Constrained Spacecraft Rendezvous on Elliptic Orbits Using Time Shift Governors

No AccessTechnical NotesConstrained Spacecraft Rendezvous on Elliptic Orbits Using Time Shift GovernorsTaehyeun Kim, Anouck Girard and Ilya KolmanovskyTaehyeun Kim https://orcid.org/0009-0008-4630-695XUniversity of Michigan, Ann Arbor, Michigan 48109-2140, Anouck GirardUniversity of Michigan, Ann Arbor, Michigan 48109-2140 and Ilya KolmanovskyUniversity of Michigan, Ann Arbor, Michigan 48109-2140Published Online:26 Sep 2025https://doi.org/10.2514/1.G009122SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookXLinked InRedditEmail About References [1] Cavrois B., Reynaud S., Personne G., Chavy S. and Strandmoe S., "ATV GNC and Safety Functions Synthesis: Overall Design, Main Performances and Operations," AIAA Guidance, Navigation and Control Conference and Exhibit, AIAA Paper 2008-7481, 2008. https://doi.org/10.2514/6.2008-7481 LinkGoogle Scholar[2] Ryan S., "The Difficulties with Replacing Crew Launch Abort Systems with Designed Reliability," Journal of System Safety, Vol. 58, No. 1, 2023, pp. 19–24. https://doi.org/10.56094/jss.v58i1.216 CrossrefGoogle Scholar[3] Chouinard C., Knight R., Jones G., Tran D. and Koblick D., "Automated and Adaptive Mission Planning for Orbital Express," SpaceOps 2008 Conference, AIAA Paper 2008-3383, 2008. https://doi.org/10.2514/6.2008-3383 LinkGoogle Scholar[4] Weiss A., Baldwin M., Erwin R. S. and Kolmanovsky I., "Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies," IEEE Transactions on Control Systems Technology, Vol. 23, No. 4, 2015, pp. 1638–1647. https://doi.org/10.1109/TCST.2014.2379639 CrossrefGoogle Scholar[5] Park H., Zagaris C., Virgili Llop J., Zappulla R., Kolmanovsky I. and Romano M., "Analysis and Experimentation of Model Predictive Control for Spacecraft Rendezvous and Proximity Operations with Multiple Obstacle Avoidance," AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2016-5273, 2016. https://doi.org/10.2514/6.2016-5273 LinkGoogle Scholar[6] Mammarella M., Capello E. and Guglieri G., "Robust Model Predictive Control for Automated Rendezvous Maneuvers in Near-Earth and Moon Proximity," SPACE and Astronautics Forum and Exposition, AIAA Paper 2018-5343, 2018. https://doi.org/10.2514/6.2018-5343 Google Scholar[7] Agrawal D. R. and Panagou D., "Safe Control Synthesis via Input Constrained Control Barrier Functions," 2021 60th IEEE Conference on Decision and Control (CDC), Inst. of Electrical and Electronics Engineers, New York, 2021, pp. 6113–6118. https://doi.org/10.1109/CDC45484.2021.9682938 Google Scholar[8] Schwenzer M., Ay M., Bergs T. and Abel D., "Review on Model Predictive Control: An Engineering Perspective," International Journal of Advanced Manufacturing Technology, Vol. 117, No. 5, 2021, pp. 1327–1349. https://doi.org/10.1007/s00170-021-07682-3 Google Scholar[9] Bahati G., Cosner R. K., Cohen M. H., Bena R. M. and Ames A. D., "Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree," arXiv preprint arXiv:2504.00397, 2025. https://doi.org/10.48550/arXiv.2504.00397 Google Scholar[10] Garone E., Di Cairano S. and Kolmanovsky I., "Reference and Command Governors for Systems with Constraints: A Survey on Theory and Applications," Automatica, Vol. 75, Jan. 2017, pp. 306–328.https://doi.org/10.1016/j.automatica.2016.08.013 CrossrefGoogle Scholar[11] Kalabić U., Kolmanovsky I. and Gilbert E., "Reference Governors for Linear Systems with Nonlinear Constraints," 50th IEEE Conference on Decision and Control and European Control Conference, Inst. of Electrical and Electronics Engineers, New York, 2011, pp. 2680–2686.https://doi.org/10.1109/CDC.2011.6161238 Google Scholar[12] Hu Q. and Chi B., "Spacecraft Rendezvous and Docking Using the Explicit Reference Governor Approach," IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 53, No. 7, 2023, pp. 4131–4141. https://doi.org/10.1109/TSMC.2023.3241989 CrossrefGoogle Scholar[13] Frey G. R., Petersen C. D., Leve F. A., Garone E., Kolmanovsky I. and Girard A. R., "Time Shift Governor for Coordinated Control of Two Spacecraft Formations," International Federation of Automatic Control-PapersOnLine, Vol. 49, No. 18, 2016, pp. 296–301. https://doi.org/10.1016/j.ifacol.2016.10.180 Google Scholar[14] Kim T., Kolmanovsky I. and Girard A., "Time Shift Governor for Spacecraft Proximity Operation in Elliptic Orbits," AIAA SCITECH 2024 Forum, AIAA Paper 2024-2452, 2024. https://doi.org/10.2514/6.2024-2452 LinkGoogle Scholar[15] Kim T., Kolmanovsky I. and Girard A., "Time Shift Governor for Constrained Control