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Research Article

Midcourse correction of Earth–Moon distant retrograde orbit transfer trajectories based on high-order state transition tensors

Yongchen Yin1,2,3, Ming Wang1,2, Yu Shi1, Hao Zhang1()
Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences, Beijing 100094, China
University of Chinese Academy of Sciences, Beijing 100049, China
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
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This paper presents an efficient method for the midcourse correction of DRO transfer orbits and reports that the orbital error can be reduced significantly using the high-order STT guidance algorithm.

Abstract

Midcourse correction design is key to space transfers in the cislunar space. Autonomous guidance has garnered significant attention for its promise to decrease the dependence on ground control systems. This study addresses the problem of midcourse corrections for Earth–Moon transfer orbits based on high-order state transition tensors (STTs). The scenarios considered are direct Earth–Moon transfers and low-energy transfers to lunar distant retrograde orbits (DROs), where the latter involve weak stability boundary (WSB) and lunar gravity assist (LGA) techniques. Semi-analytical formulas are provided for computing the trajectory correction maneuvers (TCMs) using high-order STTs derived using the differential algebraic method. Monte Carlo simulations are performed to evaluate the effectiveness of the proposed approach. Compared with existing explicit guidance algorithms, the STT-based approach is much cheaper computationally and features fewer final position errors. These results are promising for fast and efficient orbital autonomous correction guidance approaches in the cislunar space.

Keywords

cislunar spacetransfer orbitmidcourse correctionstate transition tensor (STT)Monte Carlo simulation

References

[1]

Ouyang, Z. Y., Zou, Y. L., Li, C. L., Liu, J. Z., Xu, L. Lunar exploration and containable development for human society. Bulletin of Mineralogy Petrology and Geochemistry, 2003, 22(4): 328–333. (in Chinese)

Google Scholar
[2]

Wen, C., Gao, Y. Solution and stability analysis of resonance orbits of DRO and HEO (3: 1 / 2: 1) in Earth Moon Space. Manned Spaceflight, 2018, 24(6): 703–718. (in Chinese)

Google Scholar
[3]
Gates, M., Muirhead, B., Naasz, B., McDonald, M., Mazanek, D., Stich, S., Chodas, P., Reuter, J. NASA’s Asteroid Redirect Mission concept development summary. In: Proceedings of the 2015 IEEE Aerospace Conference, 2015: 1–13.
Crossref
[4]

Liu, J. K., Wang, W. B., Zhang, H., Shu, L. Z., Gao, Y. Autonomous orbit determination and timekeeping in lunar distant retrograde orbits by observing X-ray pulsars. NAVIGATION, 2021, 68(4): 687–708.

Crossref Google Scholar
[5]
Capdevila, L., Guzzetti, D., Howell, K. Various transfer options from Earth into Distant Retrograde Orbits in the vicinity of the Moon. In: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting, 2014: 118.
[6]

Belbruno, E. A., Miller, J. K. Sun-perturbed Earth-to-Moon transfers with ballistic capture. Journal of Guidance, Control, and Dynamics, 1993, 16(4): 770–775.

Crossref Google Scholar
[7]

Xu, M., Xu, S. J. Exploration of distant retrograde orbits around Moon. Acta Astronautica, 2009, 65(5–6): 853–860.

Crossref Google Scholar
[8]

Zhang, C., Zhang, H. Lunar-gravity-assisted low-energy transfer from Earth into DROs. Acta Aeronautica et Astronautica Sinica, 2023, 44(2): 326507. (in Chinese)

Google Scholar
[9]

McCarthy, B. P., Howell, K. C. Leveraging quasi-periodic orbits for trajectory design in cislunar space. Astrodynamics, 2021, 5(2): 139–165.

Crossref Google Scholar
[10]
Stern, R. G., Potter, J. E. Optimization of Midcourse Velocity Corrections. In: Peaceful Uses of Automation in Outer Space. Aseltine, J. A., Ed. Boston, MA, USA: Springer, 1966: 70–84.
Crossref
[11]

He, W., Xu, S. J. Study on midcourse correction of low energy consumption Earth–Moon transfer orbit. Aerospace Control, 2007, 25(5): 22–27. (in Chinese)

Google Scholar
[12]

Stern, R. G., Potter, J. E. Optimization of midcourse velocity corrections. IFAC Proceedings Volumes, 1965, 2(1): 70–83.

