太阳帆轨迹间接优化技术收敛性分析
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摘要
间接法是求解太阳帆航天器轨迹优化问题的一种常用方法.然而,间接法往往由于协态初值敏感性而存在收敛性难题.为了改善数值求解收敛性,协态变量归一化等多种间接优化技术已在深空探测轨迹优化研究中被提出.但是,对于太阳帆轨迹优化问题,鲜有间接优化技术对收敛性影响分析.本文以太阳帆航天器交会探测小行星为背景,研究协态变量归一化技术、同伦技术及间接法求解中太阳帆动力学模型坐标系(直角坐标系或球坐标系)与收敛性关系.首先,构建基于不同间接优化技术的间接法求解模型,采用数值打靶法求解最优的协态变量值.然后,根据协态变量所需猜测次数和协态变量初值估计的准确程度,对比分析3种技术对提升优化收敛性能的作用.仿真结果表明,同伦法的初值估计准确度最高、收敛性也最好.
The indirect method is commonly used for solving the solar sail spacecraft trajectory optimization problem. However, the convergence difficulty usually tends to happen due to the sensitivity of the initial costates. In order to improve the numerical convergence properties, many indirect optimization techniques, such as the normalization of the costate vector,have been proposed in the research of deep space trajectory optimization problem. However, there is little literature focused on the analysis of the convergence properties for different indirect optimization techniques. This paper takes the asteroid rendezvous mission with solar sail spacecraft as background, and analyzes the relationship between the indirect optimization techniques which includes the normalization of the costate vector, the homotopic approach and different coordinate systems(the Cartesian and the Spherical coordinate system) for solar sail dynamic models and the convergence properties. First, dynamic models based on different indirect optimization techniques are developed. The shooting method is used to solve for the optimal costates. Then, the convergence properties of the three techniques are compared and analyzed according to the times of initial guesses and the accuracy of the guessed costates. The results of the numerical simulations show that the homotopic approach can achieve the highest accuracy of initial guesses and the best convergence properties.
The indirect method is commonly used for solving the solar sail spacecraft trajectory optimization problem. However, the convergence difficulty usually tends to happen due to the sensitivity of the initial costates. In order to improve the numerical convergence properties, many indirect optimization techniques, such as the normalization of the costate vector,have been proposed in the research of deep space trajectory optimization problem. However, there is little literature focused on the analysis of the convergence properties for different indirect optimization techniques. This paper takes the asteroid rendezvous mission with solar sail spacecraft as background, and analyzes the relationship between the indirect optimization techniques which includes the normalization of the costate vector, the homotopic approach and different coordinate systems(the Cartesian and the Spherical coordinate system) for solar sail dynamic models and the convergence properties. First, dynamic models based on different indirect optimization techniques are developed. The shooting method is used to solve for the optimal costates. Then, the convergence properties of the three techniques are compared and analyzed according to the times of initial guesses and the accuracy of the guessed costates. The results of the numerical simulations show that the homotopic approach can achieve the highest accuracy of initial guesses and the best convergence properties.
引文
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7 Peloni A,Ceriotti M,Dachwald B.Solar-sail trajectory design for a multiple near-Earth-asteroid rendezvous mission.J Guid Control Dyn,2016,39:2712-2724
8 Peloni A,Dachwald B,Ceriotti M.Multiple near-Earth asteroid rendezvous mission:Solar-sailing options.Adv Space Res,2018,62:2084-2098
9 Heiligers J,Scheeres D J.Solar-sail orbital motion about asteroids and binary asteroid systems.J Guid Control Dyn,2018,41:1947-1962
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12 Conway B A.A survey of methods available for the numerical optimization of continuous dynamic systems.J Optim Theor Appl,2012,152:271-306
13 Gong S P,Gao Y F,Li J F.Solar sail time-optimal interplanetary transfer trajectory design.Res Astron Astrophys,2011,11:981-996
14 Zeng X,Alfriend K T,Li J,et al.Optimal solar sail trajectory analysis for interstellar missions.J Astronaut Sci,2012,59:502-516
15 Ma Y Y,Pan B F.Solar sail time-optimal trajectory optimization using Kustaanheimo-Stiefel transformation.In:The Fourth International Symposium on Solar Sailing.Kyoto,2017
