Open Access
 Issue JNWPU Volume 41, Number 3, June 2023 529 - 536 https://doi.org/10.1051/jnwpu/20234130529 01 August 2023

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 运动数学模型

1) 相对运动的纵向分量(Δr, ΔL, ΔVr, ΔVu)与侧向分量(Δz, ΔVz)无关;

2) 主动航天器在纵向平面中相对于被动航天器沿着椭圆运动, 其半轴关系为2∶1;

3) 如果椭圆中心位于被动航天器的下方, 椭圆中心将沿着主动航天器的运动方向移动; 如果椭圆中心位于被动航天器的上方, 椭圆中心与主动航天器的运动方向相反;

4) 侧向平面的运动表示为谐波振动。

 图1运动的长期和周期性分量

## 2 具有双主动区域的控制程序设计

1) 限制在0~0.2π范围内的持续时间为t0的等待区域;

2) 持续时间为t1的第一个主动区域;

3) 持续时间为tp的被动区域;

4) 持续时间为t2的第二个主动区域;

 图2控制结构

### 2.2 2个同号推力开关的程序优化

 图3无量纲变量Δrav, ΔLav的相轨迹示例
 图4相对运动椭圆的无量纲短半轴无量纲时间的相关性示例

## 3 控制参数计算和帕累托集构建

 图5问题(33)的解决方案，两次和三次推力开关的控制程序比较

## References

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## All Figures

 图1运动的长期和周期性分量 In the text
 图2控制结构 In the text
 图3无量纲变量Δrav, ΔLav的相轨迹示例 In the text
 图4相对运动椭圆的无量纲短半轴无量纲时间的相关性示例 In the text
 图5问题(33)的解决方案，两次和三次推力开关的控制程序比较 In the text

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