Earth-moon distant retrograde orbits (DROs) periodically circle around the moon with high stability, suitable for the deployment of a cislunar station. However, due to the navigation and control errors and uncertainty in dynamic parameter, the actual trajectory drifts from the nominal DRO. To further improve the on-orbit station-keeping (SK) accuracy, robust guidance methods for DRO SK are provided. For reducing the influences of navigation and control errors, a robust SK point design method based on Lyapunov exponents is developed. Trajectory convergence under initial position and velocity error is studied using an equivalent method. The robust DRO-SK point is designed to perform trajectory guidance periodically. To deal with the uncertainty in dynamic parameter, a model-free uncertainty fitting method is develop based on reinforcement learning (RL). The uncertainty is identified, fitted, and predicted using the nominal and actual trajectories to improve the accuracy of trajectory propagation. The optimal state and reward for RL-based uncertainty fitting are investigated. Furthermore, a double-loop guidance framework for on-orbit guidance is established based on a predictor-corrector guidance method. In the inner loop, the RL-based uncertainty fitting method is employed; in the outer loop, the robust SK point is taken as a periodic SK point for the cislunar station. The performance of the robust guidance method is analyzed through numerical simulations.
[1] Li Z., Yang Z., Li H. and Zou W., "Integrated Orbital Design Method for Manned Lunar Exploration with Relaxed Temporal Constraints," Journal of Spacecraft and Rockets, Vol. 62, No. 2, 2024, pp. 1-12. https://doi.org/10.2514/1.A36062 Google Scholar
[2] Huang X., Ding B., Yang B., Xie R., Guo J. and Li S., "Design of Entire-Flight Pinpoint Return Trajectory for Lunar DRO via Deep Neural Network," Aerospace, Vol. 11, No. 7, 2024, p. 566. https://doi.org/10.3390/aerospace11070566 CrossrefGoogle Scholar
[3] Burns J. O., Mellinkoff B., Spydell M., Fong T., Kring D. A., Pratt W. D., Cichan T. and Edwards C. M., "Science on the Lunar Surface Facilitated by Low Latency Telerobotics from a Lunar Orbital Platform-Gateway," Acta Astronautica, Vol. 154, No. 7, Jan. 2019, pp. 195-203. https://doi.org/10.1016/j.actaastro.2018.04.031 Google Scholar
[4] Zhang P., Dai W., Niu R., Zhang G., Liu G., Liu X., Bo Z., Wang Z., Zheng H., Liu C. and et al., "Overview of the Lunar In Situ Resource Utilization Techniques for Future Lunar Missions," Space: Science & Technology, Vol. 3, June 2023, p. 0037. https://doi.org/10.34133/space.0037 Google Scholar
[5] Chavy-Macdonald M. A., Oizumi K., Kneib J. P. and Aoyama K., "The Cis-Lunar Ecosystem -- A Systems Model and Scenarios of the Resource Industry and Its Impact," Acta Astronautica, Vol. 188, 2021, pp. 545-558. https://doi.org/10.1016/j.actaastro.2021.06.017 CrossrefGoogle Scholar
[6] Parsay K. and Folta D. C., "Transfer to Distant Retrograde Orbits via Rideshare to Sun-Earth Point," Journal of Guidance, Control, and Dynamics, Vol. 45, No. 1, 2022, pp. 179-284. https://doi.org/10.2514/1.G005991 LinkGoogle Scholar
[7] Pires P. and Winter O. C., "Location and Stability of Distant Retrograde Orbits Around the Moon," Monthly Notices of the Royal Astronomical Society, Vol. 494, No. 2, 2020, pp. 2727-2735. https://doi.org/10.1093/mnras/staa887 CrossrefGoogle Scholar
