基于同伦方法的地月系L_2点小推力转移轨道优化  

Optimization of Low-Thrust Transfer to L_2 Libration Point Using Homotopy Method

作　　者：潘迅[1] 泮斌峰[1] PAN Xun;PAN Binfeng(School of Astronautics, Northwestern Polytechnical University, Xi'an, 710072, China)

机构地区：[1]西北工业大学航天学院,西安710072

出　　处：《载人航天》2019年第1期25-30,共6页Manned Spaceflight

基　　金：国家自然科学基金(11672234)

摘　　要：针对地月系下航天器从GEO轨道到L2点的时间最优小推力转移轨道问题,基于庞德里亚金极值原理,推导了限制性三体问题模型下的小推力转移轨道优化问题的最优性一阶必要条件,即推力保持最大值,且方向始终沿主矢量反方向,并将优化问题转换为两点边值问题。通过与同伦方法相结合,解决了间接法求解过程中收敛域小的困难。首先构造了针对推力幅值进行同伦的同伦函数,以大推力幅值的轨道转移问题作为同伦初始问题,然后选取连续同伦中的伪弧长法为同伦曲线跟踪方法,通过迭代求解了不同同伦参数值下的子问题,最终得到原问题下的小推力转移轨道。最后,在数值仿真中得到了不同推力值下的转移轨道,验证了该同伦方法在求解小推力转移轨道中的有效性。The minimum-time low-thrust transfer trajectory optimization problem from a GEO to L2 Libration point was studied.The optimal conditions of the minimum-time problem for the circular-re-stricted three-body problem were deduced based on the Pontryagin maximum principle,and the opti-mization problem was transformed into a two-point boundary-value problem.The homotopy method was applied to overcome the difficulties such as the narrow convergence domain in the indirect meth-od.The homotopy function for thrust magnitude was constructed and the high-thrust problem was considered as the homotopy initial problem.Then the continuous pseudo arclength continuation meth-od was selected as the homotopy path tracking method.By solving the sub-problems with different homotopy parameter iteratively,the low-thrust transfer trajectory of the original problem was finally obtained.In the end,the transfer trajectories with different thrust magnitude were obtained in the numerical simulation,and the effectiveness of the homotopy method was verified.

关 键 词：小推力 轨迹优化 同伦方法 限制性三体问题 平动点 深空探测中图分 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]