月面应急直接上升交会轨迹快速规划方法

班焕恒; 周聪; 闫晓东

doi:10.13700/j.bh.1001-5965.2023.0160

月面应急直接上升交会轨迹快速规划方法

doi: 10.13700/j.bh.1001-5965.2023.0160

班焕恒^{1, 2},
周聪^{1, 2},
闫晓东^{1, 2, ,}

1.
西北工业大学航天学院，西安 710072
2.
陕西省空天飞行器设计重点实验室，西安 710068

详细信息

通讯作者:
E-mail：yan804@nwpu.edu.cn

中图分类号: V448.2
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- 被引次数: 0
出版历程
- 收稿日期: 2023-04-04
- 录用日期: 2023-07-11
- 网络出版日期: 2023-07-31
- 整期出版日期: 2025-04-30

Rapid planning method for lunar direct ascent and rendezvous trajectory in emergency cases

BAN Huanheng^{1, 2},
ZHOU Cong^{1, 2},
YAN Xiaodong^{1, 2
, ,}

1.
School of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China
2.
Shaanxi Aerospace Flight Vehicle Design Key Laboratory，Xi’an 710068，China

More Information

Corresponding author: E-mail：yan804@nwpu.edu.cn

摘要

摘要:
当月面探测器出现某些突发状况而需要返回环月轨道器或地球时，上升器需具备自主规划出合适的应急上升交会轨迹的能力。以上升交会时间最短为目标函数，基于序列二阶锥规划方法，建立直接上升交会轨迹优化模型，并构建求解直接上升交会轨迹优化问题的凸优化算法。为提高计算效率，对内点法进行定制化改进，主要改进有：线性方程组求解过程定制化改进；内点法热启动；二阶锥规划子问题求解精度动态调整。仿真结果表明：所提月面应急上升交会轨迹优化方法可实现上升器的快速上升交会。与采用通用内点法求解器的传统序列二阶锥规划方法相比，在求解精度不变的情况下，所提的序列二阶锥规划问题求解加速方法可达到9.5倍左右的加速比。综合运用所提方法，有望实现月面上升器的自主在线轨迹规划。
- 月面应急上升交会 /
- 序列二阶锥规划方法 /
- 内点法定制化 /
- 内点法热启动 /
- 在线轨迹规划
Abstract:
When a lunar detector encounters unexpected conditions and needs a return to the lunar orbiter or Earth, the lunar ascender should be able to plan an appropriate ascent and rendezvous trajectory independently in emergency cases. In this paper, a direct ascent and rendezvous trajectory optimization model was established based on a successive second-order cone programming method, and minimum ascent and rendezvous time was chosen as the objective function. Additionally, a convex optimization algorithm was proposed to solve the ascent and rendezvous trajectory optimization problem. In order to enhance computational efficiency, the interior point method was customized and modified. The main adaptations included: the process of solving linear equations was customized and modified; a warm starting was used in the interior point method; the second-order cone programming subproblem solving accuracy was adjusted dynamically. Simulation results demonstrate that the proposed lunar ascent and rendezvous trajectory optimization method in emergency cases facilitates the rapid ascent and rendezvous process of the lunar ascender. Moreover, when compared to the traditional successive second-order cone programming method employing a general interior point method solver, the proposed acceleration technique achieves a speedup ratio of approximately 9.5 times while maintaining the same level of solving accuracy. Consequently, the method outlined in this paper holds significant potential for enabling autonomous online trajectory planning of lunar ascenders.

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图 1 月心球面坐标系

Figure 1. Lunar center spherical coordinate system

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图 2 月面应急上升交会示意图

Figure 2. Lunar ascent and rendezvous process in emergency cases

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图 3 推力方向几何示意图

Figure 3. Geometry of thrust direction

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图 4 仿射方向并行计算流程

Figure 4. Parallel calculation process of affine direction

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图 5 基于定制化改进内点法的序列二阶锥规划流程

Figure 5. Successive second-order cone programming based on customized and modified interior point method

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图 6 三维轨迹

Figure 6. 3D trajectories

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图 7 速度和质量曲线

Figure 7. Velocity and mass curves

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图 8 推力曲线

Figure 8. Thrust curves

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图 9 不同启动方法迭代次数

Figure 9. Iteration times of different starting methods

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图 10 优化问题变化趋势

Figure 10. Optimization problem evolution trend

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图 11 不同方法的求解耗时统计图

Figure 11. Statistics of runtime by different methods

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表 1 不同排序方法的矩阵非零元素个数对比

Table 1. Number of non-zero elements of matrix for different ordering methods

离散点数(N₁+N₂)	非零元素个数
离散点数(N₁+N₂)	近似最小度算法	局部填充最小算法
11+21	8194	7209
21+41	17059	14416
31+61	26977	21709
41+81	34435	28916

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表 2 上升器参数

Table 2. Parameters of ascender

上升器总重m_wet/kg	上升器干重m_dry/kg	主发动机推力P₁/N	主发动机比冲I_sp1/s	推力器总推力P₂/N	推力器比冲I_sp2/s
800	370	3000	313.7	960	290

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表 3 不同M值下的计算结果对比

Table 3. Comparison of calculation results under different M values

$M$	序列二阶锥规划迭代次数	内点法总迭代次数
20	15	96
40	15	102
60	15	102
100	10	60
200	10	64
400	10	72
600	12	84
1 000	11	89

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表 4 不同离散点数下的参数设置

Table 4. Parameter setting under different discrete points

离散点数(N₁+N₂)	热启动参数 $\omega$	精度提高倍数 $M$
11+21	0.992 0	200
21+41	0.999 2	100
31+61	0.999 6	100
41+81	0.999 6	100

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表 5 不同方法的求解耗时统计

Table 5. Statistics of runtime by different methods

离散点数 (N₁+N₂)	原方法耗时/ms	定制化方法耗时/ms	改进方法耗时/ms
11+21	133.60	82.60	13.15
21+41	225.20	136.70	24.00
31+61	344.10	205.10	35.10
41+81	495.00	308.10	51.60

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表 6 不同方法加速比

Table 6. Speedup ratios of different methods

离散点数 (N₁+N₂)	定制化方法加速比	改进方法加速比
11+21	1.62	10.19
21+41	1.65	9.39
31+61	1.68	9.81
41+81	1.61	9.58

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表 7 不同方法的求解精度

Table 7. Solving accuracies of different methods

离散点数 (N₁+N₂)	方法	位置误差/km	速度误差/ (m·s⁻¹)
11+21	原方法	16.280 4	33.529 9
	定制化方法^[27]	16.280 4	33.529 9
	改进方法	16.155 7	33.268 1
21+41	原方法	7.942 4	16.482 4
	定制化方法^[27]	7.942 4	16.482 4
	改进方法	8.118 8	16.841 4
31+61	原方法	5.262 3	10.938 1
	定制化方法^[27]	5.262 3	10.938 1
	改进方法	5.312 4	11.029 8
41+81	原方法	4.080 0	8.472 8
	定制化方法^[27]	4.080 0	8.472 8
	改进方法	3.933 3	8.172 2

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