基于ALPSO算法的低轨卫星小推力离轨最优控制方法

doi:10.3969/j.issn.1001-506X.2021.01.24

摘要/Abstract

摘要：

低轨卫星在到寿后,需要在一定时间内离轨,而轨道高度高于800 km的卫星难以在自然条件下离轨。为了使卫星在规定时间内离轨,提出一种基于增广拉格朗日粒子群优化(augmented Lagrangian particle swarm optimization, ALPSO)算法的低轨卫星小推力离轨最优控制算法。首先依据小推力的特点列出摄动方程,并利用哈密尔顿方程求出带协状态参数的最优控制率。而后分别阐述了粒子群算法和增广拉格朗日方法,并据此得出了算法流程。最后与遗传算法的优化结果进行对比。结果表明, ALPSO算法迭代次数较少,收敛精度较高,降低轨道高度的第一种处置轨道适用于轨道高度821 km的卫星离轨,离轨时间为857天。该算法可用于低轨卫星小推力离轨问题的求解。

关键词: 低轨卫星, 小推力离轨, 粒子群优化算法, 最优控制

Abstract:

The low earth orbit satellite needs to deorbit within a certain period of time after reaching their lifetime, while satellite with orbit height above 800 km is difficult to deorbit under natural conditions. In order to make the satellite deorbit within a specified time, an optimal control algorithm for low thrust deorbit of the low earth orbit satellite based on the augmented Lagrangian particle swarm optimization (ALPSO) algorithm is proposed. Firstly, the perturbation equation is listed according to the characteristics of low thrust, and the Hamilton equation is used to acquire the optimal control rate with co-state parameters. Then, the particle swarm algorithm and the augmented Lagrangian method are expounded respectively, and the algorithm flow is obtained accordingly. Finally, it is compared with the optimization results of the genetic algorithm. The results show that the ALPSO algorithm has fewer iterations and higher convergence accuracy. The first disposal orbit with reduced orbit altitude is suitable for satellite deorbit with an orbit altitude of 821 km, and the deorbit time is 857 days. The algorithm can be applied to solve the low thrust deorbit problem of the low earth orbit satellite.

Key words: low earth orbit satellite, low thrust deorbit, particle swarm optimal algorithm, optimal control

中图分类号:

V412.2

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.

Jiuyang LI, Min HU, Xuyu WANG, Jiahui XU, Feifei LI. Optimal control method for low thrust deorbit of the low earth orbit satellite based on ALPSO algorithm[J]. Systems Engineering and Electronics, 2021, 43(1): 199-207.

