Abstract
The ground-based experimental tests are crucial to verify the related technologies of the drag-free satellite. This work presents a design method of the ground simulator testbed for emulating the planar dynamics of the space drag-free systems. In this paper, the planar dynamic characteristics of the drag-free satellite with double test masses are analyzed and non-dimensionalized. A simulator vehicle composed of an air bearing testbed and two inverted pendulums is devised on the basic of equivalent mass and equivalent stiffness proposed firstly in this paper. And the dynamic model of the simulator equivalent to the sensitive axis motion of the test mass and the planar motion of the satellite is derived from the Euler-Lagrange method. Then, the dynamic equivalence conditions between the space prototype system and the ground model system are derived from Pi theorem. To satisfy these conditions, the scaling laws of two systems and requirements for the inverted pendulum are put forward. Besides, the corresponding control scaling laws and a closed-loop control strategy are deduced and applied to establishing the numerical simulation experiments of underactuated system. Subsequently, the comparative simulation results demonstrate the similarity of dynamical behavior between the scaled-down ground model and the space prototype. As a result, the rationality and effectiveness of the design method are proved, facilitating the ground simulation of future gravitational wave detection satellites.
摘要
为了设计无拖曳卫星相关技术演示验证的地面仿真平台, 本文基于量纲分析和π理论等方法提出了一种与空间无拖曳卫星平面 动力学行为相似的地面模型设计方法. 该方法从双检验质量无拖曳卫星动力学模型中分析出相似特征, 设计了由倒立摆和平面气浮台 组成的地面气浮模拟装置. 文中利用欧拉-拉格朗日方法推导了等效于检验质量敏感轴平动和卫星平面运动的模拟器动力学模型, 得出 地面模型系统等效空间原型系统的动力学等效条件. 此外, 本文首次提出了等效质量和等效刚度的概念, 并在此基础上提出了满足等 效条件的相似律设计要求以及倒立摆的设计要求. 在物理相似性条件下, 本文设计了欠驱动系统的闭环控制策略, 推导出相应的控制 相似律并应用于数值仿真. 最后, 等效缩放后仿真结果与原型仿真结果的对比验证了二者动力学行为具有相似性, 也证明了本文提出 的相似性设计方法的合理性和有效性, 为未来引力波探测计划的无拖曳卫星地面仿真设计提供了更多依据.
Article PDF
Avoid common mistakes on your manuscript.
References
B. Lange, The drag-free satellite, AIAA J. 2, 1590 (1964).
B. Ziegler, and M. Blanke, in Drag-free motion control of satellite for high-precision gravity field mapping: Proceedings of the International Conference on Control Applications, Glasgow, 2002.
T. Edwards, M. C. W. Sandford, and A. Hammesfahr, LISA—a study of the ESA cornerstone mission for observing gravitational waves, Acta Astronaut. 48, 549 (2001).
W. R. Hu, and Y. L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4, 685 (2017).
W. H. Ruan, C. Liu, Z. K. Guo, Y. L. Wu, and R. G. Cai, The LISA–Taiji network, Nat. Astron. 4, 108 (2020).
J. Luo, L. S. Chen, H. Z. Duan, Y. G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, C. G. Shao, V. T. Toth, H. B. Tu, Y. Wang, Y. Wang, H. C. Yeh, M. S. Zhan, Y. Zhang, V. Zharov, and Z. B. Zhou, TianQin: A space-borne gravitational wave detector, Class. Quantum Grav. 33, 035010 (2016).
H. Bock, A. Jäggi, G. Beutler, and U. Meyer, GOCE: Precise orbit determination for the entire mission, J. Geod. 88, 1047 (2014).
J. Li, W. J. Bencze, D. B. DeBra, G. Hanuschak, T. Holmes, G. M. Keiser, J. Mester, P. Shestople, and H. Small, On-orbit performance of Gravity Probe B drag-free translation control and orbit determination, Adv. Space Res. 40, 1 (2007).
A. Schleicher, T. Ziegler, R. Schubert, N. Brandt, P. Bergner, U. Johann, W. Fichter, and J. Grzymisch, In-orbit performance of the LISA Pathfinder drag-free and attitude control system, CEAS Space J. 10, 471 (2018).