16 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
17 Guo T,Jiang F,Li J.Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization.Acta Astronaut,2012,71:38-50
18 Jiang F,Baoyin H,Li J.Practical techniques for low-thrust trajectory optimization with homotopic approach.J Guid Control Dyn,2012,35:245-258
19 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
20 Gong S,Li J,Jiang F.Interplanetary trajectory design for a hybrid propulsion system.Aerospace Sci Tech,2015,45:104-113
21 Sullo N,Peloni A,Ceriotti M.Low-thrust to solar-sail trajectories:A homotopic approach.J Guid Control Dyn,2017,40:2796-2806
22 Junkins J L,Taheri E.Exploration of alternative state vector choices for low-thrust trajectory optimization.J Guid Control Dyn,2019,42:47-64
23 Zeng X Y.Solar Sail Spacecraft Novel Trajectory Design in Deep Space Exploration(in Chinese).Dissertation for Doctoral Degree.Beijing:Tsinghua University,2013[曾祥远.深空探测太阳帆航天器新型轨道设计.博士学位论文.北京:清华大学,2013]
24 McInnes C R.Solar Sailing:Technology,Dynamics and Mission Applications.London:Springer-Verlag,1999.34-170
25 MoréJ J,Garbow B S,Hillstrom K E.User guide for MINPACK-1.Technical Report.Argonne:Argonne National Laboratory,1980
26 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
2 Dachwald B,Wie B.Solar sail trajectory optimization for intercepting,impacting,and deflecting near-Earth asteroids.In:Proceedings of the AIAA Guidance,Navigation,and Control Conference and Exhibit.San Francisco:AIAA,2005
3 Dachwald B.Optimal solar sail trajectories for missions to the outer solar system.J Guid Control Dyn,2005,28:1187-1193
4 Ball A J,Ulamec S,Dachwald B,et al.A small mission for in situ exploration of a primitive binary near-Earth asteroid.Adv Space Res,2009,43:317-324
5 Brophy J R,Friedman L,Culick F.Asteroid retrieval feasibility.In:2012 IEEE Aerospace Conference.Big Sky,MT:IEEE,2012.1-16
6 Zeng X,Gong S,Li J.Fast solar sail rendezvous mission to near Earth asteroids.Acta Astronaut,2014,105:40-56
7 Peloni A,Ceriotti M,Dachwald B.Solar-sail trajectory design for a multiple near-Earth-asteroid rendezvous mission.J Guid Control Dyn,2016,39:2712-2724
8 Peloni A,Dachwald B,Ceriotti M.Multiple near-Earth asteroid rendezvous mission:Solar-sailing options.Adv Space Res,2018,62:2084-2098
9 Heiligers J,Scheeres D J.Solar-sail orbital motion about asteroids and binary asteroid systems.J Guid Control Dyn,2018,41:1947-1962
10 Mengali G,Quarta A A.Rapid solar sail rendezvous missions to asteroid 99942 Apophis.J Spacecraft Rockets,2006,46:134-140
11 Betts J T.Survey of numerical methods for trajectory optimization.J Guid Control Dyn,1998,21:193-207
12 Conway B A.A survey of methods available for the numerical optimization of continuous dynamic systems.J Optim Theor Appl,2012,152:271-306
13 Gong S P,Gao Y F,Li J F.Solar sail time-optimal interplanetary transfer trajectory design.Res Astron Astrophys,2011,11:981-996
14 Zeng X,Alfriend K T,Li J,et al.Optimal solar sail trajectory analysis for interstellar missions.J Astronaut Sci,2012,59:502-516
15 Ma Y Y,Pan B F.Solar sail time-optimal trajectory optimization using Kustaanheimo-Stiefel transformation.In:The Fourth International Symposium on Solar Sailing.Kyoto,2017
16 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
17 Guo T,Jiang F,Li J.Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization.Acta Astronaut,2012,71:38-50
18 Jiang F,Baoyin H,Li J.Practical techniques for low-thrust trajectory optimization with homotopic approach.J Guid Control Dyn,2012,35:245-258
19 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
20 Gong S,Li J,Jiang F.Interplanetary trajectory design for a hybrid propulsion system.Aerospace Sci Tech,2015,45:104-113
21 Sullo N,Peloni A,Ceriotti M.Low-thrust to solar-sail trajectories:A homotopic approach.J Guid Control Dyn,2017,40:2796-2806
22 Junkins J L,Taheri E.Exploration of alternative state vector choices for low-thrust trajectory optimization.J Guid Control Dyn,2019,42:47-64
23 Zeng X Y.Solar Sail Spacecraft Novel Trajectory Design in Deep Space Exploration(in Chinese).Dissertation for Doctoral Degree.Beijing:Tsinghua University,2013[曾祥远.深空探测太阳帆航天器新型轨道设计.博士学位论文.北京:清华大学,2013]
24 McInnes C R.Solar Sailing:Technology,Dynamics and Mission Applications.London:Springer-Verlag,1999.34-170
25 MoréJ J,Garbow B S,Hillstrom K E.User guide for MINPACK-1.Technical Report.Argonne:Argonne National Laboratory,1980
26 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