面向工程约束的小推力转移轨道设计与优化
|
摘要
针对深空探测任务中电推进系统需要设置多个工作点、推力分级输出的需求,研究多模式电推进约束下的小行星探测转移轨道优化设计问题,分析推力分档对转移轨道的影响,建立小推力转移轨道动力学模型和优化模型;提出一种基于直接法的轨道优化策略,包括优化模型离散化、初值生成、序列二次规划(SQP)算法进行局部优化,并引入粒子群(PSO)算法搭配SQP算法提高初值的搜索效率和解的全局最优性;通过一次火星借力交会颖神星(1974 QU2)为例进行仿真分析.结果表明,所提优化策略能够有效解决多模式约束下的小推力转移轨道优化设计问题,具有良好的收敛性,在工作功率区间内,增加推力档数能够提高能源利用率,降低燃料消耗量,缩短推力器的开机时间,同时在非工作功率区间内应避免无效的分档.
Multimode electric propulsion system is widely used in deep space exploration. Its thrust is output in stages with the change of input power, which also means that continuous power changes lead to discontinuous thrust changes. In the design and optimization of low-thrust trajectory, the discontinuity of thrust is often neglected and regarded as a continuous parameter. The optimal design of low-thrust transfer trajectory constrained by multimode electric propulsion is studied, and the influence of thrust grading characteristics on the trajectory is analyzed in this paper. A specific optimization strategy is proposed, including three main steps: model discretization based on direct method, fast generation of initial value based on particle swarm optimization(PSO), and optimization based on sequential quadratic programming(SQP). The dynamic model and optimization model of low-thrust transfer trajectory is established. Then,the optimization model is discretized based on the direct method and the original optimal control problem is transformed into a parameter optimization problem in the form of nonlinear programming(NLP). A hybrid optimization algorithm based on PSO and SQP is proposed to solve the new NLP problem. PSO is used to search the initial value efficiently and guarantee the global performance of the initial value and SQP is used for local optimization based on initial value, which can give full play to the excellent global optimization performance of PSO and the outstanding local optimization performance of SQP. The effectiveness of the proposed optimization strategy is verified by a simulation example of the main belt asteroid Metis(1974 QU2) rendezvous mission with once Mars gravity assist. The results show that the optimal control curve obtained is in accordance with the optimal control form of bang-bang control derived from the theory, and the thruster has just two situations at any time: shutdown or startup with maximum thrust. In the working power range,increasing the number of thrust stages can improve the rate of energy utilization, thereby improving the efficiency of thruster, shortening the startup time and reducing fuel consumption. Meanwhile, ineffective grading should be avoided in the non-working power range.
Multimode electric propulsion system is widely used in deep space exploration. Its thrust is output in stages with the change of input power, which also means that continuous power changes lead to discontinuous thrust changes. In the design and optimization of low-thrust trajectory, the discontinuity of thrust is often neglected and regarded as a continuous parameter. The optimal design of low-thrust transfer trajectory constrained by multimode electric propulsion is studied, and the influence of thrust grading characteristics on the trajectory is analyzed in this paper. A specific optimization strategy is proposed, including three main steps: model discretization based on direct method, fast generation of initial value based on particle swarm optimization(PSO), and optimization based on sequential quadratic programming(SQP). The dynamic model and optimization model of low-thrust transfer trajectory is established. Then,the optimization model is discretized based on the direct method and the original optimal control problem is transformed into a parameter optimization problem in the form of nonlinear programming(NLP). A hybrid optimization algorithm based on PSO and SQP is proposed to solve the new NLP problem. PSO is used to search the initial value efficiently and guarantee the global performance of the initial value and SQP is used for local optimization based on initial value, which can give full play to the excellent global optimization performance of PSO and the outstanding local optimization performance of SQP. The effectiveness of the proposed optimization strategy is verified by a simulation example of the main belt asteroid Metis(1974 QU2) rendezvous mission with once Mars gravity assist. The results show that the optimal control curve obtained is in accordance with the optimal control form of bang-bang control derived from the theory, and the thruster has just two situations at any time: shutdown or startup with maximum thrust. In the working power range,increasing the number of thrust stages can improve the rate of energy utilization, thereby improving the efficiency of thruster, shortening the startup time and reducing fuel consumption. Meanwhile, ineffective grading should be avoided in the non-working power range.