Y. L. Wu, Z. R. Luo, J. Y. Wang, M. Bai, W. Bian, R. G. Cai, Z. M. Cai, J. Cao, D. J. Chen, L. Chen, L. S. Chen, M. W. Chen, W. B. Chen, Z. Y. Chen, L. X. Cong, J. F. Deng, X. L. Dong, L. Duan, S. Q. Fan, S. S. Fan, C. Fang, Y. Fang, K. Feng, P. Feng, Z. Feng, R. H. Gao, R. L. Gao, Z. K. Guo, J. W. He, J. B. He, X. Hou, L. Hu, W. R. Hu, Z. Q. Hu, M. J. Huang, J. J. Jia, K. L. Jiang, G. Jin, H. B. Jin, Q. Kang, J. G. Lei, B. Q. Li, D. J. Li, F. Li, H. S. Li, H. W. Li, L. F. Li, W. Li, X. K. Li, Y. M. Li, Y. G. Li, Y. P. Li, Y. P. Li, Z. Li, Z. Y. Lin, C. Liu, D. B. Liu, H. S. Liu, H. Liu, P. Liu, Y. R. Liu, Z. Y. Lu, H. W. Luo, F. L. Ma, L. F. Ma, X. S. Ma, X. Ma, Y. C. Man, J. Min, Y. Niu, J. K. Peng, X. D. Peng, K. Q. Qi, L. É. Qiang, C. F. Qiao, Y. X. Qu, W. H. Ruan, W. Sha, J. Shen, X. J. Shi, R. Shu, J. Su, Y. L. Sui, G. W. Sun, W. L. Tang, H. J. Tao, W. Z. Tao, Z. Tian, L. F. Wan, C. Y. Wang, J. Wang, J. Wang, L. L. Wang, S. X. Wang, X. P. Wang, Y. K. Wang, Z. Wang, Z. L. Wang, Y. X. Wei, Y. X. Di Wu, L. M. Wu, P. Z. Wu, Z. H. Wu, D. X. Xi, Y. F. Xie, G. F. Xin, L. X. Xu, P. Xu, S. Y. Xu, Y. Xu, S. W. Xue, Z. B. Xue, C. Yang, R. Yang, S. J. Yang, S. Yang, Y. Yang, Z. G. Yang, Y. L. Yin, J. P. Yu, T. Yu, À. B. Zhang, C. Zhang, M. Zhang, X. Q. Zhang, Y. Z. Zhang, J. Zhao, W. W. Zhao, Y. Zhao, J. H. Zheng, C. Y. Zhou, Z. C. Zhu, X. B. Zou, and Z. M. Zou, China’s first step towards probing the expanding universe and the nature of gravity using a space borne gravitational wave antenna, Commun. Phys. 4, 34 (2021).
L. Wu, P. Xu, S. Zhao, L. E. Qiang, Z. Luo, and Y. Wu, Global gravity field model from Taiji-1 observations, Microgravity Sci. Technol. 34, 77 (2022).
A. S. Pau, A. Heather, B. Stanislav, B. John, B. Enrico, B. Peter, B. Emanuele, B. Pierre, B. Michael, B. Daniele, C. Jordan, C. Chiara, C. Vitor, C. Monica, C. John, C. Neil, C. Curt, D. Karsten, D. Rita, F. Luigi, F. Valerio, F. Ewan, G. Jonathan, G. B. Lluis, G. Domenico, G. Ferran, G. Catia, H. Hubert, H. Gerhard, H. Tho-Thomas, H. Martin, H. B. Kelly, H. Daniel, H. Mauro, I. Henri, J. Philippe, K. Nikos, K. Christian, K. Antoine, K. Bill, K. Natalia, L. L. Shane, L. Jeffrey, L. Ivan, M. Nary, M. Davor, M. Joseph, M. Ignacio, M. K. Kirk, T. M. W. Sean, M. Cole, M. Guido, N. Germano, N. Gijs, N. Miquel, P. Antoine, P. Paolo, P. Eric, P. Ed, R. Jens, R. David, R. Norna, R. Elena, R. Giuliana, S. Bernard, S. Alberto, S. David, S. Jacob, F. S. Carlos, S. Tim, T. Nicola, T. Ira, T. Michael, V. Michele, V. Alberto, V. Daniele, V. Stefano, V. Marta, W. Gudrun, W. Harry, W. Peter, W. William, Z. John, and Z. Peter, Laser interferometer space antenna, arXiv: 1702.00786.
Z. Luo, Y. Wang, Y. Wu, W. Hu, and G. Jin, The Taiji program: A concise overview, Prog. Theor. Exp. Phys. 2021(5), 05A108 (2021).
Y. Gong, J. Luo, and B. Wang, Concepts and status of Chinese space gravitational wave detection projects, Nat. Astron. 5, 881 (2021).
I. Kawano, M. Mokuno, T. Kasai, and T. Suzuki, First autonomous rendezvous using relative GPS navigation by ETS-VII, Navigation 48, 49 (2001).
M. Wilde, C. Clark, and M. Romano, Historical survey of kinematic and dynamic spacecraft simulators for laboratory experimentation of on-orbit proximity maneuvers, Prog. Aerospace Sci. 110, 100552 (2019).
