一种多约束条件下的三脉冲交会优化设计方法

doi:10.12305/j.issn.1001-506X.2022.08.26

摘要/Abstract

摘要：

针对空间快速接近定点观测任务, 研究了具有交会时间和转移路径约束的多约束条件下的共面圆轨道间远距离三脉冲最优交会问题, 将Hill制导方法与粒子群算法相结合求解转移路径点以及转移时机的最优解。在求解过程中, 提出一种等价变换的方法, 将原始待求量转化为一组新的相互独立的待求变量, 将原始的各约束项转化为易描述和处理的搜索空间边界条件, 为完成算法的初始化过程带来了便利, 使得算法设计过程更为简洁。最后, 给出了两组三脉冲最优交会仿真实验, 仿真结果不仅验证了所提算法的有效性, 而且表明, 相对于常规的设置惩罚项处理约束的方法, 采用本文所提出的等价变换方法处理约束项后, 算法表现出更强大的搜索能力及更好的稳定性。

关键词: 三脉冲交会, Hill制导, 粒子群优化, 多约束, 等价变换

Abstract:

The optimal three-impulse remote rendezvous between coplanar circles under multi-constraints including rendezvous time constraint and transfer path constraint is studied for the fast approaching and fixed-point observation mission in space. The Hill guidance and particle swarm optimization are combined to solve the optimal solution of transfer path point and transfer time. An equivalent transformation is proposed to transform the original variables to be solved into a new set of variables which are independent of each other. By applying this transformation algorithm, the original constraints are converted into the searching space boundaries which are easy to describe and cope with, such that it is convenient to perform the initialization and conduct the algorithm design. Finally, two simulation experiments of optimal three-impulse rendezvous are given. The results not only verify effectiveness of the proposed algorithm, but also indicate that compared with the conventional penalization method used to deal with constraints, the algorithm adopting the proposed equivalent transformation shows more powerful search ability and stronger stability.

Key words: three-impulse rendezvous, Hill guidance, particle swarm optimization, multi-constraint, equivalent transformation

中图分类号:

V488

李君龙, 李松洲, 周荻. 一种多约束条件下的三脉冲交会优化设计方法[J]. 系统工程与电子技术, 2022, 44(8): 2612-2620.

Junlong LI, Songzhou LI, Di ZHOU. Optimization method for three-impulse rendezvous under multi-constraints[J]. Systems Engineering and Electronics, 2022, 44(8): 2612-2620.

