月面返回最优轨道设计
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摘要
随着航天科技的发展,人类对月球的探索正在日益深入,而我国的探月工程也正在有序而顺利的实施中。月面返回技术是月球探测的一项关键技术,而如何设计返回轨道,如何使返回过程实现燃料消耗尽可能小,成为我国探月工程三期必须要解决的问题。
本文首先对月面返回动力上升段的轨道进行探讨。主要针对航天器月面返回动力上升段燃料消耗问题,综合考虑月球自转,科里奥利力的影响,建立航天器在月球三维空间中的动力学模型。以燃耗最优为指标,利用pontryagin极大值原理,得到航天器在月面返回动力上升段发动机推力方向的最优开环控制律。考虑终点位置和速度约束求解共轭变量初值,最终求得可行的航天器最优轨迹。
本文还对月地转移轨道的相关特性进行了分析和设计。首先在基于月球影响球概念的三维模型下对月地转移轨道有关特性进行了初步的分析。然后对月地转移轨道轨道进行了初步的设计方法研究。最后在分析了各主要摄动力的作用后,在比较精确的动力学模型中进行了月地转移轨道设计。
With the development of aerospace science and technology, the exploration to moon is carried frequently and in deep, and the lunar exploration program of our country has been implementing smoothly and orderly. Returning from the moon is a key technology for the moon exploration, and how to reduce the fuel consumption in the process has become the crucial problem must be resolved in China's lunar exploration third stage program.
Firstly,this article discusses the orbit of the section of the lunar surface back to power up. Face the problem of fuel consumption, considering influence factor of rotation of moon and geostrophic force, precise three dimensional dynamics for lunar probe returning from the moon were presented. To realize the minimal fuel strategy , an optimal control law of the thrust direction was proposed based on the maximum principle. Solving it concerning both velocity and position restrictions, the optimal orbit of returning from the moon was obtained. The research result is valuable to engineering application.
The article also analyze the nature of transfer orbit from moon to earth. Firstly, use the concept of the impacting ball of the moon, in the 3D space, analyze the property of transfer orbit. Through computer simulation, we obtained some of the main parameters correlation curve, finally, Secondly, propose a fast search algorithm for moon-earth transfer orbit; Finally, through the analysis of the effectiveness of each main disturbing force, design the moon-earth transfer orbit with the precisely dynamical model.
本文首先对月面返回动力上升段的轨道进行探讨。主要针对航天器月面返回动力上升段燃料消耗问题,综合考虑月球自转,科里奥利力的影响,建立航天器在月球三维空间中的动力学模型。以燃耗最优为指标,利用pontryagin极大值原理,得到航天器在月面返回动力上升段发动机推力方向的最优开环控制律。考虑终点位置和速度约束求解共轭变量初值,最终求得可行的航天器最优轨迹。
本文还对月地转移轨道的相关特性进行了分析和设计。首先在基于月球影响球概念的三维模型下对月地转移轨道有关特性进行了初步的分析。然后对月地转移轨道轨道进行了初步的设计方法研究。最后在分析了各主要摄动力的作用后,在比较精确的动力学模型中进行了月地转移轨道设计。
With the development of aerospace science and technology, the exploration to moon is carried frequently and in deep, and the lunar exploration program of our country has been implementing smoothly and orderly. Returning from the moon is a key technology for the moon exploration, and how to reduce the fuel consumption in the process has become the crucial problem must be resolved in China's lunar exploration third stage program.
Firstly,this article discusses the orbit of the section of the lunar surface back to power up. Face the problem of fuel consumption, considering influence factor of rotation of moon and geostrophic force, precise three dimensional dynamics for lunar probe returning from the moon were presented. To realize the minimal fuel strategy , an optimal control law of the thrust direction was proposed based on the maximum principle. Solving it concerning both velocity and position restrictions, the optimal orbit of returning from the moon was obtained. The research result is valuable to engineering application.
The article also analyze the nature of transfer orbit from moon to earth. Firstly, use the concept of the impacting ball of the moon, in the 3D space, analyze the property of transfer orbit. Through computer simulation, we obtained some of the main parameters correlation curve, finally, Secondly, propose a fast search algorithm for moon-earth transfer orbit; Finally, through the analysis of the effectiveness of each main disturbing force, design the moon-earth transfer orbit with the precisely dynamical model.