图/表 13

图1

图2

图3

表1

表2

图4

图5

图6

图7

图8

表3

图9

图10

参考文献 32

1	张国云, 樊恒海, 蔡立锋, 等. 基于升轨方式的低轨卫星主动离轨处置策略[J]. 航天器工程, 2018, 27 (2): 19- 25. doi: 10.3969/j.issn.1673-8748.2018.02.004
	ZHANG G Y , FAN H H , CAI L F , et al. Active deorbit disposal strategy for LEO satellite based on orbit elevation[J]. Spacecraft Engineering, 2018, 27 (2): 19- 25. doi: 10.3969/j.issn.1673-8748.2018.02.004
2	YAKOVLEV M. The IADC space debris mitigation guidelines and supporting documents[C]//Proc.of the 4th European Conference on Space Debris, 2005.
3	REID T G, NEISH A M, WALTER T F, et al. Leveraging commercial broadband LEO constellations for navigation[C]//Proc.of the ION GNSS, 2016: 2300-2314.
4	RADTKE J , KEBSCHULL C , STOLL E . Interactions of the space debris environment with mega constellations-using the example of the OneWeb constellation[J]. Acta Astronautica, 2017, 131 (3): 55- 68.
5	MCDOWELL J C . The low earth orbit satellite population and impacts of the SpaceX Starlink constellation[J]. The Astrophysical Journal Letters, 2020, 892 (2): L36. doi: 10.3847/2041-8213/ab8016
6	HUANG S, COLOMBO C, ALESSI E M. Trade-off study on large constellation deorbiting using low-thrust and deorbiting balloons[C]//Proc.of the 10th International Workshop on Satellite Constellations and Formation Flying, 2019.
7	GUGLIELMO D , OMAR S , BEVILACQUA R , et al. Drag deorbit device: a new standard reentry actuator for CubeSats[J]. Journal of Spacecraft and Rockets, 2019, 56 (1): 129- 145. doi: 10.2514/1.A34218
8	PETERS T V , BRIZ V J F , ESCORIAL O D , et al. Attitude control analysis of tethered de-orbiting[J]. Acta Astronautica, 2018, 146 (5): 316- 331.
9	黄国强, 陆宇平, 南英, 等. 多目标连续小推力深空探测器轨道全局优化[J]. 系统工程与电子技术, 2012, 34 (8): 1652- 1659.
	HUANG G Q , LU Y P , NAN Y , et al. Trajectory global optimization for multi-objective in space exploration by low-thrust control[J]. Systems Engineering and Electronics, 2012, 34 (8): 1652- 1659.
10	FROMM C M, HERBERTZ A. Using electric propulsion for the de-orbiting of satellites[C]//Proc.of the 5th CEAS Air & Space Conference, 2015.
11	HUANG S, COLOMBO C, ALESSI E, et al. Large constellation de-orbiting with low-thrust propulsion[C]//Proc.of the 29th AAS/AIAA Space Flight Mechanics Meeting, 2019.
12	TROFIMOV S, OVCHINNIKOV M. Optimal low-thrust deorbiting of passively stabilized LEO satellites[C]//Proc.of the 64th International Astronautical Congress, 2013: 5224-5230.
13	魏静萱, 王宇平. 求解约束优化问题的改进粒子群算法[J]. 系统工程与电子技术, 2008, 30 (4): 739- 742. doi: 10.3321/j.issn:1001-506X.2008.04.036
	WEI J X , WANG Y P . Smooth scheme and line search based particle swarm optimization for constrained optimization problems[J]. Systems Engineering and Electronics, 2008, 30 (4): 739- 742. doi: 10.3321/j.issn:1001-506X.2008.04.036
14	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
15	MANSELL J R, DICKMANN S, SPENCER D A. Swarm optimization of lunar transfers from earth orbit with radiation dose constraints[C]//Proc.of the 29th AAS/AIAA Space Flight Mechanics Meeting, 2019: 1911-1928.
16	JAGANNATHA B B , BOUVIER J B H , HO K . Preliminary design of low-energy, low-thrust transfers to Halo orbits using feedback control[J]. Journal of Guidance, Control, and Dynamics, 2019, 42 (2): 260- 271. doi: 10.2514/1.G003759
17	PONTANI M, CONWAY B A. Particle swarm optimization of low-thrust orbital transfers and rendezvous[C]//Proc.of the 21st AAS/AIAA Space Flight Mechanics Meeting, 2011: 889-908.
18	ABRAHAM A J, SPENCER D B, HART T J. Optimization of preliminary low-thrust trajectories from GEO-energy orbits to Earth-Moon, L1, lagrange point orbits using particle swarm optimization[C]//Proc.of the AAS/AIAA Astrodynamics Specialist Conference, 2014: 13-925.
19	ZOTES F A , PENAS M S . Particle swarm optimisation of interplanetary trajectories from Earth to Jupiter and Saturn[J]. Engineering Applications of Artificial Intelligence, 2012, 25 (1): 189- 199. doi: 10.1016/j.engappai.2011.09.005
20	沈如松,杨雪榕.基于粒子群算法的小推力同步轨道入轨优化[C]//第30届中国控制会议, 2011: 2093-2098.
	SHEN R S, YANG X R. Optimization of low-thrust transfers to synchronous orbit using PSO algorithm[C]//Proc.of the 30th Chinese Control Conference, 2011: 2093-2098.
21	JIN J S , YUAN R . Low-thrust trajectory design with constrained particle swarm optimization[J]. Aerospace Science and Technology, 2014, 36 (7): 114- 124.
22	WANG X S , PENG Y M , LU X , et al. Design and optimization of low thrust transfer trajectory for engineering constraints[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2019, 49 (8): 77- 87.
23	尚海滨,崔平远,栾恩杰.基于平均法的小推力转移轨道优化研究[C]//第25届中国控制会议, 2006: 651-655.
	SHANG H B, CUI P Y, LUAN E J. Optimization of low-thrust transfer trajectory based on averaging method[C]//Proc.of the 25th China Control Conference, 2006: 651-655.
24	林书宇,马雪阳.电推进卫星轨道转移优化策略综述[C]//中国空天安全会议, 2017: 486-500.
	LIN S Y, MA X Y. A survey of transfer orbit trajectory optimization for electric propulsion satellite[C]//Proc.of the Chinese Aerospace Safety Symposium, 2017: 486-500.
25	BATTIN R H . An introduction to the mathematics and methods of astrodynamics, revised edition[M]. Reston: American Institute of Aeronautics and Astronautics, 1999.
26	CONWAY B A . Spacecraft trajectory optimization[M]. 29th ed New York: Cambridge University Press, 2010.
27	JANSEN P W , PEREZ R E . Constrained structural design optimization via a parallel augmented lagrangian particle swarm optimization approach[J]. Computers & Structures, 2011, 89 (13/14): 1352- 1366.
28	KENNEDY J, EBERHART R. Particle swarm optimization[C]//Proc.of the ICNN'95-International Conference on Neural Networks, 1995: 1942-1948.
29	于颖, 於孝春, 李永生. 扩展拉格朗日乘子粒子群算法解决工程优化问题[J]. 机械工程学报, 2009, 45 (12): 167- 172.
	YU Y , YU X C , LI Y S . Solving engineering optimization problem by augmented lagrange particle swarm optimization[J]. Journal of Mechanical Engineering, 2009, 45 (12): 167- 172.
30	杨希祥, 江振宇, 张为华. 基于粒子群算法的固体运载火箭上升段弹道优化设计研究[J]. 宇航学报, 2010, 31 (5): 1304- 1309. doi: 10.3873/j.issn.1000-1328.2010.05.008
	YANG X X , JIANG Z Y , ZHANG W H . A particle swarm optimization algorithm-based solid launch vehicle ascent trajectory optimum design[J]. Journal of Astronautics, 2010, 31 (5): 1304- 1309. doi: 10.3873/j.issn.1000-1328.2010.05.008
31	VAN D B F. An analysis of particle swarm optimizers[D]. Pretoria: University of Pretoria, 2007.
32	杜学武, 靳祯. 不等式约束优化问题的一个精确增广拉格朗日函数[J]. 上海交通大学学报, 2006, 40 (9): 1636- 1640. doi: 10.3321/j.issn:1006-2467.2006.09.038
	DU X W , JIN Z . An exact augmented Lagrangian function for nonlinear programming problems with inequality constraints[J]. Journal of Shanghai Jiaotong University, 2006, 40 (9): 1636- 1640. doi: 10.3321/j.issn:1006-2467.2006.09.038