图/表 13

图1

图2

图3

图4

表1

表2

图5

图6

表3

图7

表4

图8

图9

参考文献 32

1	SUN L . Adaptive fault-tolerant constrained control of cooperative spacecraft rendezvous and docking[J]. IEEE Trans.on Industrial Electronics, 2019, 67 (4): 3107- 3115.
2	WANG Z W , DONG Y M , FENG W M , et al. Optimization for far-distance and fuel-limited cooperative rendezvous between two coplanar spacecraft based on Lambert method[J]. Proc.of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2020, 234 (7): 1301- 1310. doi: 10.1177/0954410019900447
3	REN F , FENG W M . Homotopy-SQP coupled method for optimal control of far-distance nonplanar rapid cooperative rendezvous with multiple specific-direction thrusts[J]. Advances in Space Research, 2021, 68, 3176- 3190. doi: 10.1016/j.asr.2021.06.019
4	PATEL P, UDREA B, NAYAK M. Optimal guidance trajectories for a nanosat docking with a non-cooperative resident space object[C]//Proc. of the IEEE Aerospace Conference, 2015.
5	SASAKI T , NAKAJIMA Y , YAMAMOTO T . Proximity approaches and design strategies for non-cooperative rendezvous V-bar hopping vs. spiral approach[J]. Transactions of the Japan Society for Aeronautical and Space Sciences, 2021, 64 (3): 136- 146. doi: 10.2322/tjsass.64.136
6	HAO S, ZHANG Y, JIA L. Rendezvous trajectory optimization of space debris after collision[C]//Proc. of the 4th IAA Conference on Dynamics and Control of Space Systems, 2018: 1401-1410.
7	FEDERICI L , ZAVOLI A , COLASURDO G . Evolutionary optimization of multirendezvous impulsive trajectories[J]. International Journal of Aerospace Engineering, 2021,
8	王华, 唐国金. 用遗传算法求解双冲量最优交会问题[J]. 中国空间科学技术, 2003, (1): 26- 30. doi: 10.3321/j.issn:1000-758X.2003.01.005
	WANG H , TANG G J . Solving optimal rendezvous using two impulses based on genetic algorithms[J]. Chinese Space Science and Technology, 2003, (1): 26- 30. doi: 10.3321/j.issn:1000-758X.2003.01.005
9	冉茂鹏, 王青. 一种基于EPSO的航天器交会轨迹优化方法[J]. 宇航学报, 2013, 34 (9): 1195- 1201.
	RAN M P , WANG Q . Spacecraft rendezvous trajectory optimization method based on EPSO[J]. Journal of Astronautics, 2013, 34 (9): 1195- 1201.
10	SENTINELLA M , CASALINO L . Cooperative evolutionary algorithm for space trajectory optimization[J]. Celestial Mechanics and Dynamical Astronomy, 2009, 105 (1): 211- 227.
11	SAMSAM S, CHHABRA R. Multi-impulse shape-based trajectory optimization for target chasing in on-orbit servicing missions[C]//Proc. of the IEEE Aerospace Conference, 2021: 1-11.
12	ZHOU H Y , WANG X G , CUI N G . Fuel-optimal multi-impulse orbit transfer using a hybrid optimization method[J]. IEEE Trans.on Intelligent Transportation Systems, 2020, 21 (4): 1359- 1368. doi: 10.1109/TITS.2019.2905586
13	FEDERICI L, BENEDIKTER B, ZAVOLI A. Machine learning techniques for autonomous spacecraft guidance during proximity operations[C]//Proc. of the AIAA Science and Technology Forum and Exposition, 2021: 1-18.
14	GONG M , ZHOU D , SHAO C T , et al. Optimal multiple-impulse time-fixed rendezvous using evolutionary algorithms[J]. Journal of Spacecraft and Rockets, 2021, doi: 10.2514/1.A34946
15	JAMES M , MANORANJAN M , SANDEEP K , et al. Optimal bi-impulse orbital transfers station keeping applications[J]. Journal of Guidance, Control, and Dynamics, 2021, 44 (11): 2057- 2066. doi: 10.2514/1.G005918
16	任远, 崔平远, 栾恩杰. 最优两脉冲行星际轨道转移优化算法[J]. 航空学报, 2007, 28 (6): 32- 36.
	REN Y , CUI P Y , LUAN E J . Interplanetary optimum two-impulse transfer trajectories[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28 (6): 32- 36.
