月面软着陆的制导与控制方法研究
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摘要
月面软着陆是人类进行月球探测面临的一个关键性问题,而导航、制导与控制又是月面软着陆的关键性技术。本文以国家自然科学基金重点资助项目“月球探测系统的建模、传感、导航和控制基础理论及关键技术研究”为背景,在系统总结这一领域研究现状的基础上,应用最优控制与非线性控制方法,依照最优性、稳定性的要求,针对登月飞行器定点软着陆的制导与控制,进行了深入研究。
本文研究重点是设计飞行器软着陆过程的动力下降段和最终着陆段的制导律和控制律。主要分为两大部分:第一部分是动力下降段的燃料最优制导律的设计,第二部分是最终着陆段姿轨联合控制律的设计。
首先,针对月面定点软着陆问题,在考虑月球自转和登月飞行器侧向移动的基础上,基于落点坐标系建立了登月飞行器动力下降段三维动力学模型。随后,根据飞行器姿态运动学和动力学特性,建立了姿态动力学模型。并在此基础上,分析了姿态与轨道耦合关系,建立了飞行器姿轨耦合动力学模型。
其次,考虑到控制信号的幅值限制、状态约束和终端约束等要求,对动力下降段的燃料最优控制问题进行了研究。利用约束变换技术将该问题转化为标准的具有不等式约束和终端约束的非线性最优控制问题。然后利用时间尺度变换技术和强化技术将标准的规范型最优控制问题转化为静态参数优化问题,随后采用经典的优化方法,利用优化软件MISER3.2可以得到最优连续解的一组分段线性逼近解,即分段参数化控制器,并给出了仿真结果。
基于获得的参数化最优解,得到轨控发动机最优推力大小和最优推力方向。由于轨控发动机固联于飞行器机体,推力方向通过姿态调整实现。因此,为保证在动力下降过程中轨控发动机的燃料最优推力方向,设计了姿态跟踪控制律。通过仿真,验证了姿态跟踪控制律的有效性,并分析了由于姿态跟踪存在的延迟性对动力下降过程带来的影响。
最后,为进一步提高软着陆的着陆精度和机动性,针对飞行器软着陆的最终着陆段,基于姿态轨道耦合动力学模型,提出了姿态轨道联合控制律,并证明了闭环系统的渐进稳定性。最后通过仿真,与传统的最终着陆方法进行对比,验证了所提出的姿轨联合控制着陆方案的有效性和优越性。
Lunar soft landing is a key problem of the whole lunar exploration. Moreover, Guidance, Navigation and Control (GNC) are the vital techniques. With the National Natural Science Foundation of key projects“Research on basic theories and key technologies of modeling, sensing, navigation and control of lunar exploration systems”, based on precursors’results, this dissertation systematically studies the guidance and control of the pinpoint soft lunar landing with the methods of optimal control, nonlinear control.
This paper mainly contains two parts: The design of the fuel optimal guidance law for the powered descending phase while another part is the design of the integrated translational and attitude control law for the terminal landing phase.
At first, with the consideration of the moon self-rotation and the lateral movement of the lunar module, based on the target coordinate frame, the three dimensional accurate dynamic model of the lunar module is derived. Then, the attitude dynamic model of the module is also obtained. With the analysis of the coupled relation between the orbit and attitude, the integrated translational and attitude coupled dynamic model of the module is derived.
With the constraint transformation and enhancing technique, the fuel optimal control problem for the powered descending phase is transformed into a static parametric optimal problem, by using the optimal software MISER3.2, the piecewise parametric guidance law is derived and the numerical simulation shows the validity of the method.
Next, according to the optimal guidance law, the optimal magnitude and direction of the thruster is derived. Because the thruster position on the module is fixed, the change of thruster direction is fulfilled with the attitude system. Hence, to ensure the right thruster direction in the powered descending phase, the attitude tracking control law is designed and the simulation proves its validity. Apart from these, for the whole integrated translational and attitude coupled system, the influence caused by the time-delay in attitude tracking system is also analyzed.