Crossref Google Scholar
[13]

Zhou, W., Yang, W. Mid-correction of trans-lunar trajectory of lunar explorer. Journal of Astronautics, 2004, 25(1): 89–92. (in Chinese)

Google Scholar
[14]

Qi, Y., de Ruiter, A. Trajectory correction for lunar flyby transfers to libration point orbits using continuous thrust. Astrodynamics, 2022, 6(3): 285–300.

Crossref Google Scholar
[15]

Park, R. S., Scheeres, D. J. Nonlinear semi-analytic methods for trajectory estimation. Journal of Guidance, Control, and Dynamics, 2007, 30(6): 1668–1676.

Crossref Google Scholar
[16]

Boone, S., McMahon, J. Orbital guidance using higher-order state transition tensors. Journal of Guidance, Control, and Dynamics, 2021, 44(3): 493–504.

Crossref Google Scholar
[17]

Di Lizia, P., Armellin, R., Ercoli-Finzi, A., Berz, M. High-order robust guidance of interplanetary trajectories based on differential algebra. Journal of Aerospace Engineering, Sciences and Applications, 2008, 1(1): 43–57.

Crossref Google Scholar
[18]

Hou, X. Y., Liu, L. On quasi-periodic motions around the triangular libration points of the real Earth–Moon system. Celestial Mechanics and Dynamical Astronomy, 2010, 108(3): 301–313.

Crossref Google Scholar
[19]

Turner, G. Results of long-duration simulation of distant retrograde orbits. Aerospace, 2016, 3(4): 37.

Crossref Google Scholar
[20]

Wu, X., Zeng, L., Gong, Y. DRO computation and its perturbative force in the Earth–Moon system. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(5): 883–892. (in Chinese)

Google Scholar
[21]

Breakwell, J. V. Fuel requirements for crude interplanetary guidance. Advances in Astronautical Science, 1960, 5: 53–65.

Google Scholar
[22]

Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D. Low energy transfer to the moon. Celestial Mechanics and Dynamical Astronomy, 2001, 81(1–2): 63–73.

Crossref Google Scholar
[23]

Oberth, H. Ways to Spaceflight. Munich/Berlin: R. Oldenbourg Publishing House, 1929.

[24]

Muralidharan, V., Howell, K. C. Stretching directions in cislunar space: Applications for departures and transfer design. Astrodynamics, 2023, 7(2): 153–178.

Crossref Google Scholar
[25]

Yang, Z., Luo, Y., Zhang, J. Nonlinear semi-analytical uncertainty propagation of trajectory under impulsive maneuvers. Astrodynamics, 2019, 3(1): 61–77.

Crossref Google Scholar
[26]

Szebehely, V. Theory of Orbits. New York: Academic Press, 1967.

[27]

Qi, Y., Xu, S. J. Study of lunar gravity assist orbits in the restricted four-body problem. Celestial Mechanics and Dynamical Astronomy, 2016, 125(3): 333–361.

Crossref Google Scholar
[28]

Bani Younes, A. Exact computation of high-order state transition tensors for perturbed orbital motion. Journal of Guidance, Control, and Dynamics, 2019, 42(6): 1365–1371.

Crossref Google Scholar
[29]

Park, R. S., Scheeres, D. J. Nonlinear mapping of Gaussian statistics: Theory and applications to spacecraft trajectory design. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1367–1375.

Crossref Google Scholar
[30]

Chen, G., Yang, C., Zhang, C., Zhang, H. Distant retrograde orbits and its bifurcations in Earth–Moon system. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(12): 2576–2588. (in Chinese)

Google Scholar
Astrodynamics
Volume 7 Issue 3,
September 2023
Pages 335-349
DOI: 10.1007/s42064-023-0162-8
Cite this article:
Yin Y, Wang M, Shi Y, et al. Midcourse correction of Earth–Moon distant retrograde orbit transfer trajectories based on high-order state transition tensors. Astrodynamics, 2023, 7(3): 335-349. https://doi.org/10.1007/s42064-023-0162-8
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