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No AccessFull-Length Paper

Solar Radiation Pressure Hamiltonian Feedback Control for Unstable Libration-Point Orbits

Published Online:https://doi.org/10.2514/1.G002090

This work investigates a Hamiltonian structure-preserving control that uses the acceleration of solar radiation pressure for the stabilization of unstable periodic orbits in the circular restricted three-body problem. This control aims to stabilize the libration-point orbits in the sense of Lyapunov by achieving simple stability. It also preserves the Hamiltonian nature of the controlled system. The Hamiltonian structure-preserving control is then extended to a general case in which complex and conjugate eigenvalues occur at high-amplitude orbits. High-amplitude orbits are currently of interest to the European Space Agency for future libration-point orbit missions because they require a lower insertion Δv compared to low-amplitude orbits. Based on the design of the feedback control, the purpose of this work is to verify when the use of solar radiation pressure is feasible and to determine the structural requirements and the spacecraft’s pointing accuracy.

References

  • [1] Szebehely V., Theory of Orbits in the Restricted Problem of Three Bodies, Academic Press, New York, 1967, Chaps. 1, 7. Google Scholar

  • [2] Gordon S. C., “Orbit Determination Error Analysis and Comparison of Station-Keeping Costs for Lissajousw and Halo-Type Libration Point Orbits and Sensitivity Analysis Using Experimental Design Techniques,” NASA Rept.  N93-24721, Feb. 1993, pp. 395–409. Google Scholar

  • [3] Perozzi E. and Ferraz-Mello S., Space Manifold Dynamics: Novel Spaceways for Science and Exploration, Springer, New York, 2010, Chaps. 1, 7. doi:https://doi.org/10.1007/978-1-4419-0348-8 CrossrefGoogle Scholar

  • [4] Farquhar R. W., “Halo-Orbit and Lunar-Swingby Missions of the 1990’s,” Acta Astronautica, Vol. 24, 1991, pp. 227–234. doi:https://doi.org/10.1016/0094-5765(91)90170-A AASTCF 0094-5765 CrossrefGoogle Scholar

  • [5] Olive J. P., Overbeek T. V. and Fleck B., “SOHO Monthly Trending Report,” The Space Academy Foundation Rept.  SOHO/PRG/TR/769, Rome, Italy, 2013. Google Scholar

  • [6] Bauske R., “Operational Manoeuvre Optimization for the ESA Missions Herschel and Planck,” Proceedings of the 21st International Symposium on Space Flight Dynamics (ISSFD), CNES, Toulouse, France, Sept. 2009, http://issfd.org/. Google Scholar

  • [7] Hechler M. and Cobos J., “Herschel, Planck and Gaia Orbit Design,” Proceedings of the 7th International Conference on Libration Point Orbits and Application, Worlds Scientific Publ., Singapore, 2003, pp. 115–126. Google Scholar

  • [8] Canalias E., Gómez G., Marcote M. and Masdemont J. J., “Assessment of Mission Design Including Utilization of Libration Points and Weak Stability Boundaries,” Department de Matematica Aplicada, UPC, Ariadna Id: 03/4103, 2004, https://pdfs.semanticscholar.org/1bb5/1a1cc954a1d1fa02ef4003ba4c61e50f29c8.pdf. Google Scholar

  • [9] Hénon M., “Numerical Exploration of the Restricted Problem. V,” Astronomy and Astrophysics, Vol. 1, 1968, pp. 223–238. Google Scholar

  • [10] Franz H., “Wind Lunar Backflip and Distant Prograde Orbit Implementation,” Proceedings of the AAS/AIAA Spaceflight Mechanics, Vol. 108, No. 1, 2001, pp. 999–1017. Google Scholar

  • [11] Lara M. and Russell R. P., “On the Family g of the Restricted Three-Body Problem,” Recoge los contenidos presentados a: Jornadas de Trabajo en Mecánica Celeste (9. 2006. Jaca), Monography of the Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de, edited by Latasa M. P. P. and Sanchez A. E., No. 30, Zaragoza, 2007, pp. 51–65. Google Scholar

  • [12] Farrés A., Jorba Á., Mondelo J. M. and Villac B., “Periodic Motion for an Imperfect Solar Sail Near an Asteroid,” The 3rd International Symposium on Solar Sailing, Glasgow, Scotland, U.K., June 2013. Google Scholar

  • [13] Scheeres D. J., Orbital Motion in Strongly Perturbed Environments, Springer, New York, 2012, p. 350, Chap. 18. CrossrefGoogle Scholar