At last, to improve the landing precision and flexibility in the terminal landing phase, based on the coupled nonlinear model of the module, the integrated translational and control law is designed. With the Lyapunov’s stability theorem, the closed-loop system proves asymptotically stable. The comparison with the traditional terminal landing strategy in the simulation shows the superiority and validity of the integrated control law.
本文研究重点是设计飞行器软着陆过程的动力下降段和最终着陆段的制导律和控制律。主要分为两大部分:第一部分是动力下降段的燃料最优制导律的设计,第二部分是最终着陆段姿轨联合控制律的设计。
首先,针对月面定点软着陆问题,在考虑月球自转和登月飞行器侧向移动的基础上,基于落点坐标系建立了登月飞行器动力下降段三维动力学模型。随后,根据飞行器姿态运动学和动力学特性,建立了姿态动力学模型。并在此基础上,分析了姿态与轨道耦合关系,建立了飞行器姿轨耦合动力学模型。
其次,考虑到控制信号的幅值限制、状态约束和终端约束等要求,对动力下降段的燃料最优控制问题进行了研究。利用约束变换技术将该问题转化为标准的具有不等式约束和终端约束的非线性最优控制问题。然后利用时间尺度变换技术和强化技术将标准的规范型最优控制问题转化为静态参数优化问题,随后采用经典的优化方法,利用优化软件MISER3.2可以得到最优连续解的一组分段线性逼近解,即分段参数化控制器,并给出了仿真结果。
基于获得的参数化最优解,得到轨控发动机最优推力大小和最优推力方向。由于轨控发动机固联于飞行器机体,推力方向通过姿态调整实现。因此,为保证在动力下降过程中轨控发动机的燃料最优推力方向,设计了姿态跟踪控制律。通过仿真,验证了姿态跟踪控制律的有效性,并分析了由于姿态跟踪存在的延迟性对动力下降过程带来的影响。
最后,为进一步提高软着陆的着陆精度和机动性,针对飞行器软着陆的最终着陆段,基于姿态轨道耦合动力学模型,提出了姿态轨道联合控制律,并证明了闭环系统的渐进稳定性。最后通过仿真,与传统的最终着陆方法进行对比,验证了所提出的姿轨联合控制着陆方案的有效性和优越性。
Lunar soft landing is a key problem of the whole lunar exploration. Moreover, Guidance, Navigation and Control (GNC) are the vital techniques. With the National Natural Science Foundation of key projects“Research on basic theories and key technologies of modeling, sensing, navigation and control of lunar exploration systems”, based on precursors’results, this dissertation systematically studies the guidance and control of the pinpoint soft lunar landing with the methods of optimal control, nonlinear control.
This paper mainly contains two parts: The design of the fuel optimal guidance law for the powered descending phase while another part is the design of the integrated translational and attitude control law for the terminal landing phase.
At first, with the consideration of the moon self-rotation and the lateral movement of the lunar module, based on the target coordinate frame, the three dimensional accurate dynamic model of the lunar module is derived. Then, the attitude dynamic model of the module is also obtained. With the analysis of the coupled relation between the orbit and attitude, the integrated translational and attitude coupled dynamic model of the module is derived.
With the constraint transformation and enhancing technique, the fuel optimal control problem for the powered descending phase is transformed into a static parametric optimal problem, by using the optimal software MISER3.2, the piecewise parametric guidance law is derived and the numerical simulation shows the validity of the method.
Next, according to the optimal guidance law, the optimal magnitude and direction of the thruster is derived. Because the thruster position on the module is fixed, the change of thruster direction is fulfilled with the attitude system. Hence, to ensure the right thruster direction in the powered descending phase, the attitude tracking control law is designed and the simulation proves its validity. Apart from these, for the whole integrated translational and attitude coupled system, the influence caused by the time-delay in attitude tracking system is also analyzed.
At last, to improve the landing precision and flexibility in the terminal landing phase, based on the coupled nonlinear model of the module, the integrated translational and control law is designed. With the Lyapunov’s stability theorem, the closed-loop system proves asymptotically stable. The comparison with the traditional terminal landing strategy in the simulation shows the superiority and validity of the integrated control law.