[8] Peng C., Zhang H., Wen C., Zhu Z. and Gao Y., "Exploring More Solutions for Low-Energy Transfers to Lunar Distant Retrograde Orbits," Celestial Mechanics and Dynamical Astronomy, Vol. 134, No. 4, 2022, pp. 2022-pp. 4. https://doi.org/10.1007/s10569-021-10056-2 Google Scholar
[9] Conte D., Di Carlo M., Ho K., Spencer D. B. and Vasile M., "Earth-Mars Transfers Through Moon Distant Retrograde Orbits," Acta Astronautica, Vol. 154, No. 143, 2018, pp. 372-379. https://doi.org/10.1016/j.actaastro.2017.12.007 Google Scholar
[10] Oshima K., "Continuation and Stationkeeping Analyses on Planar Retrograde Periodic Orbits Around the Earth," Advances in Space Research, Vol. 69, No. 5, 2022, pp. 2210-2222. https://doi.org/10.1016/j.asr.2021.12.020 CrossrefGoogle Scholar
[11] Zhang R., Wang Y., Shi Y., Zhang C. and Zhang H., "Performance Analysis of Impulsive Station-Keeping Strategies for Cis-Lunar Orbits with the Ephemeris Model," Acta Astronautica, Vol. 198, Sept. 2022, pp. 152-160. https://doi.org/10.1016/j.actaastro.2022.05.054 CrossrefGoogle Scholar
[12] Chen H., Hou X. and Bando M., "Stable Orbiting Around Small Moons Using J2-Perturbed Elliptic Restricted Problem," Journal of Guidance, Control, and Dynamics, Vol. 47, No. 7, 2024, pp. 1-14. https://doi.org/10.2514/1.G008001 Google Scholar
[13] Khoroshylov S. V. and Redka M. O., "Deep Learning for Space Guidance, Navigation, and Control," Space Science and Technology, Vol. 27, No. 6, 2021, pp. 38-52. https://doi.org/10.15407/knt2021.06.038 Google Scholar
[14] Chai R., Tsourdos A., Savvaris A., Chai S., Xia Y. and Chen C. L. P., "Review of Advanced Guidance and Control Algorithms for Space/Aerospace Vehicles," Progress in Aerospace Sciences, Vol. 122, April 2021, Paper 200696. https://doi.org/10.1016/j.paerosci.2021.100696 CrossrefGoogle Scholar
[15] Wang X., Li Y., Quan Z. and Wu J., "Optimal Trajectory-Tracking Guidance for Reusable Launch Vehicle Based on Adaptive Dynamic Programming," Engineering Applications of Artificial Intelligence, Vol. 117, Jan. 2023, Paper 105497. https://doi.org/10.1016/j.engappai.2022.105497 Google Scholar
[16] Yao Q., Jahanshahi H., Moroz I., Bekiros S. and Allassafi M. O., "Indirect Neural-Based Finite-Time Integral Sliding Mode Control for Trajectory Tracking Guidance of Mars Entry Vehicle," Advances in Space Research, Vol. 71, No. 9, 2023, pp. 3723-3733. https://doi.org/10.1016/j.asr.2022.11.059 CrossrefGoogle Scholar
[17] Elobaid M., Mattioni M., Monaco S. and Normand-Cyrot D., "Station-Keeping of L2 Halo Orbits Under Sampled-Data Model Predictive Control," Journal of Guidance, Control, and Dynamics, Vol. 45, No. 7, 2022, pp. 1337-1346. https://doi.org/10.2514/1.G006349 LinkGoogle Scholar
[18] Jung Y., Lee H., Lee Y. and Ahn J., "Composite Zero-Effort-Miss Guidance with Predictor-Corrector Steps for Ballistic Interception," Journal of Guidance, Control, and Dynamics, Vol. 47, No. 2, 2024, pp. 311-325. https://doi.org/10.2514/1.G007760 LinkGoogle Scholar
[19] Wand X., Yin W., Yang Y., Shen Y. and Yan T., "Design of Predictor-Corrector Guidance Law for High-Speed Vehicle Based on DDPG," Aerospace Control, Vol. 42, No. 2, 2024, pp. 22-28. Google Scholar
[20] Davis D., Bhatt S., Howell K., Jang J. W., Whitley R., Clark F., Guzzetti D., Zimovan E. and Barton G., "Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits," AAS/AIAA Space Flight Mechanics Meeting, American Astronautical Soc., Texa, 2017, pp. 1-20. Google Scholar
