A novel methodology is proposed for designing low-thrust trajectories to quasi-periodic, near-rectilinear Halo orbits that leverages ephemeris-driven, “invariant manifold analogs” as long-duration asymptotic terminal coast arcs. The proposed methodology generates end-to-end, eclipse-conscious, fuel-optimal transfers in an ephemeris model using an indirect formulation of optimal control theory. The end-to-end trajectories are achieved by patching Earth-escape spirals to a judiciously chosen set of states on precomputed manifolds. The results elucidate the efficacy of employing such a hybrid optimization algorithm for solving end-to-end analogous fuel-optimal problems using indirect methods and leveraging a composite smooth control construct. Multiple representative cargo resupply trajectories are generated for the Lunar Orbital Platform-Gateway. A novel process is introduced to incorporate eclipse-induced coast arcs and their impact within optimization. The results quantify accurate $Δ V$ costs required for achieving efficient eclipse-conscious transfers for several launch opportunities in 2025 and are anticipated to find applications for analogous uncrewed missions.

References

[1] Williams S. N. and Coverstone-Carroll V., “Benefits of Solar Electric Propulsion for the Next Generation of Planetary Exploration Missions,” Journal of the Astronautical Sciences, Vol. 45, No. 2, 1997, pp. 143–159. https://doi.org/10.1007/BF03546373 Crossref Google Scholar
[2] Forward R. L., “Advanced Space Propulsion Study-Antiproton and Beamed Power Propulsion,” Hughes Research Labs. TR DTIC ADA189218, Malibu CA, 1987. Google Scholar
[3] Pan X. and Pan B., “Practical Homotopy Methods for Finding the Best Minimum-Fuel Transfer in the Circular Restricted Three-Body Problem,” IEEE Access, Vol. 8, March 2020, pp. 47,845–47,862. https://doi.org/10.1109/ACCESS.2020.2978246 Crossref Google Scholar
[4] Betts J. T., “Survey of Numerical Methods for Trajectory Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998, pp. 193–207. https://doi.org/10.2514/2.4231 Link Google Scholar
[5] Conway B. A., “A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems,” Journal of Optimization Theory and Applications, Vol. 152, No. 2, 2012, pp. 271–306. https://doi.org/10.1007/s10957-011-9918-z Crossref Google Scholar
[6] Olympio J. T., “Optimal Control Problem for Low-Thrust Multiple Asteroid Tour Missions,” Journal of Guidance, Control, and Dynamics, Vol. 34, No. 6, 2011, pp. 1709–1720. https://doi.org/10.2514/1.53339 Link Google Scholar
[7] Betts J. T. and Erb S. O., “Optimal Low Thrust Trajectories to the Moon,” SIAM Journal on Applied Dynamical Systems, Vol. 2, No. 2, 2003, pp. 144–170. https://doi.org/10.1137/S1111111102409080 Crossref Google Scholar
[8] Pan B., Lu P., Pan X. and Ma Y., “Double-Homotopy Method for Solving Optimal Control Problems,” Journal of Guidance, Control, and Dynamics, Vol. 39, No. 8, 2016, pp. 1706–1720. https://doi.org/10.2514/1.G001553 Link Google Scholar
[9] Pérez-Palau D. and Epenoy R., “Fuel Optimization for Low-Thrust Earth–Moon Transfer via Indirect Optimal Control,” Celestial Mechanics and Dynamical Astronomy, Vol. 130, No. 2, 2018, p. 21. https://doi.org/10.1007/s10569-017-9808-2 Crossref Google Scholar
[10] Singh S. K., Taheri E., Woollands R. and Junkins J., “Mission Design for Close-Range Lunar Mapping by Quasi-Frozen Orbits,” 70th International Astronautical Congress, International Astronautical Federation (IAF), Paper IAC C.1.1.11, 2019. Google Scholar