X. L. Ding, Y. C. Wang, Y. B. Wang, and K. Xu, A review of structures, verification, and calibration technologies of space robotic systems for on-orbit servicing, Sci. China Tech. Sci. 64, 462 (2021).
A. Caon, F. Branz, and A. Francesconi, Development and test of a robotic arm for experiments on close proximity operations, Acta Astronaut. 195, 287 (2022).
L. Zong, and M. R. Emami, Control verifications of space manipulators using ground platforms, IEEE Trans. Aerosp. Electron. Syst. 57, 341 (2021).
S. B. McCamish, M. Romano, S. Nolet, C. M. Edwards, and D. W. Miller, Flight testing of multiple-spacecraft control on SPHERES during close-proximity operations, J. Spacecraft Rockets 46, 1202 (2009).
C. Menon, A. Aboudan, S. Cocuzza, A. Bulgarelli, and F. Angrilli, Free-flying robot tested on parabolic flights: Kinematic control, J. Guidance Control Dyn. 28, 623 (2005).
C. Zhang, C. Yang, L. Hu, S. Chen, Y. Zhao, L. Duan, and Q. Kang, Beijing drop tower microgravity adjustment towards 10−3∼10−5 g level by cold-gas thrusters, Microgravity Sci. Technol. 35, 39 (2023).
S. Chesi, O. Perez, and M. Romano, A dynamic, hardware-in-the-Loop, three-axis simulator of spacecraft attitude maneuvering with nanosatellite dimensions, J. Small Spacecraft. 4, 315 (2015).
M. Ciarcià, R. Cristi, and M. M. Romano, Emulating scaled Clohessy-Wiltshire dynamics on an air-bearing spacecraft simulation testbed, J. Guidance Control Dyn. 40, 2496 (2017).
Y. Eun, S. Y. Park, and G. N. Kim, Development of a hardware-in-the-loop testbed to demonstrate multiple spacecraft operations in proximity, Acta Astronaut. 147, 48 (2018).
B. R. Fernandez, L. Herrera, J. Hudson, and M. Romano, Development of a tip-tilt air-bearing testbed for physically emulating proximity-flight orbital mechanics, Adv. Space Res. 71, 4332 (2023).
C. Zhang, J. He, M. Chen, L. Duan, and Q. Kang, Ground semiphysical simulation experiment study of one-dimensional drag-free control, Int. J. Mod. Phys. A 36, 2140016 (2021).
C. Yang, J. W. He, L. Duan, and Q. Kang, A torsional thrust stand for measuring the thrust response time of micro-Newton thrusters, Int. J. Mod. Phys. A 36, 2140015 (2021).
A. Sonin, The Physical Basis of Dimensional Analysis, 2nd ed. (Department of Mechanical Engineering, MIT, Cambridge, 2001). pp. 29–43.
E. Buckingham, On physically similar systems; illustrations of the use of dimensional equations, Phys. Rev. 4, 345 (1914).
I. I. Zappulla Richard, J. Virgili-Llop, C. Zagaris, H. Park, and M. Romano, Dynamic air-bearing hardware-in-the-loop testbed to experimentally evaluate autonomous spacecraft proximity maneuvers, J. Spacecraft Rockets 54, 825 (2017).
N. M. J. Woodhouse, Lagrangian mechanics, in: Introduction to Analytical Dynamics: Revised Edition, edited by N. Woodhouse (Springer, London, 2009). pp. 67–98.
A. Naceri, N. Boccardo, L. Lombardi, A. Marinelli, D. Hidalgo, S. Haddadin, M. Laffranchi, and L. De Michieli, From human to robot grasping: Force and kinematic synergies, in: Tactile Sensing, Skill Learning, and Robotic Dexterous Manipulation (Elsevier, 2022). pp. 133–148.
T. A. Johansen, and T. I. Fossen, Control allocation—A survey, Automatica 49, 1087 (2013).
Acknowledgements
The work was supported by the National Key Research and Development Program of China (Grant No. 2021YFC2202604), and the Strategy Priority Research Program of Chinese Academy of Sciences (Grant No. XDA1502110101).
Author information
Authors and Affiliations
Contributions
Author contributions All authors have contributed to the study of concepts and design. Mingwei Chen wrote the first draft of the manuscript. Chu Zhang helped organize the manuscript. Chu Zhang and Jianwu He provided the original idea. Chao Yang provided necessary simulation materials. Mingwei Chen completed the simulation and processed the data. Li Duan and Qi Kang offered guidance and support.
Corresponding author
Ethics declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Chen, M., Zhang, C., He, J. et al. Dynamic equivalence conditions for an air-bearing simulator emulating scaled drag-free control dynamics. Acta Mech. Sin. 41, 524026 (2025). https://doi.org/10.1007/s10409-024-24026-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10409-024-24026-x