引文
1 B. H. Foing, G. D. Racca, A. Marini and et.al. SMART-1: Mission to the Moon: Technology and Science Goals. Advanced Space Research. 2003, 31(11): 2323-2333
2卢波.月球探测的意义及发展态势.国际太空. 1998, 4(1):1-4
3 F. H. Bernard, Lunar Exploration, Planetary and space science, 2002, 50: V-VI
4王景全,宋智. 21世纪国际与行星探测的发展趋势.国际太空. 1998, (4):4-9
5 Q. Yan, W. J. Gao, F. Liu. Technology of Surveying and Mapping in Moon Exploring. Science of Surveying and Mapping. 2004, 29(4):63-68
6 Carrico J, Carrington D, Hametz M. Maneuver Planning and Results for Clementine. AAS 95-129: 477-499
7 Kaufman B, Middour J, Richon K. Mission Design of the Clementine Space Experiment. AAS 95-124: 407-422
8 Middour J, Hope A, Dasenbrock R. Trajectory and Maneuver Planning Products and Procedures for Clementine Operations. AAS 95-125
9栾恩杰.中国探月工程—中国航天第三个里程碑.中国航天. 2007, 02: 3-7
10王大轶.月球软着陆的制导控制研究.哈尔滨工业大学博士学位论文. 2000: 2-10
11曾国强.月球探测器轨道动力学和制导方法研究.国防科技大学博士论文. 2002: 4-20
12 R.K. Cheng. Lunar Terminal Guidance, Lunar Missions and Exploration. Wiley, New York. 1964: 305-355
13 J. A. Jungmann. The Exact Analytic Solution of the Lunar Landing Problem. AAS Spacecraft Mechnics Specialists Conference, USA, 1967, 11:381-397
14 S. J. Citron. A Terminal Guidance Technique for Lunar Landing. AIAA Journal. 1964, 2:503-509
15 D. Y. Wang, T.S. Li, H. Yan and X.R. Ma. A Suboptimal Fuel Guidance Law for Lunar Soft Landing. Journal of Astronautics. 2000, 21: 55-63
16 C. N. Souza. An Optimal Guidance Law for Planetary Landing. AIAA Guidance, Navigation and Control Conference, USA. 1997, 1376-1381
17 Y. C. Tian. Automatic Control Algorithm of Spacecraft Fixed-point Landing. Journal of Astronautics. 1998, 19(2):86-90
18徐延万.控制系统.导弹与航天丛书.宇航出版社. 1989:19-23
19 X. L. Liu, G. R. Duan, K. L. Teo. Optimal Soft Landing Control for Moon Lander. Automatica. 2008, 44:1097-1103
20 K. Uchiyama. Guidance Law for Lunar Lander with Input Contraint. AIAA Guidance, Navigation and Control Conference and Exhibit, South Carolina. 2007, AIAA 2007-6848.
21 J.Y. Zhou, D. Zhou, G.R. Duan. Opimal Orbit Design of Lunar Modules Soft Landing. Proc of the 25th Chinese Control Conference, Harbin, 2006.
