Equinoctial Lyapunov Control Law for Low-Thrust Rendezvous

No AccessEngineering NotesEquinoctial Lyapunov Control Law for Low-Thrust RendezvousSanjeev Narayanaswamy and Christopher J. DamarenSanjeev Narayanaswamy https://orcid.org/0000-0002-3037-3620University of Toronto, Toronto, Ontario M3H 5T6, Canada and Christopher J. Damaren https://orcid.org/0000-0002-2036-2506University of Toronto, Toronto, Ontario M3H 5T6, CanadaPublished Online:27 Feb 2023https://doi.org/10.2514/1.G006662SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations About References [1] De Ruiter A. H. J., Damaren C. J. and Forbes J. R., Spacecraft Dynamics and Control: An Introduction, Wiley, Chichester, England, U.K., 2013, pp. 65–128. Google Scholar[2] Hakima H., Bazzocchi M. C. F. and Emami M. R., “A Deorbiter CubeSat for Active Orbital Debris Removal,” Advances in Space Research, Vol. 61, No. 9, 2018, pp. 2377–2392. https://doi.org/10.1016/j.asr.2018.02.021 CrossrefGoogle Scholar[3] Bucci L. and Lavagna M. R., “Analytical Formulation for Light and Fast Low-Thrust Guidance Design to Perform Multi-Target On-Orbit Servicing,” AIAA Guidance, Navigation, and Control Conference, AIAA Paper 2016-0877, 2016. https://doi.org/10.2514/6.2016-0877 Google Scholar[4] Guelman M. and Aleshin M., “Optimal Bounded Low-Thrust Rendezvous with Fixed Terminal-Approach Direction,” Journal of Guidance, Control, and Dynamics, Vol. 24, No. 2, 2001, pp. 378–385. https://doi.org/10.2514/2.4722 LinkGoogle Scholar[5] Kumar Yajur, “Optimal Low Thrust Transfer for Relative Orbital Motion,” M.Tech. Thesis, Indian Institute of Technology, Kanpur, India, 2016. Google Scholar[6] Luo Y., Zhang J. and Tang G., “Survey of Orbital Dynamics and Control of Space Rendezvous,” Chinese Journal of Aeronautics, Vol. 27, No. 1, 2014, pp. 1–11. https://doi.org/10.1016/j.cja.2013.07.042 CrossrefGoogle Scholar[7] Kluever C. A. and Tanck G. S., “A Feedback Guidance Scheme for Orbital Rendezvous,” Journal of the Astronautical Sciences, Vol. 47, Nos. 3–4, 1999, pp. 229–237. https://doi.org/10.1007/BF03546201 CrossrefGoogle Scholar[8] Kechichian J. A., “Optimal Low-Thrust Rendezvous Using Equinoctial Orbit Elements,” Acta Astronautica, Vol. 38, No. 1, 1996, pp. 1–14. https://doi.org/10.1016/0094-5765(95)00121-2 CrossrefGoogle Scholar[9] Olympio J. and Frouvelle N., “Space Debris Selection and Optimal Guidance for Removal in the SSO with Low-Thrust Propulsion,” Acta Astronautica, Vol. 99, June 2014, pp. 263–275. https://doi.org/10.1016/j.actaastro.2014.03.005 CrossrefGoogle Scholar[10] Haberkorn T., Martinon P. and Gergaud J., “Low Thrust Minimum-Fuel Orbital Transfer: A Homotopic Approach,” Journal of Guidance, Control, and Dynamics, Vol. 27, No. 6, 2004, pp. 1046–1060. https://doi.org/10.2514/1.4022 LinkGoogle Scholar[11] Sims J., Finlayson P., Rinderle E., Vavrina M. and Kowalkowski T., “Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design,” AIAA Paper 2006-6746, 2006. https://doi.org/10.2514/6.2006-6746 Google Scholar[12] Yam C. H., Lorenzo D. D. and Izzo D., “Low-Thrust Trajectory Design as a Constrained Global Optimization Problem,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 225, No. 11, 2011, pp. 1243–1251. https://doi.org/10.1177/0954410011401686 CrossrefGoogle Scholar[13] Novak D. M. and Vasile M., “Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 34, No. 1, 2011, pp. 128–147. https://doi.org/10.2514/1.50434 LinkGoogle Scholar[14] Petropoulos A. E. and Longuski J. M., “Shape-Based Algorithm for the Automated Design of Low-Thrust, Gravity Assist Trajectories,” Journal of Spacecraft and Rockets, Vol. 41, No. 5, 2004, pp. 787–796. https://doi.org/10.2514/1.13095 LinkGoogle Scholar[15] Wall B. J. and Conway B. A., “Shape-Based Approach to Low-Thrust Rendezvous Trajectory Design,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 1, 2009, pp. 95–101. https://doi.org/10.2514/1.36848 LinkGoogle Scholar[16] Taheri E., Kolmanovsky I. and Atkins E., “Shaping Low-Thrust Trajectories with Thrust-Handling Feature,” Advances in Space Research, Vol. 61, No. 3, 2018, pp. 