[11] Williams J., Senent J. S., Ocampo C., Mathur R. and Davis E. C., “Overview and Software Architecture of the Copernicus Trajectory Design and Optimization System,” 4th International Conference on Astrodynamics Tools and Techniques, May 2010. Google Scholar
[12] Whiffen G., “Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design,” AIAA/AAS Astrodynamics Specialist Conference and Exhibit, AIAA Paper 2006-6741, 2006. https://doi.org/10.2514/6.2006-6741 Link Google Scholar
[13] 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 Link Google Scholar
[14] Shannon J., Ozimek M., Atchison J. and Hartzell C., “Rapid Design and Exploration of High-Fidelity Low-Thrust Transfers to the Moon,” 2020 IEEE Aerospace Conference, Inst. of Electrical and Electronics Engineers, New York, 2020, pp. 1–12. https://doi.org/10.1109/AERO47225.2020.9172483 Google Scholar
[15] Yang G., “Earth-Moon Trajectory Optimization Using Solar Electric Propulsion,” Chinese Journal of Aeronautics, Vol. 20, No. 5, 2007, pp. 452–463. https://doi.org/10.1016/S1000-9361(07)60067-3 Crossref Google Scholar
[16] Feistel A. and Ranieri C., “Modeling Perturbations and Operational Considerations When Using Indirect Optimization with Equinoctial Elements,” AAS/AIAA Space Flight Mechanics Meeting, 2009, pp. 1737–1756. Google Scholar
[17] Anderson R. L. and Lo M. W., “Role of Invariant Manifolds in Low-Thrust Trajectory Design,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 6, 2009, pp. 1921–1930. https://doi.org/10.2514/1.37516 Link Google Scholar
[18] Dellnitz M., Junge O., Post M. and Thiere B., “On Target for Venus–Set Oriented Computation of Energy Efficient Low Thrust Trajectories,” Celestial Mechanics and Dynamical Astronomy, Vol. 95, Nos. 1–4, 2006, pp. 357–370. https://doi.org/10.1007/s10569-006-9008-y Crossref Google Scholar
[19] Vaquero M. and Howell K. C., “Leveraging Resonant-Orbit Manifolds to Design Transfers Between Libration-Point Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 37, No. 4, 2014, pp. 1143–1157. https://doi.org/10.2514/1.62230 Link Google Scholar
[20] Singh S. K., Anderson B. D., Taheri E. and Junkins J. L., “Exploiting Manifolds of L1 Halo Orbits for End-to-End Earth-Moon Low-Thrust Trajectory Design,” Acta Astronautica, Vol. 183, June 2021, pp. 255–272. https://doi.org/10.1016/j.actaastro.2021.03.017 Crossref Google Scholar
[21] Singh S. K., Anderson B. D., Taheri E. and Junkins J. L., “Low-Thrust Transfers to Candidate Near-Rectilinear Halo Orbits facilitated by Invariant Manifolds,” 2020 AAS/AIAA Astrodynamics Specialist Virtual Lake Tahoe Conference, American Astronautical Soc. Paper 20-565, Aug. 2020. Google Scholar
[22] Qu Q., Xu M. and Peng K., “The Cislunar Low-Thrust Trajectories via the Libration Point,” Astrophysics and Space Science, Vol. 362, No. 5, 2017, p. 96. https://doi.org/10.1007/s10509-017-3075-2 Google Scholar
[23] Cox A. D., Howell K. C. and Folta D. C., “Trajectory Design Leveraging Low-Thrust, Multi-Body Equilibria and Their Manifolds,” Journal of the Astronautical Sciences, Vol. 67, No. 3, 2020, pp. 977–1001. https://doi.org/10.1007/s40295-020-00211-6 Crossref Google Scholar
[24] Topputo F., Vasile M. and Bernelli-Zazzera F., “Low Energy Interplanetary Transfers Exploiting Invariant Manifolds of the Restricted Three-Body Problem,” Journal of the Astronautical Sciences, Vol. 53, No. 4, 2005, pp. 353–372. https://doi.org/10.1007/BF03546358 Crossref Google Scholar
[25] Capdevila L. R. and Howell K. C., “A transfer Network Linking Earth, Moon, and the Triangular Libration Point Regions in the Earth-Moon System,” Advances in Space Research, Vol. 62, No. 7, 2018, pp. 1826–1852. https://doi.org/10.1016/j.asr.2018.06.045 Crossref Google Scholar