17	马艳红, 胡军. 基于序优化理论的三脉冲交会燃料寻优[J]. 宇航学报, 2009, 30 (2): 663- 668. doi: 10.3873/j.issn.1000-1328.2009.02.045
	MA Y H , HU J . Three-impulse rendezvous fuel optimization based on ordinal optimization theory[J]. Journal of Astronautics, 2009, 30 (2): 663- 668. doi: 10.3873/j.issn.1000-1328.2009.02.045
18	PRUSSING J E . Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit[J]. AIAA Journal, 1969, 7 (5): 928- 935. doi: 10.2514/3.5246
19	CARTER T E , ALVAREZ S A . Quadratic-based computation of four-impulse optimal rendezvous near circular orbit[J]. Journal of Guidance, Control, and Dynamics, 2000, 23 (1): 109- 117. doi: 10.2514/2.4493
20	靳锴, 罗建军, 郑茂章, 等. 考虑导航误差和摄动影响的椭圆轨道最优交会制导[J]. 控制理论与应用, 2018, 35 (10): 1484- 1493.
	JIN K , LUO J J , ZHENG M Z , et al. Guidance design with navigation errors for relative motion in noncircular perturbed orbits[J]. Control Theory and Applications, 2018, 35 (10): 1484- 1493.
21	ORTOLANO N , GELLER D K , AVERY A . Autonomous optimal trajectory planning for orbital rendezvous, satellite inspection, and final approach based on convex optimization[J]. The Journal of the Astronautical Sciences, 2021, 68 (2): 444- 479. doi: 10.1007/s40295-021-00260-5
22	HEYDARI A . Optimal impulsive control using adaptive dynamic programming and its application in spacecraft rendezvous[J]. IEEE Trans.on Neural Networks and Learning Systems, 2021, 32 (10): 4544- 4552. doi: 10.1109/TNNLS.2020.3021037
23	ZHANG J , PARKS G T , LUO Y Z , et al. Multispacecraft refueling optimization considering the J2 perturbation and window constraints[J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (1): 111- 122. doi: 10.2514/1.61812
24	DU B X , ZHAO Y , DUTTA A , et al. Optimal scheduling of multispacecraft refueling based on cooperative maneuver[J]. Advances in Space Research, 2015, 55 (12): 2808- 2819. doi: 10.1016/j.asr.2015.02.025
25	VENIGALLA C , SCHEERES D J . Minimum bounds on multispacecraft ΔV optimal cooperative rendezvous[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (12): 2333- 2348. doi: 10.2514/1.G004978
26	CHEN S Y , JIANG F H , LI H Y , et al. Optimization for multitarget, multispacecraft impulsive rendezvous considering J2 perturbation[J]. Journal of Guidance, Control, and Dynamics, 2021, 44 (10): 1811- 1822. doi: 10.2514/1.G005602
27	PARK C , GUIBOUT V , SCHEERES D J . Solving optimal continuous thrust rendezvous problems with generating functions[J]. Journal of Guidance, Control, and Dynamics, 2013, 29 (2): 396- 401.
28	CHU X Y , LIANG Z C , LI Y Y . Trajectory optimization for rendezvous with bearing-only tracking[J]. Acta Astronautica, 2020, 171, 311- 322. doi: 10.1016/j.actaastro.2020.03.017
29	DU L F, HUANG W W, LIU X D, et al. Fuel-optimal and low-thrust rendezvous in elliptical orbits with fixed terminal-approach direction[C]//Proc. of the 27th IEEE Control and Decision Conference, 2015: 1570-1576.
30	MA H L , XU S J . Optimization of bounded low-thrust rendezvous with terminal constraints by interval analysis[J]. Aerospace Science and Technology, 2018, 79, 58- 69. doi: 10.1016/j.ast.2018.05.031
31	CHI Z M , WU D , JIANG F H , et al. Optimization of variable-specific-impulse gravity-assist trajectories[J]. Journal of Spacecraft and Rockets, 2020, 57 (2): 291- 299. doi: 10.2514/1.A34541
32	刘暾, 赵钧. 空间飞行器动力学[M]. 哈尔滨: 哈尔滨工业大学出版社, 2003: 83- 87.
	LIU T , ZHAO J . Dynamics of spacecraft[M]. Harbin: Harbin Institute of Technology Press, 2003: 83- 87.

