optimization objects. The efficiency of the proposed approach is verified by the simulation example of Earth-Mars Halo-to-Halo transfer trajectory.