of Spacecraft Orbit and Attitude Relative Motion in Bicircular Restricted Four-Body Problem," 2024 American Control Conference (ACC), Inst. of Electrical and Electronics Engineers, New York, 2024, pp. 3074–3080. https://doi.org/10.23919/ACC60939.2024.10644260 Google Scholar[16] Flores R., Burhani B. M. and Fantino E., "A Method for Accurate and Efficient Propagation of Satellite Orbits: A Case Study for a Molniya Orbit," Alexandria Engineering Journal, Vol. 60, No. 2, 2021, pp. 2661–2676. https://doi.org/10.1016/j.aej.2020.12.056 CrossrefGoogle Scholar[17] Foust J., "ESA Delays BepiColombo Orbital Insertion Because of Thruster Problem," 2024, https://spacenews.com/esa-delays-bepicolombo-orbital-insertion-because-of-thruster-problem/?utm_medium=email&utm_source=rasa_io&utm_campaign=newsletter [retrieved 30 Oct. 2024]. Google Scholar[18] Dunn M., "Two Astronauts are Left Behind in Space as Boeing's Troubled Capsule Returns to Earth Empty," 2024, https://apnews.com/article/nasa-stuck-astronauts-boeing-starliner-92dca67a1fbecf05f5f0e6e2e79afc3b [retrieved 30 Oct. 2024]. Google Scholar[19] Montenbruck O., Gill E. and Lutze F., "Satellite Orbits: Models, Methods, and Applications," Applied Mechanics Reviews, Vol. 55, No. 2, 2002, pp. B27–B28. https://doi.org/10.1115/1.1451162 CrossrefGoogle Scholar[20] Cheng M., Ries J. C. and Tapley B. D., "Variations of the Earth's Figure Axis from Satellite Laser Ranging and GRACE," Journal of Geophysical Research: Solid Earth, Vol. 116, No. B1, 2011, pp. 1–2. https://doi.org/10.1029/2010JB000850 Google Scholar[21] Cotorruelo A., Limon D. and Garone E., "Output Admissible Sets and Reference Governors: Saturations are Not Constraints!," IEEE Transactions on Automatic Control, Vol. 65, No. 3, 2019, pp. 1192–1196. https://doi.org/10.1109/TAC.2019.2921672 CrossrefGoogle Scholar[22] Garone E. and Kolmanovsky I. V., "Command Governors with Inexact Optimization and Without Invariance," Journal of Guidance, Control, and Dynamics, Vol. 45, No. 8, 2022, pp. 1523–1528. https://doi.org/10.2514/1.G006420 LinkGoogle Scholar[23] Dong K., Luo J. and Limon D., "A Novel Stable and Safe Model Predictive Control Framework for Autonomous Rendezvous and Docking with a Tumbling Target," Acta Astronautica, Vol. 200, Nov. 2022, pp. 176–187. https://doi.org/10.1016/j.actaastro.2022.08.012 CrossrefGoogle Scholar[24] Specht C., Bishnoi A. and Lampariello R., "Autonomous Spacecraft Rendezvous Using Tube-Based Model Predictive Control: Design and Application," Journal of Guidance, Control, and Dynamics, Vol. 46, No. 7, 2023, pp. 1243–1261. https://doi.org/10.2514/1.G007280 LinkGoogle Scholar[25] Ikeya K., Liu K., Girard A. and Kolmanovsky I., "Learning Reference Governor for Constrained Spacecraft Rendezvous and Proximity Maneuvering," Journal of Spacecraft and Rockets, Vol. 60, No. 4, 2023, pp. 1127–1141. https://doi.org/10.2514/1.A35483 LinkGoogle Scholar[26] Verner J. H., "Explicit Runge–Kutta Pairs with Lower Stage-Order," Numerical Algorithms, Vol. 65, No. 3, 2014, pp. 555–577. https://doi.org/10.1007/s11075-013-9783-y Google Scholar[27] Rackauckas C. and Nie Q., "DifferentialEquations.jl—A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia," Journal of Open Research Software, Vol. 5, No. 1, 2017, p. 15. https://doi.org/10.5334/jors.151 Google Scholar[28] Rackauckas C., "ODE Solver Multi-Language Wrapper Package Work-Precision Benchmarks (MATLAB, SciPy, Julia, deSolve (R))," 2022, https://docs.sciml.ai/SciMLBenchmarksOutput/html/MultiLanguage/wrapper_packages.html [retrieved 30 Oct. 2024]. Google Scholar Next article FiguresReferencesRelatedDetails What's Popular Articles in Advance Altmetrics Metrics Downloaded 0 times 0 citation in Crossref CrossmarkInformationCopyright © 2025 by Copyright © 2025 by Taehyeun Kim, Anouck Girard, and Ilya Kolmanovsky. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. 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 https://aiaa.org/publications/publish-with-aiaa/rights-and-permissions/. TopicsAerospace SciencesAstrodynamicsAstronauticsControl TheoryGuidance, Navigation, and Control SystemsOrbital ManeuversSpace OrbitSpace RendezvousSpacecraft Guidance and Control KeywordsSpacecraft RendezvousOrbital ManeuversModel Predictive ControlSpacecraft Guidance and ControlConstrained ControlPredictive ControlTime Shift GovernorAcknowledgmentThis research is supported by the U.S. Air Force Office of Scientific Research under grant number FA9550-23-1-0678.Digital Received13 February 2025Accepted12 July 2025Published online26 September 2025