轨道参数	目标飞行器	追赶飞行器
半长轴a/km	7 178	7 128
偏心率e	1.900 52e-16	7.547 06e-16
轨道倾角i/(°)	0	0
升交点赤经Ω/(°)	0	0
近心点角距ω/(°)	0	0
真近角f/(°)	0.693 7	0

初始化参数	变换前	变换后
k_max	100	100
w	0.8	0.8
c_p	2	2
c_g	2	2
N	100	100
X_min	[0, 0, 0, －100, －50]^T	[0,0,0,0,0]^T
X_max	[600, 600, 600, －1, 50]^T	[1,1,1,1,1]^T
V_min	－[6, 6, 6, 0.5, 0.5]^T	－[0.01, 0.01, 0.01, 0.01, 0.01]^T
V_max	[6, 6, 6, 0.5, 0.5]^T	[0.01, 0.01, 0.01, 0.01, 0.01]^T

结果参数	变换前	变换后
总冲量最小值/(m/s)	293.08	272.17
总冲量最大值/(m/s)	430.44	329.68
总冲量平均值/(m/s)	352.89	300.02
总冲量标准差/(m/s)	32.44	11.52
终端误差最小值/m	0.01	1.21
终端误差最大值/m	18.11	21.27
终端误差平均值/m	4.30	9.83
终端误差标准差/m	4.45	3.94

结果参数	变换前	变换后
最优解([Δt₀, Δt₁, Δ t₂, x₂, y₂]^T)	[16.18, 296.50, 285.63, －33.36, －35.45]^T	[4.23, 333.55, 259.42, －30.52, －30.95]^T
第一脉冲/(m/s)	[108.60, 17.17]^T	[104.56, 22.59]^T
第二脉冲/(m/s)	[－8.29, 15.70]^T	[1.14, 2.13]^T
第三脉冲/(m/s)	[－73.88, －147.95]^T	[－79.22, －142.13]^T
总冲量/(m/s)	293.08	272.17
终端误差/m	18.11	16.02

[1]	杨建峰, 肖和业, 李亮, 白俊强, 董维浩. 基于模糊聚类和专家评分机制的无人机多层次模块划分方法[J]. 系统工程与电子技术, 2022, 44(8): 2530-2539.
[2]	曹鹏宇, 杨承志, 石礼盟, 吴宏超. 基于PSO-DBSCAN和SCGAN的未知雷达信号处理方法[J]. 系统工程与电子技术, 2022, 44(4): 1158-1165.
[3]	姜尚, 魏波, 梁伟阁, 孙东彦, 李进军, 马野. 考虑齿隙的多约束导引控制一体化设计方法[J]. 系统工程与电子技术, 2022, 44(4): 1318-1328.
[4]	杜思予, 全英汇, 沙明辉, 方文, 邢孟道. 基于进化PSO算法的稀疏捷变频雷达波形优化[J]. 系统工程与电子技术, 2022, 44(3): 834-840.
[5]	石宸睿, 田露, 徐湛, 职如昕, 陈晋辉. 基于PSO-BP的应急通信感知装备效能评价方法[J]. 系统工程与电子技术, 2022, 44(11): 3455-3462.
[6]	路复宇, 童宁宁, 冯为可, 万鹏程. 自适应杂交退火粒子群优化算法[J]. 系统工程与电子技术, 2022, 44(11): 3470-3476.
[7]	李浩洋, 向建军, 彭芳, 王帅, 李志军. 基于粒子群优化的波束空间广义旁瓣相消算法[J]. 系统工程与电子技术, 2022, 44(10): 3037-3045.
[8]	谢磊, 丁达理, 魏政磊, 汤安迪, 张鹏. AdaBoost-PSO-LSTM网络实时预测机动轨迹[J]. 系统工程与电子技术, 2021, 43(6): 1651-1658.
[9]	都延丽, 刘武, 唐明明, 王玉惠. 可重复使用运载器多约束鲁棒预测校正制导[J]. 系统工程与电子技术, 2021, 43(5): 1316-1325.
[10]	王坤, 侯树贤, 王力. 基于自适应变异PSO-SVM的APU性能参数预测模型[J]. 系统工程与电子技术, 2021, 43(2): 526-536.
[11]	赵帅, 刘松涛, 汪慧阳. 基于PSO-CNN的LPI雷达波形识别算法[J]. 系统工程与电子技术, 2021, 43(12): 3552-3563.
[12]	孙世岩, 姜尚, 田福庆, 梁伟阁. 带多约束的多弹分布式自适应协同导引律[J]. 系统工程与电子技术, 2021, 43(1): 181-190.
[13]	王晓海, 孟秀云, 李传旭. 基于MPC的无人机航迹跟踪控制器设计[J]. 系统工程与电子技术, 2021, 43(1): 191-198.
[14]	李玖阳, 胡敏, 王许煜, 徐家辉, 李菲菲. 基于ALPSO算法的低轨卫星小推力离轨最优控制方法[J]. 系统工程与电子技术, 2021, 43(1): 199-207.
[15]	何春蓉, 朱江. 基于注意力机制的GRU神经网络安全态势预测方法[J]. 系统工程与电子技术, 2021, 43(1): 258-266.