[21] Davis D., Phillips S., Howell K., Vutukuri S. and McCarthy B. P., "Stationkeeping and Transfer Trajectory Design for Spacecraft in Cislunar Space," AAS/AIAA Astrodynamics Specialist Conference, Springer Nature, London, 2017, p. 8. Google Scholar
[22] Sirbu G. and Leonardi M., "Fully Autonomous Orbit Determination and Synchronization for Satellite Navigation and Communication Systems in Halo Orbits," Remote Sensing, Vol. 15, No. 5, 2023, p. 1173. https://doi.org/10.3390/rs15051173 CrossrefGoogle Scholar
[23] Chihang Y., Ming W. and Zhang H., "Close Relative Motion on Distant Retrograde Orbits," Chinese Journal of Aeronautics, Vol. 36, No. 3, 2023, pp. 335-356. https://doi.org/10.1016/j.cja.2022.11.012 Google Scholar
[24] Zhang R., Wang Y., Shi Y., Zhang C. and Zhang H., "Performance Analysis of Impulsive Station-Keeping Strategies for Cis-Lunar Orbits with the Ephemeris Model," Acta Astronautica, Vol. 198, Sept. 2022, pp. 152-160. https://doi.org/10.1016/j.actaastro.2022.05.054 CrossrefGoogle Scholar
[25] Gao C., Masdemont J. J., Gómez G. and Yuan J., "Low-Thrust Station-Keeping Control for Lunar Near Rectilinear Halo Orbits," Celestial Mechanics and Dynamical Astronomy, Vol. 135, No. 2, 2023, p. 14. https://doi.org/10.1007/s10569-023-10130-x Google Scholar
[26] Gurfil P., "Milankovitch-Lyapunov Geostationary Satellite Stationkeeping," Journal of Guidance, Control, and Dynamics, Vol. 154, No. 7, 2024, pp. 1-8. https://doi.org/10.2514/1.G008263 Google Scholar
[27] Zavoli A. and Federici L., "Reinforcement Learning for Robust Trajectory Design of Interplanetary Missions," Journal of Guidance, Control, and Dynamics, Vol. 44, No. 8, 2021, pp. 1440-1453. https://doi.org/10.2514/1.G005794 LinkGoogle Scholar
[28] Lin X., Zhang G. and Ma H., "Analytical Uncertainty Propagation and Robust Trajectory Optimization for Continuous-Thrust Relative Motion," Journal of Guidance, Control, and Dynamics, Vol. 46, No. 9, 2023, pp. 1745-1758. https://doi.org/10.2514/1.G007355 LinkGoogle Scholar
[29] Yang H., Hu J., Li S. and Bai X., "Reinforcement-Learning-Based Robust Guidance for Asteroid Approaching," Journal of Guidance, Control, and Dynamics, Vol. 47, No. 10, 2024, pp. 2058-2072. https://doi.org/10.2514/1.G008085 LinkGoogle Scholar
[30] Kikuchi S., Tsuda Y., Yoshikawa M. and Kawaguchi J., "Stability Analysis of Coupled Orbit-Attitude Dynamics Around Asteroids Using Finite-Time Lyapunov Exponents," Journal of Guidance, Control, and Dynamics, Vol. 42, No. 6, 2019, pp. 1289-1305. https://doi.org/10.2514/1.G003879 LinkGoogle Scholar
[31] Canales D., Howell K. C., Fantino E. and Gilliam A. J., "Transfers Between Moons with Escape and Capture Patterns via Lyapunov Exponent Maps," Journal of Guidance, Control, and Dynamics, Vol. 46, No. 11, 2023, pp. 2133-2149. https://doi.org/10.2514/1.G007195 LinkGoogle Scholar
[32] Page A., Candelas P. and Belmar F., "On the Use of Local Fitting Techniques for the Analysis of Physical Dynamic Systems," European Journal of Physics, Vol. 27, No. 2, 2006, pp. 273-279. https://doi.org/10.1088/0143-0807/27/2/010 Google Scholar
[33] Weiss A., Kalabić U. V. and Di Cairano S., "Station Keeping and Momentum Management of Low-Thrust Satellites Using MPC," Aerospace Science and Technology, Vol. 76, 2018, pp. 229-241. https://doi.org/10.1016/j.ast.2018.02.014 CrossrefGoogle Scholar
[34] Zou L., Wang Z., Hu J. and Zhou D., "Moving Horizon Estimation with Unknown Inputs under Dynamic Quantization Effects," IEEE Transactions on Automatic Control, Vol. 65, No. 12, 2020, pp. 5368-5375. https://doi.org/10.1109/TAC.2020.2968975 Google Scholar