[26] Zhang R., Wang Y., Zhang H. and Zhang C., “Transfers from Distant Retrograde Orbits to Low Lunar Orbits,” Celestial Mechanics and Dynamical Astronomy, Vol. 132, No. 8, 2020, pp. 1–30. https://doi.org/10.1007/s10569-020-09982-4 Google Scholar
[27] Oshima K., “The Use of Vertical Instability of $L_1$ and $L_2$ Planar Lyapunov Orbits for Transfers from Near Rectilinear Halo Orbits to Planar Distant Retrograde Orbits in the Earth–Moon System,” Celestial Mechanics and Dynamical Astronomy, Vol. 131, No. 3, 2019, pp. 1–28. https://doi.org/10.1007/s10569-019-9892-6 Google Scholar
[28] Trofimov S., Shirobokov M., Tselousova A. and Ovchinnikov M., “Transfers from Near-Rectilinear Halo Orbits to Low-Perilune Orbits and the Moon’s Surface,” Acta Astronautica, Vol. 167, Feb. 2020, pp. 260–271. https://doi.org/10.1016/j.actaastro.2019.10.049 Crossref Google Scholar
[29] Taheri E., Junkins J. L., Kolmanovsky I. and Girard A., “A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1,” Acta Astronautica, Vol. 172, July 2020, pp. 151–165. https://doi.org/10.1016/j.actaastro.2020.02.042 Crossref Google Scholar
[30] Gomez G., Jorba A., Masdemont J. and Simó C., “A Dynamical Systems Approach for the Analysis of the SOHO Mission,” ESA, Spacecraft Flight Dynamics (SEE N 92-24719 15-12), 1991, pp. 449–454. Google Scholar
[31] Koon W. S., Lo M. W., Marsden J. E. and Ross S. D., “Low Energy Transfer to the Moon,” Celestial Mechanics and Dynamical Astronomy, Vol. 81, No. 1, 2001, pp. 63–73. https://doi.org/10.1023/A:1013359120468 Crossref Google Scholar
[32] Lo M. W., Williams B. G., Bollman W. E., Han D., Hahn Y., Bell J. L., Hirst E. A., Corwin R. A., Hong P. E., Howell K. C. and Barden B., “Genesis Mission Design,” Journal of the Astronautical Sciences, Vol. 49, No. 1, 2001, pp. 169–184. https://doi.org/10.1007/BF03546342 Crossref Google Scholar
[33] Geffroy S. and Epenoy R., “Optimal Low-Thrust Transfers with Constraints—Generalization of Averaging Techniques,” Acta Astronautica, Vol. 41, No. 3, 1997, pp. 133–149. https://doi.org/10.1016/S0094-5765(97)00208-7 Crossref Google Scholar
[34] Cerf M., “Fast Solution of Minimum-Time Low-Thrust Transfer with Eclipses,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 233, No. 7, 2019, pp. 2699–2714. https://doi.org/10.1177/0954410018785971 Crossref Google Scholar
[35] Woollands R. and Taheri E., “Optimal Low-Thrust Gravity Perturbed Orbit Transfers with Shadow Constraints,” 2019 AAS/AIAA Astrodynamics Specialist Conference, Vol. 171, Univelt Inc., 2019, pp. 1303–1317. Google Scholar
[36] Aziz J. D., “Low-Thrust Many-Revolution Trajectory Optimization,” Ph.D. Thesis, Univ. of Colorado, Boulder, CO, 2018. Google Scholar
[37] Taheri E., “Optimization of Many-Revolution Minimum-Time Low-Thrust Trajectories Using Sundman Transformation,” AIAA Scitech 2021 Forum, AIAA Paper 2021-1343, 2021. https://doi.org/10.2514/6.2021-1343 Link Google Scholar
[38] Aziz J., Scheeres D., Parker J. and Englander J., “A Smoothed Eclipse Model for Solar Electric Propulsion Trajectory Optimization,” Transactions of the Japan Society for Aeronautical and Space Sciences, Aerospace Technology Japan, Vol. 17, No. 2, 2019, pp. 181–188. https://doi.org/10.2322/tastj.17.181 Crossref Google Scholar
[39] 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 Link Google Scholar
[40] Liu H. and Tongue B. H., “Indirect Spacecraft Trajectory Optimization Using Modified Equinoctial Elements,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 2, 2010, pp. 619–623. https://doi.org/10.2514/1.45498 Link Google Scholar