引文
1 Rayman M D,Williams S N.Design of the first interplanetary solar electric propulsion mission.J Spacecraft Rockets,2002,39:589-595
2 Watanabe S,Tsuda Y,Yoshikawa M,et al.Hayabusa2 mission overview.Space Sci Rev,2017,208:3-16
3 Sun X J,Zhang X M,Tian L C.Scheme design of electric propulsion system for asteroid sample and return mission(in Chinese).Vacuum,2018,1:40-45[孙小菁,张兴民,田立成.小行星探测及采样返回任务电推进系统方案设计.真空,2018,1:40-45]
4 Zhu Z F,Gao Y.Survey of two classes of continuation methods for solving optimal Bang-Bang control of low-thrust space trajectories(in Chinese).J Deep Space Explor,2017,4:101-110[朱政帆,高扬.空间小推力最优Bang-Bang控制的两类延拓解法综述.深空探测学报,2017,4:101-110]
5 Hargraves C R,Paris S W.Direct trajectory optimization using nonlinear programming and collocation.J Guidance Control Dyn,1987,10:338-342
6 Betts J T.Optimal interplanetary orbit transfers by direct transcription.J Astronaut Sci,1994,42:247-268
7 Fahroo F,Ross I M.Direct trajectory optimization by a Chebyshev pseudospectral method.J Guidance Control Dyn,2002,25:160-166
8 Herman A L,Conway B A.Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules.J Guidance Control Dyn,1996,19:592-599
9 Jiang F,Baoyin H,Li J.Practical techniques for low-thrust trajectory optimization with homotopic approach.J Guidance Control Dyn,2012,35:245-258
10 Guo T D.Study of indirect and pseudospectral methods for low thrust trajectory optimization in deep space exploration(in Chinese).Dissertation for Doctoral Degree.Beijing:Tsinghua University,2012.50-53[郭铁丁.深空探测小推力轨迹优化的间接法与伪谱法研究.博士学位论文.北京:清华大学,2012.50-53]
11 Yang H,Li J,Baoyin H.Low-cost transfer between asteroids with distant orbits using multiple gravity assists.Adv Space Res,2015,56:837-847
12 Bertrand R,Epenoy R.New smoothing techniques for solving bang-bang optimal control problems-Numerical results and statistical interpretation.Optim Control Appl Meth,2002,23:171-197
13 Chi Z,Yang H,Chen S,et al.Homotopy method for optimization of variable-specific-impulse low-thrust trajectories.Astrophys Space Sci,2017,362:216
14 Ren Y.Design and optimization of low-thrust interplanetary transfer trajectory(in Chinese).Dissertation for Doctoral Degree.Harbin:Harbin Institute of Technology,2007.19-20[任远.星际探测中的小推力转移轨道设计与优化方法研究.博士学位论文.哈尔滨:哈尔滨工业大学,2007.19-20]
15 Zhao Z H,Shang H B,Cui P Y.Low thrust gravity assist transfer trajectory design and optimization based on hybrid optimization method(in Chinese).In:Control Theory Committee of China Automation Society Volume C.Beijing,2011.1910-1914[赵遵辉,尚海滨,崔平远.基于混合优化方法的小推力借力转移轨道设计与优化.见:中国自动化学会控制理论专业委员会C卷.北京,2011.1910-1914]
16 Zhou Z Y,Tan T L.Optimization for asteroids spacecraft trajectory(in Chinese).Aerosp Shanghai,2014,31:57-64[周誌元,谭天乐.小行星探测器轨迹优化方法.上海航天,2014,31:57-64]
17 Gill P E,Murray W,Saunders M A.SNOPT:An SQP algorithm for large-scale constrained optimization.SIAM Rev,2005,47:99-131
18 Xie C Q,Zhang Y C H.Optimal control problems for the low-thrust orbit.In:Proceedings of the 2016 IEEE Chinese Guidance,Navigation and Control Conference.2016.2684-2689