引文
1王大轶,李铁寿,马兴瑞.月球最优软着陆两点边值问题的数值解法.航天控制,2000,(3):44~49.
2周净扬,周荻.月球探测器软着陆精确建模及最优轨道设计.宇航学报,2007,28(6): 1462~1471.
3徐敏,李俊峰.月球探测器软着陆的最优控制.清华大学学报, 2001,41(8):81~ 89.
4 ARMSTRONG E S, SUDDATH J H. Application of pontryagin maximum principle to the lunar orbit rendezvous problem. Langley Station, Hampton, Virginia,USA: NASA Langley Research Center, 1963.
5高玉东,郗晓宁,白玉涛.月球探测器返回轨道快速搜索设计.宇航学报, 2008, 29(5): 765~771.
6白玉涛,郗晓宁,刘磊,王功波.月球探测器返回轨道特性分析.国防科技大学学报. 2008, 30(4):11~16.
7高玉东.月球探测器地月空间转移轨道研究.国防科技大学博士论文. 2008: 48~54
8郗晓宁,曾国强,任萱,赵汉元.月球探测器轨道设计.国防工业出版社,2001
9林胜勇,李珠基,和兴锁.月球卫星轨道设计优化.空间科学学报, 2004 24(5): 360~365.
10和兴锁,林胜勇,张亚峰.月球探测器直接软着陆最优轨道设计.宇航学报, 2007,28(2):409~413
11李立涛,杨涤,崔祜涛.奔月轨道的一种求解方法.宇航学报.2003.24(2). 150~155.
12林晓辉,孙兆伟,杨涤.地月转移轨道快速设计方法研究.哈尔滨工业大学学报. 2005, 37(2):234~237.
13周文艳,杨维廉.月球探测器转移轨道的中途修正.宇航学报.2004,25(1)89~92
14 ARMSTRONG E S, CHILDS A G, MARKOS A T. A method for computing extremal maximum-range thrust-limited rocket trajectories with application tolunar transport[R].USA: NASA, 1970.
15 MIELE A, WANG T, MANCUSO S. Optimal free-return trajectories for moon missions and mars missions . The Journal of the Astronautical Sciences, 2000, 48 (2): 183-206.
16 THORNE J D, HALL C D. Minimum-time continuous-thrust orbit transfer [J].The Journal of the Astronautical Sciences, 1997,45(4):411-432.
17 WILSON J W, SIMONSEN L C, SHINN J L, DUBEY R R, JORDAN W, KIM M.Radiation analysis for the human lunar return mission . Langley Station, Hampton, Virginia, USA: NASA Langley Research Center, 1997.
18 RYAN P, RUSSELL, CESAR A. Geometric analysis of free-Return trajectories following a gravity-assisted flyby. Journal of Spacecraft and Rocket, 2005,42(1):138-151.
19盛英华,张晓东,梁建国,赵金才.载人登月飞行模式研究.宇航学报, 2009,30(1):1~8.
20李爽.星际探测中小推力转移轨道设计与优化方法研究.哈尔滨工业大学博士论文. 2007: 2~18
21乔栋.深空探测转移轨道设计方法研究及在小天体探测中的应用.哈尔滨工业大学博士论文. 2007: 3~27
22郭敏华.月球软着陆的建模与控制.哈尔滨工业大学博士论文,2007
23王大轶.月球软着陆的制导控制研究.哈尔滨工业大学博士论文,2000
24孙军伟.月球探测器自主导航与控制方法研究.哈尔滨工业大学博士论文,2006
25刘宇飞.深空自主导航方法研究及在接近小天体中的应用.哈尔滨工业大学博士论文,2007
26邢继祥,张春蕊徐洪泽.最优控制应用基础. 2003
27崔祜涛,崔平远.软着陆小卫星的自主导航与制导.宇航学报.2002,23(5)
28欧阳自远,李春来,等.深空探测的进展与我国深空探测的发展战略.中国航天,2002 (12).