[41] Taheri E., Kolmanovsky I. and Atkins E., “Enhanced Smoothing Technique for Indirect Optimization of Minimum-Fuel Low-Thrust Trajectories,” Journal of Guidance, Control, and Dynamics, Vol. 39, No. 11, 2016, pp. 2500–2511. https://doi.org/10.2514/1.G000379 Link Google Scholar
[42] Junkins J. L. and Taheri E., “Exploration of Alternative State Vector Choices for Low-Thrust Trajectory Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 42, No. 1, 2019, pp. 47–64. https://doi.org/10.2514/1.G003686 Link Google Scholar
[43] Walker M., Ireland B. and Owens J., “A Set Modified Equinoctial Orbit Elements,” Celestial Mechanics, Vol. 36, No. 4, 1985, pp. 409–419. https://doi.org/10.1007/BF01227493 Crossref Google Scholar
[44] Taheri E., Junkins J. L., Kolmanovsky I. and Girard A., “A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 2,” Acta Astronautica, Vol. 172, July 2020, pp. 151–165. https://doi.org/10.1016/j.actaastro.2020.02.047 Crossref Google Scholar
[45] Ross I. M., Gong Q. and Sekhavat P., “Low-Thrust, High-Accuracy Trajectory Optimization,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4, 2007, pp. 921–933. Link Google Scholar
[46] Whitley R. J., Davis D. C., Burke L. M., McCarthy B. P., Power R. J., McGuire M. L. and Howell K. C., “Earth-Moon Near Rectilinear Halo and butTerfly Orbits for Lunar Surface Exploration,” AAS/AIAA Astrodynamics Specialists Conference, American Astronautical Soc. Paper 18-406, 2018. Google Scholar
[47] Flohrer T., Choc R. and Bastida B., “Classification of Geosynchronous Objects,” European Space Agency, ESA/ESOC, GEN-DBLOG-00086-OPS-GR, Darmstadt, No. 14, Feb. 2012. Google Scholar
[48] Lorenz S. L. and Guzman C., “Multi-Objective Optimization of Low Thrust Trajectories for Propellant Mass, Time of Flight, and Radiation Dose,” 29th AAS/AIAASpace Flight Mechanics Meeting, American Astronautical Soc. Paper 19-398, Ka’napali, Hawaii, 2019. Google Scholar
[49] Lee D. E., “White Paper: Gateway Destination Orbit Model: A Continuous 15 Year NRHO Reference Trajectory,” NTRS–NASA TR Server, JSC-E-DAA-TN72594, 2019. Google Scholar
[50] Hofer R., “High-Specific Impulse Operation of the BPT-4000 Hall Thruster for NASA Science Missions,” 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2010-6623, 2010. Abstract Google Scholar
[51] Taheri E. and Junkins J. L., “How Many Impulses Redux,” Journal of the Astronautical Sciences, Vol. 67, Dec. 2019, pp. 1–78. https://doi.org/10.1007/s40295-019-00203-1 Google Scholar
[52] Kluever C. A., “Low-Thrust Trajectory Optimization Using Orbital Averaging and Control Parameterization,” Spacecraft Trajectory Optimization, edited by Conway B., Cambridge Aerospace Series, Cambridge Univ. Press, Cambridge, England, U.K., 2010, pp. 112–138. https://doi.org/10.1017/CBO9780511778025.006 Google Scholar

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Volume 44, Number 11November 2021

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Acknowledgments

We are pleased to acknowledge the Jet Propulsion Laboratory, Air Force Research Laboratory, Dzyne, Inc., and Texas A&M University for sponsorship of various aspects of this research. This work was completed at Texas A&M University. A part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA (80NM0018D0004). We would like to thank Jon Sims and Daniel Grebow of Jet Propulsion Laboratory, California Institute of Technology, for participating in illuminating discussions throughout the course of this work.

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Received13 January 2021
Accepted3 May 2021
Published online28 June 2021

Eclipse-Conscious Transfer to Lunar Gateway Using Ephemeris-Driven Terminal Coast Arcs

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