2 Watanabe S,Tsuda Y,Yoshikawa M,et al.Hayabusa2 mission overview.Space Sci Rev,2017,208:3-16
3 Sun X J,Zhang X M,Tian L C.Scheme design of electric propulsion system for asteroid sample and return mission(in Chinese).Vacuum,2018,1:40-45[孙小菁,张兴民,田立成.小行星探测及采样返回任务电推进系统方案设计.真空,2018,1:40-45]
4 Zhu Z F,Gao Y.Survey of two classes of continuation methods for solving optimal Bang-Bang control of low-thrust space trajectories(in Chinese).J Deep Space Explor,2017,4:101-110[朱政帆,高扬.空间小推力最优Bang-Bang控制的两类延拓解法综述.深空探测学报,2017,4:101-110]
5 Hargraves C R,Paris S W.Direct trajectory optimization using nonlinear programming and collocation.J Guidance Control Dyn,1987,10:338-342
6 Betts J T.Optimal interplanetary orbit transfers by direct transcription.J Astronaut Sci,1994,42:247-268
7 Fahroo F,Ross I M.Direct trajectory optimization by a Chebyshev pseudospectral method.J Guidance Control Dyn,2002,25:160-166
8 Herman A L,Conway B A.Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules.J Guidance Control Dyn,1996,19:592-599
9 Jiang F,Baoyin H,Li J.Practical techniques for low-thrust trajectory optimization with homotopic approach.J Guidance Control Dyn,2012,35:245-258
10 Guo T D.Study of indirect and pseudospectral methods for low thrust trajectory optimization in deep space exploration(in Chinese).Dissertation for Doctoral Degree.Beijing:Tsinghua University,2012.50-53[郭铁丁.深空探测小推力轨迹优化的间接法与伪谱法研究.博士学位论文.北京:清华大学,2012.50-53]
11 Yang H,Li J,Baoyin H.Low-cost transfer between asteroids with distant orbits using multiple gravity assists.Adv Space Res,2015,56:837-847
12 Bertrand R,Epenoy R.New smoothing techniques for solving bang-bang optimal control problems-Numerical results and statistical interpretation.Optim Control Appl Meth,2002,23:171-197
13 Chi Z,Yang H,Chen S,et al.Homotopy method for optimization of variable-specific-impulse low-thrust trajectories.Astrophys Space Sci,2017,362:216
14 Ren Y.Design and optimization of low-thrust interplanetary transfer trajectory(in Chinese).Dissertation for Doctoral Degree.Harbin:Harbin Institute of Technology,2007.19-20[任远.星际探测中的小推力转移轨道设计与优化方法研究.博士学位论文.哈尔滨:哈尔滨工业大学,2007.19-20]
15 Zhao Z H,Shang H B,Cui P Y.Low thrust gravity assist transfer trajectory design and optimization based on hybrid optimization method(in Chinese).In:Control Theory Committee of China Automation Society Volume C.Beijing,2011.1910-1914[赵遵辉,尚海滨,崔平远.基于混合优化方法的小推力借力转移轨道设计与优化.见:中国自动化学会控制理论专业委员会C卷.北京,2011.1910-1914]
16 Zhou Z Y,Tan T L.Optimization for asteroids spacecraft trajectory(in Chinese).Aerosp Shanghai,2014,31:57-64[周誌元,谭天乐.小行星探测器轨迹优化方法.上海航天,2014,31:57-64]
17 Gill P E,Murray W,Saunders M A.SNOPT:An SQP algorithm for large-scale constrained optimization.SIAM Rev,2005,47:99-131
18 Xie C Q,Zhang Y C H.Optimal control problems for the low-thrust orbit.In:Proceedings of the 2016 IEEE Chinese Guidance,Navigation and Control Conference.2016.2684-2689