29郗晓宁等.近地航天器轨道基础.国防科技大学出版社,2003
30章仁为.卫星轨道姿态动力学与控制.北京航空航天大学出版社,1998
31 L. Casalino and G. Colasurdo. Improved Edelbaum’s Approach to Optimize LEO-GEO Low-Thrust Transfers. Journal of Guidance, Control, and Dynamics.2007, 30(5):1504~1510
32 M. Vasile, P.D. Pascale and S. Casotto. On the Optimality of A Shape-Based Approach Based on Pseudo-Equinoctial Elements. Acta Astronautic. 2007, 61(1-6):286~297
33 G. Mengali and A.A. Quarta. Trajectory Design with Hybrid Low-Thrust Propulsion System. Journal of Guidance, Control, and Dynamics. 2007,
30(2):419~426
34 Automated Design Optimization and Trade Studies using STK Scenarios. AIAA Aerospace Sciences Meeting and Exhibit, January 10-13, 2008
35 A. Steltzner. Mars Science Laboratory Entry Descent and Landing System. Paper 1497, 2006 IEEE Aerospace Conference, Big Sky, Montana, March 2006: 345~350
36 Larry Matthies, Andres Huertas, Yang Cheng and Andrew Johnson. Landing Hazard Detection with Stereo Vision and Shadow Analysis. AIAA 2007 Conference and Exhibit, California, 2007:1~10
37 Diego F. Pierrottet, Farzin Amzajerdian.Characterization of 3-D imaging lidar for hazardavoidance and autonomous landing on the Moon. Proceedings of SPIE.2007,6550: 87~92
38崔平远,朱圣英,崔祜涛.小天体软着陆机动控制方法研究.宇航学报. 2008, 29(2): 511~516
39 N. Mastrodemos*, D. G. Kubitschek, S. P. Synnott. Autonomous Navigation For The Deep Impact Mission Encounter With Comet Tempel1.AAS/AIAA Space Flight Mechanics Meeting, Tampa, FL, January 2006:5~12
40 R. B. Frauenholz,“Ground-Based Orbit Determination for Deep Impact.”Paper 06-173, AAS/AIAA 16th Space Flight Mechanics Conference, Tampa, 2006: 5~17
41 S. R. Chesly and D. K. Yeomans,“Comet 9P/Tempel 1 Ephemeris Development for the Deep Impact Mission.”Paper 06-178, AAS/AIAA 16th Space Flight Mechanics Conference, Tampa, 2006: 3~5
42 W. M. Owen, Jr, N. Mastrodemos, B. P. Rush, Tseng-Chang M. Wang, S. D. Gillam, S.Bhaskaran, Optical Navigation for Deep Impact, Paper AAS 06-176. 2006:1~12
2周净扬,周荻.月球探测器软着陆精确建模及最优轨道设计.宇航学报,2007,28(6): 1462~1471.
3徐敏,李俊峰.月球探测器软着陆的最优控制.清华大学学报, 2001,41(8):81~ 89.
4 ARMSTRONG E S, SUDDATH J H. Application of pontryagin maximum principle to the lunar orbit rendezvous problem. Langley Station, Hampton, Virginia,USA: NASA Langley Research Center, 1963.
5高玉东,郗晓宁,白玉涛.月球探测器返回轨道快速搜索设计.宇航学报, 2008, 29(5): 765~771.
6白玉涛,郗晓宁,刘磊,王功波.月球探测器返回轨道特性分析.国防科技大学学报. 2008, 30(4):11~16.
7高玉东.月球探测器地月空间转移轨道研究.国防科技大学博士论文. 2008: 48~54
8郗晓宁,曾国强,任萱,赵汉元.月球探测器轨道设计.国防工业出版社,2001
9林胜勇,李珠基,和兴锁.月球卫星轨道设计优化.空间科学学报, 2004 24(5): 360~365.
10和兴锁,林胜勇,张亚峰.月球探测器直接软着陆最优轨道设计.宇航学报, 2007,28(2):409~413
11李立涛,杨涤,崔祜涛.奔月轨道的一种求解方法.宇航学报.2003.24(2). 150~155.
12林晓辉,孙兆伟,杨涤.地月转移轨道快速设计方法研究.哈尔滨工业大学学报. 2005, 37(2):234~237.
13周文艳,杨维廉.月球探测器转移轨道的中途修正.宇航学报.2004,25(1)89~92
14 ARMSTRONG E S, CHILDS A G, MARKOS A T. A method for computing extremal maximum-range thrust-limited rocket trajectories with application tolunar transport[R].USA: NASA, 1970.
15 MIELE A, WANG T, MANCUSO S. Optimal free-return trajectories for moon missions and mars missions . The Journal of the Astronautical Sciences, 2000, 48 (2): 183-206.
16 THORNE J D, HALL C D. Minimum-time continuous-thrust orbit transfer [J].The Journal of the Astronautical Sciences, 1997,45(4):411-432.
