Document Type : Research Paper

Author

Assistant Professor, Aerospace Research Institute, Ministry of Science , Research and Technology, Tehran, Iran

10.22034/jsst.2024.1438

Abstract

The aim of this research is to optimize the trajectory of a low-trust spacecraft carrying biological cargo. Reducing the radiation stresses of the Van Allen belt is the optimal criterion of the optimal control problem of the orbital transfer from the low orbits to the high orbits. Since the minimum radiation stress criterion introduced in this article is not among the conventional optimality criteria, solving the above optimal control problem will be complicated and the honey bee optimization method has been used. The optimization of the path in this article is done by rewriting the motion equations based on the control variable and solving the new motion equations with the help of bee optimization. The main advantage of the method used in this problem is the use of optimal control theory and population-based optimization methods with a global approach. In the presented new method, the optimal control problem is simplified by redefining the differential equation system, and the results show the accuracy and ease of solution. Results of the optimal criterion of the minimum time and the minimum radiation stresses presented in this article, the criterion of the minimum radiation causes an increase of 8.89% in the transfer time.

Keywords

Main Subjects

[1] I. Shafieenejad and S. Ghasemi, "Effects of Gravitational and Radiate Stresses on Plants Growth for Space Travels," Journal of Technology in Aerospace Engineering, vol. 2, no. 4, pp. 1-5, 2019, (in persian).
[2]   I. Shafieenejad and S. Ghasemi, R. Safarzadeh  "New Beginnings in Biospace Science Case Study: Return to the Moon," Fourth National Conference on Mechanical and Aerospace Engineering, Tehran, Iran, 2019 (in persian).
[3]   P. Ye, Z. Sun, H. Zhang, and F. Li, "An overview of the mission and technical characteristics of Change’4 Lunar Probe," Science China Technological Sciences, vol. 60, pp. 658-667, 2017, https://doi.org/10.1007/
s11431-016-9034-6
[4]   I. Shafieenejad, A.B. Novinzadeh, “Analytical solutions for two-point boundary value problems: optimal low-thrust orbit transfers” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 224, no. 7, pp. 843-853, 2010.
[5]   A. Miele, T. Wang, and P. Williams, “Computation of optimal Mars trajectories via combined chemical/electrical propulsion, part 1: baseline solutions for deep interplanetary space,” Acta Astronautica, vol. 55, no. 2, pp. 95-107, 2004. https://doi.org/10.1016/j.actaastro.2004.01.053.
[6]   B. Pinkel,“Electrical Propulsion for Space Missions: Planning Considerations”, Progress in Astronautics and Rocketry, vol.16, pp. 163-208: Elsevier, 1966. https://doi.org/10.1016/B978-1-4832-3056-6.50011-6.
[7]   I. Shafieenejad, S. Ghasemi, A. Mahmoodi, A.H. Mirsayafi “A Review of Recent Research on Space Missions with the Van Allen Belt and Biospace Approach, Part I,” Fourth National Conference on Mechanical and Aerospace Engineering, 2019. (in persian)
[8]   R. J. Bull, J. A. Atchison, and F. E. Siddique, “Van Allen Probes End of Mission Navigation and Mission Design.”  AAS Space Flight Mechanics Conference , Lake Tahoe, UT, August 2020.
[9]   U. J. Shankar, M. N. Kirk, and G. D. Rogers, "Van Allen Probes On-Orbit Verification of Spacecraft Dynamics," in The 24th International Symposium on Space Flight Dynamics, 2014.
[10] M. Da Silva and E. Rocco, “Analysis of the passage of a spacecraft between the Van Allen belts considering a low and high solar activity.” in Journal of Physics: Conference Series, 2017, vol. 911, no. 1: IOP Publishing, p. 012005.
[11] G. L. Vonpragenau, “SPACE VEHICLE,” no. June, 1975, Copyright,Work of the US Gov. Public Use Permitted. (Patent NASA-CASE-MFS-22734-1|US-PATENT-3, 866, 863).
[12] I. Shafieenejad, A. B. Novinzadeh, and V. R. Molazadeh, “Introducing a novel algorithm for minimum-time low-thrust orbital transfers with free initial condition,” Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng., vol. 229, no. 2, pp. 333–351, Feb. 2015.
[13] M. Fakoor, S. Sadeghi, and M. Bakhtiari, “Investigation of Low Thrust Optimal Orbital Transfer from LEO to GEO Considering Circular Orbits,” The Journal of the Astronautical Sciences, vol. 67, pp. 77-97, 2020.
[14] J. A. Kechichian, “The reformulation of Edelbaum’s low-thrust transfer problem using optimal control theory,” Astrodyn. Conf. 1992, vol. 20, no. 5, pp. 381–391, 1992. https://doi.org/10.2514/6.1992-4576
[15] I. Shafieenejad, A. B. Novinzadeh, and V. R. Molazadeh, “Comparing and analyzing min-time and min-effort criteria for free true anomaly of low-thrust orbital maneuvers with new optimal control algorithm,” Aerosp. Sci. Technol., vol. 35, no. 1, pp. 116–134, 2014. https://doi.org/10.1016/j.ast.2014.03.009.
[16] M. Di Carlo and M. Vasile, "Analytical solutions for low-thrust orbit transfers," Celestial Mechanics and Dynamical Astronomy, vol. 133, no. 7, p. 33, 2021.
[17] Y. Wang, C. Han, and X. Sun, "Optimization of low-thrust Earth-orbit transfers using the vectorial orbital elements," Aerospace Science and Technology, vol. 112, p. 106614, 2021, https://doi.org/10.1016/j.ast.
2021.106614.
[18] H. Weinert, "Bryson, AE/Ho, Y.-C., Applied Optimal Control, Optimization, Estimation, and Control. New York-London-Sydney-Toronto. John Wiley & Sons. 1975. 481 S.,£ 10.90," Zeitschrift Angewandte Mathematik und Mechanik, vol. 59, no. 8, pp. 402-402, 1979.
[19] D. S. Naidu, Optimal Control Systems (Electrical Engineering Series), CRC Press, 2002.
[20] M.O.Burrell, J.J.Wright, and J.W.Watts, “An analysis of energetic space radiation and dose rates,” NASA Technical Note, National Aeronautics and Space Administration, Vashington, Feb. 1968.
[21] M.B. Baker, “Geomagnetically Trapped Radiation,” AIAA Journal ,vol. 3, no. 9, 1965,  https://doi.org/10.2514/3.55177.
[22] V. Tereshko and A. Loengarov, "Collective decision making in honey-bee foraging dynamics," Computing and Information Systems, vol. 9, no. 3, p. 1, 2005.
[23] D. Karaboga, “An idea based on honey bee swarm for numerical optimization,” Technical report-tr06, Erciyes university, engineering faculty, computer engineering department , vol. 200, p. 1-10, 2005
[24] T. D. Seeley, The wisdom of the hive: the social physiology of honey bee colonies. Harvard University Press, 1995.
[25]V. Chobotov, Editor, Orbital Mechanics, Second Edition, AIAA Education Series, Reston, VA: American Institute of Aeronautics and Astronautics, Inc, 1996.