轨道根数	工作轨道	第一种处置轨道	第二种处置轨道
半长轴/km	7 200	6 528	7 200
偏心率	0.001	0.001	0.093
轨道倾角/(°)	98.500	98.500	98.500

参数	取值
种群个数N	500
最大迭代次数k_max	50
最大惯性权重ω_max	0.9
最小惯性权重ω_min	0.4
n_s阈值s	15
n_f阈值f	5
随机方向参数初值ρ₀	1
初始惩罚因子r₀	1 000
约束阈值ε_f	0.000 1

参数	λ_a	λ_e	λ_i	离轨时间/天	燃料消耗/kg
粒子群搜索范围(第一种)	[-10/a, 10/a]	[-10, 10]	[-10, 10]	—	—
粒子群搜索范围(第二种)	[-10/a, 10/a]	[-1×10⁶, 1×10⁶]	[-10, 10]	—	—
最优解(第一种处置轨道)	-1.389×10^-6	-4.074	6.563	857	2.00
最优解(第二种处置轨道)	-1.389×10^-7	-2 223.345	10	1 607	3.75

[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]	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.
[3]	唐一强, 杨霄鹏, 朱圣铭. 基于注意力机制的混合CNN-BiLSTM低轨卫星信道预测算法[J]. 系统工程与电子技术, 2022, 44(12): 3863-3870.
[4]	郭建国, 苏亚鲁. 高超飞行器自适应动态规划的控制系统设计[J]. 系统工程与电子技术, 2021, 43(6): 1628-1635.
[5]	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.
[6]	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.
[7]	李亚南, 黄海滨, 陈亮名, 庄宇飞, 王晓丽. 变化海流环境下AUV能量最优三维路径规划[J]. 系统工程与电子技术, 2021, 43(12): 3667-3674.
[8]	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.
[9]	马愈昭, 王强强, 王瑞松, 熊兴隆. 基于SVD和MPSO-SVM的光纤周界[J]. 系统工程与电子技术, 2020, 42(8): 1652-1661.
[10]	苏志刚, 陈欣然, 郝敬堂. 基于粒子群优化的圆阵列波束形成方法[J]. 系统工程与电子技术, 2020, 42(7): 1449-1454.
[11]	吴明功, 叶泽龙, 温祥西, 王宏军. 基于局部弹性路由层的关键航路段改航规划[J]. 系统工程与电子技术, 2020, 42(7): 1534-1542.
[12]	孙胜祥, 韩霜. 基于双层决策的装备订购多因素激励定价模型与算法[J]. 系统工程与电子技术, 2020, 42(6): 1338-1347.
[13]	徐涛, 吴志帅, 卢敏, 吕宗磊, 李忠虎. 面向拥堵问题的枢纽航线网络优化模型[J]. 系统工程与电子技术, 2020, 42(11): 2553-2559.
[14]	练青坡, 王宏健, 袁建亚, 高娜, 胡文月. 基于粒子群优化算法的USV集群协同避碰方法[J]. 系统工程与电子技术, 2019, 41(9): 2034-2040.
[15]	赵琳, 周俊峰, 刘源, 郝勇. 三维空间“追逃防”三方微分对策方法[J]. 系统工程与电子技术, 2019, 41(2): 322-335.