17 WILSON J W, SIMONSEN L C, SHINN J L, DUBEY R R, JORDAN W, KIM M.Radiation analysis for the human lunar return mission . Langley Station, Hampton, Virginia, USA: NASA Langley Research Center, 1997.
18 RYAN P, RUSSELL, CESAR A. Geometric analysis of free-Return trajectories following a gravity-assisted flyby. Journal of Spacecraft and Rocket, 2005,42(1):138-151.
19盛英华,张晓东,梁建国,赵金才.载人登月飞行模式研究.宇航学报, 2009,30(1):1~8.
20李爽.星际探测中小推力转移轨道设计与优化方法研究.哈尔滨工业大学博士论文. 2007: 2~18
21乔栋.深空探测转移轨道设计方法研究及在小天体探测中的应用.哈尔滨工业大学博士论文. 2007: 3~27
22郭敏华.月球软着陆的建模与控制.哈尔滨工业大学博士论文,2007
23王大轶.月球软着陆的制导控制研究.哈尔滨工业大学博士论文,2000
24孙军伟.月球探测器自主导航与控制方法研究.哈尔滨工业大学博士论文,2006
25刘宇飞.深空自主导航方法研究及在接近小天体中的应用.哈尔滨工业大学博士论文,2007
26邢继祥,张春蕊徐洪泽.最优控制应用基础. 2003
27崔祜涛,崔平远.软着陆小卫星的自主导航与制导.宇航学报.2002,23(5)
28欧阳自远,李春来,等.深空探测的进展与我国深空探测的发展战略.中国航天,2002 (12).
29郗晓宁等.近地航天器轨道基础.国防科技大学出版社,2003
30章仁为.卫星轨道姿态动力学与控制.北京航空航天大学出版社,1998
31 L. Casalino and G. Colasurdo. Improved Edelbaum’s Approach to Optimize LEO-GEO Low-Thrust Transfers. Journal of Guidance, Control, and Dynamics.2007, 30(5):1504~1510
32 M. Vasile, P.D. Pascale and S. Casotto. On the Optimality of A Shape-Based Approach Based on Pseudo-Equinoctial Elements. Acta Astronautic. 2007, 61(1-6):286~297
33 G. Mengali and A.A. Quarta. Trajectory Design with Hybrid Low-Thrust Propulsion System. Journal of Guidance, Control, and Dynamics. 2007,
30(2):419~426
34 Automated Design Optimization and Trade Studies using STK Scenarios. AIAA Aerospace Sciences Meeting and Exhibit, January 10-13, 2008
35 A. Steltzner. Mars Science Laboratory Entry Descent and Landing System. Paper 1497, 2006 IEEE Aerospace Conference, Big Sky, Montana, March 2006: 345~350
36 Larry Matthies, Andres Huertas, Yang Cheng and Andrew Johnson. Landing Hazard Detection with Stereo Vision and Shadow Analysis. AIAA 2007 Conference and Exhibit, California, 2007:1~10
37 Diego F. Pierrottet, Farzin Amzajerdian.Characterization of 3-D imaging lidar for hazardavoidance and autonomous landing on the Moon. Proceedings of SPIE.2007,6550: 87~92
38崔平远,朱圣英,崔祜涛.小天体软着陆机动控制方法研究.宇航学报. 2008, 29(2): 511~516
39 N. Mastrodemos*, D. G. Kubitschek, S. P. Synnott. Autonomous Navigation For The Deep Impact Mission Encounter With Comet Tempel1.AAS/AIAA Space Flight Mechanics Meeting, Tampa, FL, January 2006:5~12
40 R. B. Frauenholz,“Ground-Based Orbit Determination for Deep Impact.”Paper 06-173, AAS/AIAA 16th Space Flight Mechanics Conference, Tampa, 2006: 5~17
41 S. R. Chesly and D. K. Yeomans,“Comet 9P/Tempel 1 Ephemeris Development for the Deep Impact Mission.”Paper 06-178, AAS/AIAA 16th Space Flight Mechanics Conference, Tampa, 2006: 3~5
42 W. M. Owen, Jr, N. Mastrodemos, B. P. Rush, Tseng-Chang M. Wang, S. D. Gillam, S.Bhaskaran, Optical Navigation for Deep Impact, Paper AAS 06-176. 2006:1~12