879–890. https://doi.org/10.1016/j.asr.2017.11.006 CrossrefGoogle Scholar[17] Narayanaswamy S. and Damaren C. J., “Comparison of the Legendre–Gauss Pseudospectral and Hermite–Legendre–Gauss–Lobatto Methods for Low-Thrust Spacecraft Trajectory Optimization,” Aerospace Systems, Vol. 3, No. 1, 2020, pp. 53–70. https://doi.org/10.1007/s42401-019-00042-w CrossrefGoogle Scholar[18] Graham K. F. and Rao A. V., “Minimum-Time Trajectory Optimization of Multiple Revolution Low-Thrust Earth-Orbit Transfers,” Journal of Spacecraft and Rockets, Vol. 52, No. 3, 2015, pp. 711–727. https://doi.org/10.2514/1.A33187 LinkGoogle Scholar[19] Kluever C. A., “Simple Guidance Scheme for Low-Thrust Orbit Transfers,” Journal of Guidance, Control, and Dynamics, Vol. 21, No. 6, 1998, pp. 1015–1017. https://doi.org/10.2514/2.4344 LinkGoogle Scholar[20] Ruggiero A., Pergola P., Marcuccio S. and Andrenucci M., “Low-Thrust Maneuvers for the Efficient Correction of Orbital Elements,” 32nd International Electric Propulsion Conference, Electric Rocket Propulsion Society, Ohio, 2011, pp. 11–15. Google Scholar[21] Ilgen M. R., “Low Thrust OTV Guidance Using Liapunov Optimal Feedback Control Techniques,” Advances in the Astronautical Sciences, Vol. 85, AAS Paper 93-680, 1993, pp. 1527–1546. Google Scholar[22] Ghosh P., “A Survey of the Methods Available for the Design of Many-Revolution Low-Thrust Planetocentric Trajectories,” Advances in the Astronautical Sciences, Vol. 168, AAS Paper 19-297, 2019, pp. 395–414. Google Scholar[23] Petropoulos A. E., “Refinements to the Q-Law for Low-Thrust Orbit Transfers,” Advances in the Astronautical Sciences, Vol. 120, AAS Paper 05-162, 2005, pp. 963–982. Google Scholar[24] Varga G. I. and Pérez J. M. S., “Many-Revolution Low-Thrust Orbit Transfer Computation Using Equinoctial Q-Law Including J2 and Eclipse Effects,” Advances in the Astronautical Sciences, Vol. 156, AAS Paper 15-590, 2016, pp. 2463–2481. Google Scholar[25] Shannon J. L., Ozimek M. T., Atchison J. A. and Hartzell C. M., “Q-Law Aided Direct Trajectory Optimization of Many-Revolution Low-Thrust Transfers,” Journal of Spacecraft and Rockets, Vol. 57, No. 4, 2020, pp. 672–682. https://doi.org/10.2514/1.A34586 LinkGoogle Scholar[26] Naasz B. J., “Classical Element Feedback Control for Spacecraft Orbital Maneuvers,” M.S. Thesis, Virginia Tech, Blacksburg, VA, May 2002. Google Scholar[27] Hernandez S. and Akella M. R., “Lyapunov-Based Guidance for Orbit Transfers and Rendezvous in Levi-Civita Coordinates,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 4, 2014, pp. 1170–1181. https://doi.org/10.2514/1.62305 LinkGoogle Scholar[28] Leomanni M., Bianchini G., Garulli A. and Giannitrapani A., “Nonlinear Orbit Control with Longitude Tracking,” 2016 IEEE 55th Conference on Decision and Control (CDC), Inst. of Electrical and Electronics Engineers, New York, 2016, pp. 1316–1321. https://doi.org/10.1109/CDC.2016.7798448 Google Scholar[29] Petropoulos A. E., “Simple Control Laws for Low-Thrust Orbit Transfers,” Advances in the Astronautical Sciences, Vol. 116, AAS Paper 03-630, 2003, pp. 2031–2048. Google Scholar[30] Petropoulos A., “Low-Thrust Orbit Transfers Using Candidate Lyapunov Functions with a Mechanism for Coasting,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper 2004-5089, 2004. https://doi.org/10.2514/6.2004-5089 Google Scholar[31] Joseph B. E., “Lyapunov Feedback Control in Equinoctial Elements Applied to Low Thrust Control of Elliptical Orbit Constellations,” M.S. Thesis, Massachusetts Inst. of Technology, Cambridge, MA, 2006. Google Scholar[32] Niccolai L., Quarta A. A. and Mengali G., “Solar Sail Heliocentric Transfers with a Q-law,” Acta Astronautica, Vol. 188, Nov. 2021, pp. 352–361. https://doi.org/10.1016/j.actaastro.2021.07.037 CrossrefGoogle Scholar[33] Lantukh D. V., Ranieri C. L., DiPrinzio M. D. and Edelman P. J., “Enhanced Q-Law Lyapunov Control for Low-Thrust Transfer and Rendezvous Design,” Advances in the Astronautical Sciences, Vol. 162, AAS Paper 17-589, 2017, pp. 2741–2752. Google Scholar[34] Chang D. E., Chichka D. F. and Marsden J. E., “Lyapunov-Based Transfer