  • [14] Noam T., Karen R., David F. and Kimberly T., “Using Solar Radiation Pressure to Control L2 Orbits,” Proceedings of the AAS/GFC International Symposium on Space Flight Dynamics, Vol. 100, Advances in the Astronautical Sciences, Univelt, Inc., CA, May 1998, pp. 617–627. Google Scholar

  • [15] Sohon R. L., “Attitude Stabilization by Means of Solar Radiation Pressure,” ARS Journal, Vol. 29, No. 5, 1995, pp. 371–373. doi:https://doi.org/10.1016/0038-092X(59)90167-7 ARSJAY 0097-4056 Google Scholar

  • [16] Xin M., Balakrishnan S. N. and Pernicka H. J., “Libration Point Stationkeeping Using the θ-D Technique,” Journal of the Astronautical Sciences, Vol. 56, No. 2, 2008, pp. 231–250. doi:https://doi.org/10.1007/BF03256550 JALSA6 0021-9142 CrossrefGoogle Scholar

  • [17] Shahid K. and Kumar K. D., “Spacecraft Formation Control at the Sun-Earth L2 Libration Point Using Solar Radiation Pressure,” Journal of Spacecraft and Rockets, Vol. 47, No. 4, 2010, pp. 614–626. doi:https://doi.org/10.2514/1.47342 JSCRAG 0022-4650 LinkGoogle Scholar

  • [18] Gómez G., Llibre J., Matinez R., Simó C. and Rodriguez J., “On the Optimal Station Keeping Control of Halo Orbits,” Acta Astronautica, Vol. 15, No. 6, 1987, pp. 391–397. doi:https://doi.org/10.1016/0094-5765(87)90175-5 AASTCF 0094-5765 Google Scholar

  • [19] Gómez G., Llibre J., Matínez R. and Simó C., Dynamics and Mission Design Near Libration Points—Volume I: Fundamentals: The Case of Collinear Libration Points, Vol. 2, World Scientific Monograph Series in Mathematics, World Scientific, Singapore, ROS, 2001, pp. 181–183. Google Scholar

  • [20] Howell K. C. and Pernicka H. J., “Stationkeeping Method for Libration Point Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 16, No. 1, 1993, pp. 151–159. doi:https://doi.org/10.2514/3.11440 JGCODS 0731-5090 LinkGoogle Scholar

  • [21] Keeter M., “Station-Keeping Strategies for Libration Point Orbits: Target Points and Floquét Mode Approaches,” M.S. Thesis, Purdue Univ., West Lafayette, IN, 1994. Google Scholar

  • [22] McInnes A. I. S., “Strategies for Solar Sail Mission Design in the Circular Restricted Three-Body Problem,” M.S. Thesis, Purdue Univ., West Lafayette, IN, 2000. Google Scholar

  • [23] Farrés A. and Jorba Á., “A Dynamical System Approach for the Station Keeping of a Solar Sail,” Journal of the Astronautical Sciences, Vol. 56, No. 2, 2008, pp. 199–230. doi:https://doi.org/10.1007/BF03256549 Google Scholar

  • [24] Farrés A. and Jorba Á., “Dynamics of a Solar Sail Near a Halo Orbit,” Acta Astronautica, Vol. 67, Nos. 7–8, 2010, pp. 979–990. doi:https://doi.org/10.1016/j.actaastro.2010.05.022 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [25] Ceriotti M. and Farrés A., “Solar Sail Station Keeping of High-Amplitude Vertical Lyapunov Orbits in the Sun-Earth System,” The 63rd International Astronautical Congress, Italian Space Agency IAC-12.C1.1.11, Naples, Italy, Oct. 2012. Google Scholar

  • [26] Farrés A. and Jorba Á., “Station Keeping of a Solar Sail Around a Halo Orbit,” Acta Astronautica, Vol. 94, No. 1, 2014, pp. 527–539. doi:https://doi.org/10.1016/j.actaastro.2012.07.002 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [27] Scheeres D. J., Hsiao F. Y. and Vinh N. X., “Stabilizing Motion Relative to an Unstable Orbit: Applications to Spacecraft Formation Flight,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, Jan. 2003, pp. 62–73. doi:https://doi.org/10.2514/2.5015 JGCODS 0731-5090 LinkGoogle Scholar

