Rapid Spacecraft Trajectory Optimization Using State Transition Tensors and Differential Dynamic Programming

No AccessTechnical NotesRapid Spacecraft Trajectory Optimization Using State Transition Tensors and Differential Dynamic ProgrammingSpencer Boone and Jay McMahonSpencer BooneISAE-SUPAERO, Toulouse, 31055 France and Jay McMahon https://orcid.org/0000-0002-1847-4795University of Colorado Boulder, Boulder, Colorado 80309Published Online:21 Sep 2025https://doi.org/10.2514/1.G007293SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookXLinked InRedditEmail About References [1] McIntosh D., Baker J. and Matus J., "The NASA Cubesat Missions Flying on Artemis-1," 34th Annual Small Satellite Conference, Utah State Univ. Paper SSC20-WKVII-02, 2020. Google Scholar[2] McGuire M., Burke L., McCarty S., Hack K., Whitley R., Davis D. and Ocampo C., "Low Thrust Cis-Lunar Transfers Using a 40 KW-Class Solar Electric Propulsion Spacecraft," 2017 AAS/AIAA Astrodynamics Specialist Conference, AAS Paper 17-583, 2017. Google Scholar[3] Parcher D., Abrahamson M., Ardito A., Han D., Haw R., Kennedy B., Mastrodemos N., Nandi S., Park R., Rush B. and , et al., "Dawn Maneuver Design Performance at Vesta," 23rd AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 13-344, 2013. Google Scholar[4] Riedel J., Bhaskaran S., Eldred D., Gaskell R., Grasso C., Kennedy B., Kubitscheck D., Mastrodemos N., Synnott S., Vaughan A. and , et al., "AutoNav Mark3: Engineering the Next Generation of Autonomous Onboard Navigation and Guidance," AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA Paper 2006-6708, 2006. https://doi.org/10.2514/6.2006-6708 LinkGoogle Scholar[5] Boone S. and McMahon J., "Orbital Guidance Using Higher-Order State Transition Tensors," Journal of Guidance, Control, and Dynamics, Vol. 44, No. 3, 2021, pp. 493–504. https://doi.org/10.2514/1.G005493 LinkGoogle Scholar[6] Lantoine G. and Russell R., "A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory," Journal of Optimization Theory and Applications, Vol. 154, No. 2, 2012, pp. 382–417. https://doi.org/10.1007/s10957-012-0039-0 CrossrefGoogle Scholar[7] Whiffen G., "Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design," AIAA/AAS Astrodynamics Specialist Conference, AIAA Paper 2006-6741, 2006. https://doi.org/10.2514/6.2006-6741 LinkGoogle Scholar[8] Roa J., Pelaez J. and Senent J., "New Analytic Solution with Continuous Thrust: Generalized Logarithmic Spirals," Journal of Guidance, Control, and Dynamics, Vol. 39, No. 10, 2016, pp. 2336–2351. https://doi.org/10.2514/1.G000341 LinkGoogle Scholar[9] Russell R. and Lantoine G., "Optimal Control of Relative Motion in Arbitrary Fields: Application at Deimos," Journal of the Astronautical Sciences, Vol. 59, Nos. 1–2, 2012, pp. 193–215. https://doi.org/10.1007/s40295-013-0013-6 CrossrefGoogle Scholar[10] LaFarge N., Miller D., Howell K. and Linares R., "Guidance for Closed-Loop Transfers Using Reinforcement Learning with Application to Libration Point Orbits," AIAA Scitech 2020 Forum, AIAA Paper 2020-0458, 2020. https://doi.org/10.2514/6.2020-0458 AbstractGoogle Scholar[11] Hofmann C. and Topputo F., "Rapid Low-Thrust Trajectory Optimization in Deep Space Based on Convex Programming," Journal of Guidance, Control, and Dynamics, Vol. 44, No. 7, 2021, pp. 1379–1388. https://doi.org/10.2514/1.G005839 LinkGoogle Scholar[12] Park R. and Scheeres D., "Nonlinear Mapping of Gaussian Statistics: Theory and Applications to Spacecraft Trajectory Design," Journal of Guidance, Control, and Dynamics, Vol. 29, No. 6, 2006, pp. 1367–1375. https://doi.org/10.2514/1.20177 LinkGoogle Scholar[13] Boone S. and McMahon J., "Variable Time-of-Flight Spacecraft Maneuver Targeting Using State Transition Tensors," Journal of Guidance, Control, and Dynamics, Vol. 44, No. 11, 2021, pp. 2072–2080. https://doi.org/10.2514/1.G005890 LinkGoogle Scholar[14] Di Lizia P., Armellin R. and Lavagna M., "Application of High Order Expansions of Two-Point Boundary Value Problems to Astrodynamicss," Celestial Mechanics and Dynamical Astronomy, Vol. 102, No. 4, 2008, pp. 355–375. https://doi.org/10.1007/s10569-008-9170-5 Google Scholar[15] Izzo D. and Biscani F., "Audi/PyAudi," 2018. https://doi.org/10.5281/zenodo.1442738 Google Scholar[16] Jacobson D. and Mayne D., Differential Dynamic