between Elliptic Keplerian Orbits,” Discrete & Continuous Dynamical Systems-B, Vol. 2, No. 1, 2002, p. 57. https://doi.org/10.3934/dcdsb.2002.2.57 Google Scholar[35] Walker M., Ireland B. and Owens J., “A Set of Modified Equinoctial Orbit Elements,” Celestial Mechanics, Vol. 36, No. 4, 1985, pp. 409–419. https://doi.org/10.1007/BF01227493 CrossrefGoogle Scholar[36] King S., Walker M. and Kluever C., “Small Satellite LEO Maneuvers with Low-Power Electric Propulsion,” 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA Paper 2008-4516, 2008. https://doi.org/10.2514/6.2008-4516 Google Scholar[37] Yuan R., Pingyuan C. and Enjie L., “A Low-thrust Guidance Law Based on Lyapunov Feedback Control and Hybrid Genetic Algorithm,” Aircraft Engineering and Aerospace Technology, Vol. 79, No. 2, 2007, pp. 144–149. https://doi.org/10.1108/00022660710732699 CrossrefGoogle Scholar[38] Shannon J. L., Ellison D. and Hartzell C. M., “Analytical Partial Derivatives of the Q-Law Guidance Algorithm,” Advances in the Astronautical Sciences, Vol. 176, AAS Paper 21-274, 2021. Google Scholar[39] Hatten N. A., “A Critical Evaluation of Modern Low-Thrust, Feedback-Driven Spacecraft Control Laws,” M.S. Thesis, Univ. of Texas, Austin, TX, Dec. 2012. Google Scholar[40] Gurfil P., “Nonlinear Feedback Control of Low-Thrust Orbital Transfer in a Central Gravitational Field,” Acta Astronautica, Vol. 60, Nos. 8–9, 2007, pp. 631–648. https://doi.org/10.1016/j.actaastro.2006.10.001 CrossrefGoogle Scholar[41] Kluever C. A. and Oleson S. R., “Direct Approach for Computing Near-Optimal Low-Thrust Earth-Orbit Transfers,” Journal of Spacecraft and Rockets, Vol. 35, No. 4, 1998, pp. 509–515. https://doi.org/10.2514/2.3360 LinkGoogle Scholar[42] Shampine L. F. and Reichelt M. W., “The MATLAB ODE Suite,” SIAM Journal on Scientific Computing, Vol. 18, No. 1, 1997, pp. 1–22. https://doi.org/10.1137/S1064827594276424 CrossrefGoogle Scholar[43] Izzo D., Getzner I., Hennes D. and Simões L. F., “Evolving Solutions to TSP Variants for Active Space Debris Removal,” Proceedings of the 2015 Genetic and Evolutionary Computation Conference—GECCO ’15, ACM Press, New York, 2015, pp. 1207–1214. https://doi.org/10.1145/2739480.2754727 Google Scholar[44] Petropoulos A. E. and Lee S., “Optimisation of Low-Thrust Orbit Transfers Using the Q-law for the Initial Guess,” Advances in the Astronautical Sciences, Vol. 123, AAS Paper 05-392, 2005. Google Scholar Previous article FiguresReferencesRelatedDetails What's Popular Volume 46, Number 4April 2023 CrossmarkInformationCopyright © 2023 by Sanjeev Narayanaswamy and Christopher J. Damaren. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAerospace SciencesAstrodynamicsAstronauticsControl TheoryFeedback ControlGuidance, Navigation, and Control SystemsIon ThrusterOptimal Control TheoryOrbital ManeuversPropulsion and PowerSpace OrbitSpacecraft GuidanceSpacecraft Guidance and ControlSpacecraft Propulsion KeywordsOrbital ManeuversFeedback ControlEquatorial OrbitIon ThrusterLow-Thrust Electrical PropulsionRendezvous GuidanceTrajectory OptimizationSatellite RendezvousSpacecraft DynamicsThrust Vector ControlAcknowledgmentsThe authors would like to thank Graham Mackintosh of NASA FDL for creating the AI Challenge for Orbital Debris Remediation, which motivated our research into this topic. The authors are grateful to Chit Hong Yam of ispace Inc., and Stefano Campagnola of NASA JPL, who first suggested we look into the Q-Law literature. The authors also thank Dario Izzo of ESA ACT, Luís F. Simões of ML Analytics, Michael Saunders of Stanford University, and Philip Gill of University of California, San Diego, for valuable discussions. The authors would like to acknowledge the use of the Niagara supercomputer at the University of Toronto and are grateful for support by the Ontario Graduate Scholarship. Finally, the authors thank the anonymous reviewers for their insightful comments and suggestions, which were very helpful.PDF Received4 January 2022Accepted11 January 2023Published online27 February 2023

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