  • [28] Xu M. and Xu S., “Structure-Preserving Stabilization for Hamiltonian System and Its Applications in Solar Sail,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 3, May 2009, pp. 997–1004. doi:https://doi.org/10.2514/1.34757 JGCODS 0731-5090 LinkGoogle Scholar

  • [29] Bookless J. and McInnes C., “Control of Lagrange Point Orbits Using Solar Sail Propulsion,” Acta Astronautica, Vol. 62, Nos. 2–3, 2008, pp. 159–176. doi:https://doi.org/10.1016/j.actaastro.2006.12.051 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [30] Koon W. S., Lo M. W., Marsden J. E. and Ross S. D., Dynamical Systems, The Three-Body Problem and Space Mission Design, Caltech, Pasadena, CA, 2008, Chaps. 2, 23, http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf. Google Scholar

  • [31] McInnes C. R., Solar Sailing: Technology, Dynamics and Mission Applications, Springer, Glasgow, Scotland, U.K., 1998, Chaps. 2, 32. Google Scholar

  • [32] Biggs J. D., McInnes C. and Waters T., “New Periodic Orbits in the Solar Sail Restricted Three Body Problem,” Nonlinear Science and Complexity (Selected Papers of the 2nd Conference on Nonlinear Science and Complexity), edited by Machado J. A. T., Luo A. C. J., Barbosa R. S., Silva M. F. and Figueiredo L. B., Springer, The Netherlands, 2011, pp. 131–138. Google Scholar

  • [33] Vallado D. A., Foundamentals of Astrodynamics, Space Technology Library, Microcosm Press, Hawthorne, CA, 2004, p. 1135. Google Scholar

  • [34] Khalil H., Nonlinear Systems, Prentice–Hall, Upper Saddle River, NJ, 2002, Chaps. 4, 111. Google Scholar

  • [35] Ginoux J.-M., “Differential Geometry Applied to Dynamical Systems,” Nonlinear Science, Vol. 66, World Scientific Series on Nonlinear Science Series A, Singapore, 2009, Chaps. 3, 41. CrossrefGoogle Scholar

  • [36] Kuchment P., Floquet Theory for Partial Differential Equations, Vol. 60, Operator Theory: Advances and Applications, Springer, Switzerland, 1993, pp. 125–186. CrossrefGoogle Scholar

  • [37] Xu M. and Zhu J., “Applications of Hamiltonian Structure-Preserving Control to Formation Flying on a J2-Perturbed Mean Circular Orbit,” Celestial Mechanics and Dynamical Astronomy, Vol. 113, No. 4, 2012, pp. 403–433. doi:https://doi.org/10.1007/s10569-012-9430-2 CrossrefGoogle Scholar

  • [38] Xu M. and Liang Y., “Cluster Flight Control for Fractionated Spacecraft on an Elliptic Orbit,” Celestial Mechanics and Dynamical Astronomy, Vol. 125, No. 4, 2016, pp. 383–412. doi:https://doi.org/10.1007/s10569-016-9685-0 CrossrefGoogle Scholar

  • [39] Tsuda Y., Mori O., Funase R., Sawada H., Yamamoto T., Saiki T., Endo T., Yonekura K., Hoshino H. and Kawaguchi J., “Achievement of IKAROS—Japanese Deep Space Solar Sail Demonstration Mission,” Acta Astronautica, Vol. 82, No. 2, 2013, pp. 183–188. doi:https://doi.org/10.1016/j.actaastro.2012.03.032 AASTCF 0094-5765 CrossrefGoogle Scholar

  • [40] Murphy D. and Macy B., “Demonstration of a 10 m Solar Sail System,” 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Material Conference, AIAA Paper  2004-1576, 2004, pp. 698–708. LinkGoogle Scholar

  • [41] Borggräfe A., Heiligers J., Ceriotti M. and McInnes C. R., “Distributed Reflectivity Solar Sail for Extended Mission Applications,” The 3rd International Symposium on Solar Sailing, Glasgow, Scotland, U.K., June 2013. Google Scholar

  • [42] Ceriotti M., Harkness P. and McRobb M., “Variable-Geometry Solar Sailing: The Possibility of the Quasi-Rhombic Pyramid,” The 3rd International Symposium on Solar Sailing, Glasgow, Scotland, U.K., June 2013. Google Scholar

  • [43] Spigel M. R., Lipschutz S. and Liu J., Schaum’s Outline of Mathematical Handbook of Formulas and Tables, McGraw–Hill, New York, 2013, Chaps. V, 116. Google Scholar