[35] Lowe B. M. and Zingg D. W., "Flutter Prediction Using Reduced-Order Modeling with Error Estimation," AIAA Journal, Vol. 60, No. 7, 2022, pp. 4240-4255. https://doi.org/10.2514/1.J061389 LinkGoogle Scholar
[36] Azadmanesh M., Mannan F., Roshanian J., Todrov M., Georgiev K. and Hassanalian M., "Parameter Estimation Based on Prediction Error for the Soft-Landing Problem in Micro-Gravity," AIAA Aviation Forum and Ascend 2024, AIAA Paper 2024-4915, 2024. https://doi.org/10.2514/6.2024-4915 Google Scholar
[37] Fereoli G., Schaub H. and Di Lizia P., "Meta-Reinforcement Learning for Spacecraft Proximity Operations Guidance and Control in Cislunar Space," Journal of Spacecraft and Rockets, Vol. 62, No. 3, 2024, pp. 1-13. https://doi.org/10.2514/1.A36100 Google Scholar
[38] Sasfi A., Zeilinger M. N. and Köhler J., "Robust Adaptive MPC Using Control Contraction Metrics," Automatica, Vol. 155, Sept. 2023, Paper 111169. https://doi.org/10.1016/j.automatica.2023.111169. Google Scholar
[39] Federici L., Scorsoglio A., Ghilardi L. and et al., "Image-Based Meta-Reinforcement Learning for Autonomous Guidance of an Asteroid Impactor," Journal of Guidance, Control, and Dynamics, Vol. 45, No. 11, 2022, pp. 2013-2028. https://doi.org/10.2514/1.G006832 LinkGoogle Scholar
[40] Gaudet B., Linares R. and Furfaro R., "Deep Reinforcement Learning for Six Degree-of-Freedom Planetary Landing," Advances in Space Research, Vol. 65, No. 7, 2020, pp. 1723-1741. https://doi.org/10.1016/j.asr.2019.12.030 CrossrefGoogle Scholar
[41] Gaudet B., Linares R. and Furfaro R., "Adaptive Guidance and Integrated Navigation with Reinforcement Meta-Learning," Acta Astronautica, Vol. 169, April 2020, pp. 180-190. https://doi.org/10.1016/j.actaastro.2020.01.007 CrossrefGoogle Scholar
[42] LaFarge N. B., Howell K. C. and Folta D. C., "Adaptive Closed-Loop Maneuver Planning for Low-Thrust Spacecraft Using Reinforcement Learning," Acta Astronautica, Vol. 211, Oct. 2023, pp. 142-154. https://doi.org/10.1016/j.actaastro.2023.06.004 CrossrefGoogle Scholar
[43] Zhang E. and Masoud N., "Increasing GPS Localization Accuracy with Reinforcement Learning," IEEE Transactions on Intelligent Transportation Systems, Vol. 22, No. 5, 2020, pp. 2615-2626. https://doi.org/10.1109/TITS.2020.2972409 Google Scholar
[44] Hu J., Yang H., Li S. and Zhao Y., "Densely Rewarded Reinforcement Learning for Robust Low-Thrust Trajectory Optimization," Advances in Space Research, Vol. 72, No. 4, 2023, pp. 964-981. https://doi.org/10.1016/j.asr.2023.03.050 CrossrefGoogle Scholar
[45] Chen H., Hou X. and Bando M., "Stable Orbiting Around Small Moons Using J 2-Perturbed Elliptic Restricted Problem," Journal of Guidance, Control, and Dynamics, Vol. 47, No. 7, 2024, pp. 1-14. https://doi.org/10.2514/1.G008001 Google Scholar
[46] Fehse W., Automated Rendezvous and Docking of Spacecraft, Cambridge Univ. Press, Cambridge, MA, 2003, pp. 1-26. CrossrefGoogle Scholar
[47] Oguri K. and McMahon J. W., "Stochastic Primer Vector for Robust Low-Thrust Trajectory Design under Uncertainty," Journal of Guidance, Control, and Dynamics, Vol. 45, No. 1, 2022, pp. 84-102. https://doi.org/10.2514/1.G005970 LinkGoogle Scholar
[48] Wardi Y., Seatzu C., Cortés J., Egerstedt M., Shivam S. and Buckley I., "Tracking Control by the Newton-Raphson Method with Output Prediction and Controller Speedup," International Journal of Robust and Nonlinear Control, Vol. 34, No. 1, 2024, pp. 397-422. https://doi.org/10.1002/rnc.6976 CrossrefGoogle Scholar