22朱建丰,徐世杰.基于自适应模拟退火算法的月球软着陆轨迹优化.航空学报. 2007, 28(4):806-812
23段佳佳,徐世杰,朱建丰.基于蚁群算法的月球软着陆轨迹优化.宇航学报. 2008, 29(2): 476-481
24王鹏基.月球软着陆下降轨迹与制导律优化设计及研究.宇航学报. 2007, 28(5): 1175-1179
25单永正,段广仁,刘宏亮.月球探测器软着陆最优末制导策略.航天控制. 2006, 24(5):31-34
26刘浩敏,冯军华,崔祜涛.月球软着陆制导律设计及其误差分析.系统仿真学报. 2009, 21(4):936-943
27王鹏基.月球软着陆接近段最优开关制导律设计分析.导弹与航天运载技术. 2007, 4:1-4
28王鹏基.月球软着陆飞行动力学和制导控制建模与仿真.中国科学(E辑). 2009, 39(3): 521-527
29孙军伟,乔栋,崔平远.基于SQP方法的常推力月球软着陆轨道优化方法.宇航学报. 2006:99-104
30林胜勇.变推力月球软着陆制导优化研究.航天控制. 2008, 26(5):22-27
31 Xiangyu Huang, Dayi Wang. Autonomous Navigation and Guidance for Pinpoint Lunar Soft Landing. Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, Decenmber 15-18, 2007, Sanya, China: 1148-1154
32 Dayi Wang, Xiangyu Huang, Yifeng Guan. GNC System Scheme for Lunar Soft Landing Spacecraft. Advances in Space Reaseach. 2008, 42:379-385
33 Liu Xinglong, Duan Guangren. Nonlinear Optimal Control for the Soft Landing of Lunar Landers. Journal of Astronautics. 2007,28(4):921-927
34 J. H. Lee, J. C. Geromel. Quadratic Stablization of Linear Systems with Frobenius Norm Bounded Uncertainties. IEEE Transaction on Automatic. Control. 1996,41(3):453-456
35 P. L. Peres, J. C. Geromel. Quadractic Stablization of Linear Uncetain Systems in Convex Bounded Domains. Automatica. 1993, 29(2):491-493
36 B. Wie, K. W. Warren. New Approach to Attitude Momentum Control for the Space Station. Journal of Guidance, Control and Dynamics. 1989, (12):714-722
37 C. H. Won. Parameter Robust Risk-Sensitive Control Synthesis for a Satellite with Structured Parameter Uncertainties. The journal of the Astronautical Sciences. 1999, (47):117-132
38 S. N. Singh, T. C. Bossart. Exact Feedback Linearization and Control of Space Satation Using CMG. IEEE Trans on Automatic Control. 1993, 38(1):184-187
39徐帆.某型卫星姿态控制系统设计及仿真研究.哈尔滨工业大学硕士论文. 2006:23-25
40 Y. P. Chen, S. C. Lo. Sliding-mode Controller Design for Spacecraft with Actuator Dynamics. International Conference on Control. Automation and System. 1993, 29:1328-1333
41 Y. J. Chen, J. H. Keum, E. S. Sim. Sliding Mode Control of Spacecraft with Actuator Dynamics. International Conference on Control. Automation and Systems. 2001:642-646
42 J. Ahmed, V. T. Coppola, D. S. Bemstein. Asymptotic Tracking of Spacecraft Attiitude Motion with Inertia Matrix Identification. Procceedings of the 36th IEEE Conference on Decision and Control, San Diego, USA.1997:2471-2476
43 Q. M. Lam, R. N. Morgan. Spacecraft Control Law Design Using Lyapunov based Adaptive Controllers. The 1st IEEE Conference on Control Application. Dayton, USA. 1992:348-350
44 H.W.J. Lee, K.L. Teo, and L.S. Jennings. Control Parameterization Enhancing Technique for Time Optimal Control Problem. Dynamical Systems, 1997, 6: 243-261
45哈尔滨工业大学理论力学教研室.理论力学(I).高等教育出版社, 2004: 80-179
