共线平动点附近小推力轨道转移中的微分修正技术  

Differential correction method in low-thrust orbit transfers near the collinear libration points

作　　者：周敬 胡军[1,2] 韩铭麟 ZHOU Jing;HU Jun;HAN MingLin(Beijing Institute of Control Engineering,Beijing 100190,China;Science and Technology on Space Intelligent Control Laboratory,Beijing 100094,China)

机构地区：[1]北京控制工程研究所,北京100190 [2]空间智能控制技术重点实验室,北京100094

出　　处：《中国科学：技术科学》2021年第2期207-220,共14页Scientia Sinica(Technologica)

基　　金：国家重点研发计划(编号:2018YFA0703800)资助项目。

摘　　要：针对三体问题中共线平动点附近的小推力轨道转移问题,提出了一种新的间接法求解方法.首先,根据最优控制理论推导了推力幅值和方向角的最优控制律,得出协态变量初值是转移轨道唯一决定因素,据此将轨道转移问题转化为两点边值问题;然后,将状态变量和协态变量整合形成增广系统,利用微分修正原理设计了一种新的两点边值问题求解器.同时,引入调节因子和推力幅值延拓技术,以提高求解器的鲁棒性、收敛性和解决转移时间较长时轨道难以收敛的问题;最后以地月系统L1点附近Halo轨道间的转移问题为例进行了仿真分析.仿真结果表明,基于微分修正技术的小推力轨道转移设计方法,避免了常规的协态变量初值猜测过程,可以实现[-1, 1]范围内任意初值猜测情况下的迭代收敛,说明了方法的有效性,同时对于其他以两点边值问题为基础的工程实际问题也具有一定的普适性.Differential correction method in low-thrust orbit transfers near the collinear libration points. A novel indirect method is proposed to solve the problem of low-thrust transfers near the collinear libration points in a three-body problem. First, the optimal control laws of thrust amplitude and angles were deduced according to the optimal control theory. It was found that the initial value of the co-state variables is the only determining factor and accordingly the problem of orbit transfer was transformed into a two-point boundary value problem(TPBVP). The state variables and co-state variables were then combined into an augmented system, and a new TPBVP solver was designed using the differential correction method. A regulatory factor and the thrust continuation approach were introduced and adopted for improving the robustness and convergence and overcoming the divergency problem when the time of flight is relatively long. Finally, numerical simulations of transfers between Halo orbits around the L1 libration point of the EarthMoon three-body system were conducted. Simulation results show that this method avoids the routine process of guessing the initial values of co-state variables;therefore, transfers quickly converge when the initial values of co-state variables are taken randomly from[-1, 1], proving the validity and generality of the proposed method for other engineering problems based on TPBVP.

关 键 词：三体问题 共线平动点轨道 小推力转移 间接法 两点边值问题 微分修正技术 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]