地月远距离逆行轨道电推进调相控制优化方法

doi:10.12305/j.issn.1001-506X.2026.10.31

摘要/Abstract

摘要：

远距离逆行轨道（distant retrograde orbit, DRO）是地月空间的理想稳定停泊轨道，具有高比冲的小推力电推进调相是其轨道设计、部署及应急处置的技术难点，需同时考虑多天体引力与电推进的复杂耦合作用。为此，研究提出两种混合优化方法：通过序列凸优化（sequential convex programming, SCP）快速获取近似最优解，采用序列二次规划（sequential quadratic programming, SQP）迭代提高求解精度的混合方法；针对适配长时域调相场景的求解需求的SCP与滚动时域优化（receding horizon optimization, RHO）混合方法。仿真结果表明，两种混合方法的综合性能均显著优于单一SCP方案，二者分别适配不同工程需求，为DRO航天器在轨电推进调相提供了灵活可行的优化方案。

关键词: 圆型限制性三体问题, 远距离逆行轨道, 轨道调相, 小推力控制

Abstract:

The distant retrograde orbit （DRO） is an ideal stable parking orbit in the cislunar space. Low-thrust electric propulsion with high specific impulse, which is used for orbit phasing, poses a technical challenge in orbit design, deployment, and emergency disposal of DROs. It requires simultaneous consideration of the complex coupling effects between multi-body gravity and electric propulsion. To address this issue, this study proposes two hybrid optimization methods: one hybrid method that uses sequential convex programming （SCP） to quickly obtain an approximate optimal solution and sequential quadratic programming （SQP） for iterative precision improvement; and the other hybrid method combining SCP and receding horizon optimization （RHO） to meet the solution requirements of long-time-domain phasing scenarios. Simulation results show that the comprehensive performance of both hybrid methods is significantly superior to the single SCP scheme. Each method adapts to different engineering needs, providing flexible and feasible optimization solutions for the on-orbit electric propulsion phasing of DRO spacecraft.

Key words: circular restricted three-body problem, distant retrograde orbit, orbit phase adjustment, low-thrust control

中图分类号:

V 412.4
V1

任超, 张仁勇, 周庄采青, 彭超. 地月远距离逆行轨道电推进调相控制优化方法[J]. 系统工程与电子技术, 2026, 48(10): 3611-3621.

Chao Ren, Renyong Zhang, Zhuangcaiqing Zhou, Chao Peng. Optimization method for low-thrust phase adjustment control of distant retrograde orbit[J]. Systems Engineering and Electronics, 2026, 48(10): 3611-3621.

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参数	数值
初始质量$ {{m}}_{\text{wet}}/\text{kg} $	$ 700 $
结构质量$ {{m}}_{\text{dry}}/\text{kg} $	$ 100 $
最大推力$ {{T}}_{\text{max}}/\text{N} $	$ 0.55 $
最小推力$ {{T}}_{\text{min}}/\text{N} $	$ 0 $
比冲$ {{I}}_{\text{sp}}/\text{s} $	$ 3300 $

参数	数值
初始位置$ {{r}}_{\text{0}} $	[0.796408475436064, 0, 0] LU
初始速度$ {{v}}_{\text{0}}/{{\mathrm{V}}}{{\mathrm{U}}} $	[0,0.527065706230548, 0] VU
末端位置$ {{r}}_{\text{0}} $	[0.796408475436064, 0, 0] LU
末端速度$ {{v}}_{\text{0}} $	[0,0.527065706230548, 0] VU
飞行时间$ {{t}}_{\text{f}} $	11.9159310375834 TU

符号	数值	单位	物理意义
$ \boldsymbol{\mu } $	$ 1.215\times {10}^{-2} $	$ -- $	月球-地球质量比
$ \text{L}\text{U} $	$ 3.8474\times {10}^{5} $	$ \mathrm{km} $	地月距离
$ \text{V}\text{U} $	1.024083366852	$ \mathrm{km}/\mathrm{s} $	速度单位
$ \text{T}\text{U} $	4.368378	$ \text{day} $	时间单位
$ \text{M}\text{U} $	$ {m}_{\text{dry}} $	$ \text{kg} $	航天器干重
$ \text{F}\text{U} $	$ {T}_{\max } $	$ \mathrm{N} $	航天器推力最大值

算法名称	模块	参数	数值
SCP算法	−	离散点$ N $	$ 100 $
		松弛变量收敛域$ \epsilon $	$ {1\times 10}^{-4} $
		信赖域半径$ \delta $	$ {1\times 10}^{-4} $
		最大迭代数	$ 20 $
SCP-SQP算法	SCP模块	离散点$ N $	$ 100 $
		松弛变量收敛域$ \epsilon $	$ {1\times 10}^{-4} $
		信赖域半径$ \delta $	$ {1\times 10}^{-4} $
		最大迭代数	$ 3 $
	SQP模块	最大迭代数	$ 10 $
SCP-RHO算法	SCP模块	离散点$ N $	$ 100 $
		松弛变量收敛域$ \epsilon $	$ {1\times 10}^{-4} $
		信赖域半径$ \delta $	$ {1\times 10}^{-4} $
		最大迭代数	$ 3 $
	RHO模块	控制采纳率$ \eta $	$ 0.7 $
	RHO模块	滚动窗口数	$ 3 $

状态变量	SCP	SCP-SQP	SCP-RHO
位置偏差$ {r}/\text{km}$	$ 1\;147.967\;6 $	$ 0.535\;67 $	$ 5.898 $
速度偏差$ {v}/(\text{km}/\text{s}) $	$ 0.002\;468\;3 $	$ 1.117\;7\times {10}^{-6} $	$ 3.663\;7\times {10}^{-5} $
剩余质量$ {m}/\text{kg} $	$ 692.569\;7 $	$ 692.539 $	$ 692.439\;3 $
计算时间$ {t}/\text{s}$	$ 27.88 $	$ 72.850\;9 $	$ 50.89 $