46刘暾,赵钧.空间飞行器动力学.哈尔滨工业大学出版社. 2003:153-166
47章仁为.卫星轨道姿态动力学与控制.北京航天航空大学出版社. 1998:137-149
48 K. L. Teo, C. J. Goh and K. H. Wong. A Unified Computational Approach to Optimal Control Problems. Longman Scientific and Technical, England, 1991
49 L. S. Jennings and K. L. Teo. A computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica. 1990,26:371-375
50 K. L. Teo, V. Rehbock and L. S. Jennings, A New Computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica. 1993, 29:789-792
51 L.S. Jennings, K.L. Teo, C.J. Goh. MISER3.2 Optimal Control Software: Theory and User Manuals. Department of Mathematics, the University of Western Australia, Australia. 1997
52 Hassan K. Khalil. Nonlinear Systems. Third Edition. Publishing House of Electronics Industry. 2002:78-130
2卢波.月球探测的意义及发展态势.国际太空. 1998, 4(1):1-4
3 F. H. Bernard, Lunar Exploration, Planetary and space science, 2002, 50: V-VI
4王景全,宋智. 21世纪国际与行星探测的发展趋势.国际太空. 1998, (4):4-9
5 Q. Yan, W. J. Gao, F. Liu. Technology of Surveying and Mapping in Moon Exploring. Science of Surveying and Mapping. 2004, 29(4):63-68
6 Carrico J, Carrington D, Hametz M. Maneuver Planning and Results for Clementine. AAS 95-129: 477-499
7 Kaufman B, Middour J, Richon K. Mission Design of the Clementine Space Experiment. AAS 95-124: 407-422
8 Middour J, Hope A, Dasenbrock R. Trajectory and Maneuver Planning Products and Procedures for Clementine Operations. AAS 95-125
9栾恩杰.中国探月工程—中国航天第三个里程碑.中国航天. 2007, 02: 3-7
10王大轶.月球软着陆的制导控制研究.哈尔滨工业大学博士学位论文. 2000: 2-10
11曾国强.月球探测器轨道动力学和制导方法研究.国防科技大学博士论文. 2002: 4-20
12 R.K. Cheng. Lunar Terminal Guidance, Lunar Missions and Exploration. Wiley, New York. 1964: 305-355
13 J. A. Jungmann. The Exact Analytic Solution of the Lunar Landing Problem. AAS Spacecraft Mechnics Specialists Conference, USA, 1967, 11:381-397
14 S. J. Citron. A Terminal Guidance Technique for Lunar Landing. AIAA Journal. 1964, 2:503-509
15 D. Y. Wang, T.S. Li, H. Yan and X.R. Ma. A Suboptimal Fuel Guidance Law for Lunar Soft Landing. Journal of Astronautics. 2000, 21: 55-63
16 C. N. Souza. An Optimal Guidance Law for Planetary Landing. AIAA Guidance, Navigation and Control Conference, USA. 1997, 1376-1381
17 Y. C. Tian. Automatic Control Algorithm of Spacecraft Fixed-point Landing. Journal of Astronautics. 1998, 19(2):86-90
18徐延万.控制系统.导弹与航天丛书.宇航出版社. 1989:19-23
19 X. L. Liu, G. R. Duan, K. L. Teo. Optimal Soft Landing Control for Moon Lander. Automatica. 2008, 44:1097-1103
20 K. Uchiyama. Guidance Law for Lunar Lander with Input Contraint. AIAA Guidance, Navigation and Control Conference and Exhibit, South Carolina. 2007, AIAA 2007-6848.
21 J.Y. Zhou, D. Zhou, G.R. Duan. Opimal Orbit Design of Lunar Modules Soft Landing. Proc of the 25th Chinese Control Conference, Harbin, 2006.
