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基于同伦方法三体问题小推力推进转移轨道设计
潘迅, 泮斌峰
西北工业大学 航天学院, 西安 710012
摘要:
提出一种基于同伦方法限制性三体问题小推力推进转移轨道设计方法。首先根据最优控制原理分析了航天器在轨道转移中不同性能指标时的最优控制律,然后引入同伦参数构造新的性能指标,在基于遗传算法和打靶法得到能量最优的解基础上,采用伪弧长法跟踪同伦轨迹,进而得到燃料最优的转移轨道。最后对地月系下从GEO轨道到L1点Lyapunov轨道的转移轨道进行优化。仿真结果表明:利用遗传算法能优化得到较为合适的流形拼接点和协态变量初始值,利用打靶法能有效地优化得到小推力燃料最优转移轨道。
关键词:  同伦算法;伪弧长法;小推力;轨道优化;限制性三体问题
DOI:10.15982/j.issn.2095-7717.2017.03.011
分类号:V41
基金项目:
Optimization of Low-Thrust Transfers Using Homotopic Method in the Restricted Three-Body Problem
PAN Xun, PAN Binfeng
School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China
Abstract:
A method for optimization of low-thrust transfers in the restricted three-body problem is proposed. First,the optimal control laws of different performance index in trajectory optimization are deduced based on the optimal control theory. Then,a new parameter is used to construct a modified performance index. The genetic algorithm and single shooting method are used to obtain the solution of energy optimal transfer,and arc-length method is adopted to track the homotopic pathtill the fuel optimal transfer is obtained. Finally,the numerical example about transfers from GEO to Lyapunov orbit of L1 point in the Earth-Moon system is studied. Simulation results show that the initial guess can be obtained by genetic algorithm,and single shooting method can be used to obtain the fuel-optimal transfer trajectory.
Key words:  homotopy;arc-length method;low-thrust;trajectory optimization;restricted three-body problem