Programming, Elsevier, New York, 1970. Google Scholar[17] Aziz J., Scheeres D. and Lantoine G., "Hybrid Differential Dynamic Programming in the Circular Restricted Three-Body Problem," Journal of Guidance, Control, and Dynamics, Vol. 42, No. 5, 2019, pp. 1–13. https://doi.org/10.2514/1.G003617 Google Scholar[18] Conn A., Gould N. and Toint P., Trust Region Methods, Soc. for Industrial and Applied Mathematics, Philadelphia, PA, 2000. https://doi.org/10.1137/1.9780898719857 CrossrefGoogle Scholar[19] Bernstein D., "Nonquadratic Cost and Nonlinear Feedback Control," International Journal of Robust and Nonlinear Control, Vol. 3, No. 3, 1993, pp. 211–229. https://doi.org/10.1002/rnc.4590030303 CrossrefGoogle Scholar[20] Tassa Y. and Todorov E., "High-Order Local Dynamic Programming," 2011 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL), Inst. of Electrical and Electronics Engineers, New York, 2011, pp. 70–75. Google Scholar[21] Maestrini M., Di Lizia P., Armellin R. and Russell R. P., "Hybrid Differential Dynamic Programming Algorithm for Low-Thrust Trajectory Design Using Exact High-Order Transition Maps," 69th International Astronautical Congress 2018, IAC Paper 18-F1.2.3, 2018. Google Scholar[22] Yakowitz S., Algorithms and Computational Techniques in Differential Dynamic Programming, Academic Press, New York, 1989, pp. 75–91. https://doi.org/10.1016/B978-0-12-012731-3.50008-1 Google Scholar[23] Lantoine G. and Russell R. P., "A Fast Second-Order Algorithm for Preliminary Design of Low-Thrust Trajectories," 59th International Astronautical Congress, IAC Paper 08-C1.2.5, 2008. Google Scholar[24] Makino K. and Berz M., "5. Remainder Differential Algebras and Their Applications," Computational Differentiation: Techniques, Applications, and Tools, SIAM, Philadelphia, PA, 1996, pp. 63–74. Google Scholar[25] Wittig A., Di Lizia P., Armellin R., Makino K., Bernelli-Zazzera F. and Berz M., "Propagation of Large Uncertainty Sets in Orbital Dynamics by Automatic Domain Splitting," Celestial Mechanics and Dynamical Astronomy, Vol. 122, No. 3, 2015, pp. 239–261. https://doi.org/10.1007/s10569-015-9618-3 CrossrefGoogle Scholar[26] Fujiwara M. and Funase R., "Autonomous Trajectory Guidance Under Uncertain Dynamical Environment Using State Transition Tensors," 2022 IEEE Aerospace Conference (AERO), Inst. of Electrical and Electronics Engineers, New York, 2022. Google Scholar[27] Caleb T., Armellin R. and Lizy-Destrez S., "A Polynomial-Based Differential Dynamic Programming Optimisation Method for Space Trajectory Design," 75th International Astronautical Congress, Paper IAC 24,C1,IP,43,x83907, 2024. Google Scholar[28] Williams J., Lee D., Whitley R., Bokelmann K., Davis D. and Berry C., "Targeting Cislunar Near Rectilinear Halo Orbits for Human Space Exploration," 27th AAS/AIAA Space Flight Mechanics Meeting, AAS Paper 17-267, 2017. Google Scholar[29] Bezrouk C. and Parker J., "Long Term Evolution of Distant Retrograde Orbits in the Earth–Moon System," Astrophysics and Space Science, Vol. 362, No. 9, 2017, p. 176. https://doi.org/10.1007/s10509-017-3158-0 Google Scholar[30] Parrish N., "Low Thrust Trajectory Optimization in Cislunar and Translunar Space," Ph.D. Thesis, Univ. of Colorado Boulder, Boulder, CO, 2018. Google Scholar Previous article Next article FiguresReferencesRelatedDetails What's Popular Articles in Advance Altmetrics Metrics Downloaded 2 times 0 citation in Crossref CrossmarkInformationCopyright © 2025 by Spencer Boone. 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/. TopicsAlgorithms and Data StructuresComputing and InformaticsComputing, Information, and CommunicationControl TheoryData ScienceFeedback ControlGuidance, Navigation, and Control SystemsOptimal Control TheoryOptimization AlgorithmPlanetary Science and ExplorationPlanetsSolar System MoonsSpace Science and TechnologySpacecraft GuidanceSpacecraft Guidance and Control KeywordsSpacecraft Trajectory OptimizationPlanetsSolar System MoonsComputing and InformaticsNear Rectilinear Halo OrbitDistant Retrograde OrbitFeedback ControlTrajectory OptimizationOptimization AlgorithmNumerical IntegrationAcknowledgmentThis research was performed at the University of Colorado Boulder under NASA grant 80NSSC19K0222.Digital Received12 October 2022Accepted14 August 2025Published online21 September 2025