22朱建丰,徐世杰.基于自适应模拟退火算法的月球软着陆轨迹优化.航空学报. 2007, 28(4):806-812
23段佳佳,徐世杰,朱建丰.基于蚁群算法的月球软着陆轨迹优化.宇航学报. 2008, 29(2): 476-481
24王鹏基.月球软着陆下降轨迹与制导律优化设计及研究.宇航学报. 2007, 28(5): 1175-1179
25单永正,段广仁,刘宏亮.月球探测器软着陆最优末制导策略.航天控制. 2006, 24(5):31-34
26刘浩敏,冯军华,崔祜涛.月球软着陆制导律设计及其误差分析.系统仿真学报. 2009, 21(4):936-943
27王鹏基.月球软着陆接近段最优开关制导律设计分析.导弹与航天运载技术. 2007, 4:1-4
28王鹏基.月球软着陆飞行动力学和制导控制建模与仿真.中国科学(E辑). 2009, 39(3): 521-527
29孙军伟,乔栋,崔平远.基于SQP方法的常推力月球软着陆轨道优化方法.宇航学报. 2006:99-104
30林胜勇.变推力月球软着陆制导优化研究.航天控制. 2008, 26(5):22-27
31 Xiangyu Huang, Dayi Wang. Autonomous Navigation and Guidance for Pinpoint Lunar Soft Landing. Proceedings of the 2007 IEEE International Conference on Robotics and Biomimetics, Decenmber 15-18, 2007, Sanya, China: 1148-1154
32 Dayi Wang, Xiangyu Huang, Yifeng Guan. GNC System Scheme for Lunar Soft Landing Spacecraft. Advances in Space Reaseach. 2008, 42:379-385
33 Liu Xinglong, Duan Guangren. Nonlinear Optimal Control for the Soft Landing of Lunar Landers. Journal of Astronautics. 2007,28(4):921-927
34 J. H. Lee, J. C. Geromel. Quadratic Stablization of Linear Systems with Frobenius Norm Bounded Uncertainties. IEEE Transaction on Automatic. Control. 1996,41(3):453-456
35 P. L. Peres, J. C. Geromel. Quadractic Stablization of Linear Uncetain Systems in Convex Bounded Domains. Automatica. 1993, 29(2):491-493
36 B. Wie, K. W. Warren. New Approach to Attitude Momentum Control for the Space Station. Journal of Guidance, Control and Dynamics. 1989, (12):714-722
37 C. H. Won. Parameter Robust Risk-Sensitive Control Synthesis for a Satellite with Structured Parameter Uncertainties. The journal of the Astronautical Sciences. 1999, (47):117-132
38 S. N. Singh, T. C. Bossart. Exact Feedback Linearization and Control of Space Satation Using CMG. IEEE Trans on Automatic Control. 1993, 38(1):184-187
39徐帆.某型卫星姿态控制系统设计及仿真研究.哈尔滨工业大学硕士论文. 2006:23-25
40 Y. P. Chen, S. C. Lo. Sliding-mode Controller Design for Spacecraft with Actuator Dynamics. International Conference on Control. Automation and System. 1993, 29:1328-1333
41 Y. J. Chen, J. H. Keum, E. S. Sim. Sliding Mode Control of Spacecraft with Actuator Dynamics. International Conference on Control. Automation and Systems. 2001:642-646
42 J. Ahmed, V. T. Coppola, D. S. Bemstein. Asymptotic Tracking of Spacecraft Attiitude Motion with Inertia Matrix Identification. Procceedings of the 36th IEEE Conference on Decision and Control, San Diego, USA.1997:2471-2476
43 Q. M. Lam, R. N. Morgan. Spacecraft Control Law Design Using Lyapunov based Adaptive Controllers. The 1st IEEE Conference on Control Application. Dayton, USA. 1992:348-350
44 H.W.J. Lee, K.L. Teo, and L.S. Jennings. Control Parameterization Enhancing Technique for Time Optimal Control Problem. Dynamical Systems, 1997, 6: 243-261
45哈尔滨工业大学理论力学教研室.理论力学(I).高等教育出版社, 2004: 80-179
46刘暾,赵钧.空间飞行器动力学.哈尔滨工业大学出版社. 2003:153-166
47章仁为.卫星轨道姿态动力学与控制.北京航天航空大学出版社. 1998:137-149
48 K. L. Teo, C. J. Goh and K. H. Wong. A Unified Computational Approach to Optimal Control Problems. Longman Scientific and Technical, England, 1991
49 L. S. Jennings and K. L. Teo. A computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica. 1990,26:371-375
50 K. L. Teo, V. Rehbock and L. S. Jennings, A New Computational Algorithm for Functional Inequality Constrained Optimization Problems. Automatica. 1993, 29:789-792
51 L.S. Jennings, K.L. Teo, C.J. Goh. MISER3.2 Optimal Control Software: Theory and User Manuals. Department of Mathematics, the University of Western Australia, Australia. 1997
52 Hassan K. Khalil. Nonlinear Systems. Third Edition. Publishing House of Electronics Industry. 2002:78-130