ارائه رویکرد جدید برای طراحی مسیر ماهواره با سیستم پیشرانش تراست پایین در مسئله سه جسمی انتقال از مدار ژئو به مدار هالو

نوع مقاله : مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران

2 دانشجوی دکتری / دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران

چکیده

در این مقاله روش جدیدی برای طراحی مسیر ماهواره در فاز اولیه طراحی مأموریت در مسئله سه‌جسمی انتقال از مدار ژئو به مدار هالو ارائه شده است. در این روش مسیر تقریبی و نزدیک‌به بهینه از نظر زمان مأموریت، از طریق تخمین زاویه تراست حاصل می‌شود، بدین صورت که زوایای تراست در صفحه و خارج از صفحه به‌صورت سری‌های فوریه با ضرایب محدود و نامعین در نظر گرفته می‌شوند. مقادیر ضرایب با استفاده از الگوریتم بهینه‌سازی و با هدف مینیمم کردن زمان مأموریت بدست می‌آید. باتوجه‌به اینکه تعداد دورهای مسیر مشخص نیست، این پارامتر نیز به‌عنوان متغیر تصمیم گسسته مسئله بهینه‌سازی در نظر گرفته می‌شود. به‌دلیل وجود متغیرهای تصمیم پیوسته و گسسته، الگوریتم بهینه‌سازی ازداحام ذرات گسسته به‌عنوان روش بهینه‌سازی استفاده شده است. از مزایای این روش می‌توان به سادگی اجرا و حجم کم محاسبات ریاضی، در نظر گرفتن تغییرات جرم ماهواره به‌دلیل مصرف سوخت، عدم اعمال قید خاص برای زاویه تراست نظیر تراست مماسی و تعیین زمان و مسیر نزدیک‌به بهینه اشاره کرد. برای ارزیابی روش ارائه‌شده، طراحی مسیر انتقال از مدار ژئو به مدار هالو برای سطوح تراست مختلف مورد بررسی قرار گرفته است. نتایج نشان دادند که رویکرد ارائه‌شده با دقت بسیار خوبی تعداد دورهای مسیر، جرم سوخت مصرفی، زمان و مسیر نزدیک‌به بهینه را ارائه می‌دهد.

کلیدواژه‌ها

عنوان مقاله [English]

A new approach for low-thrust trajectory design for GEO to Halo transfer in three-body problem

نویسندگان [English]

  • Kamran Daneshjou 1
  • Abbasali Mohammadi Dehabadi 2
1 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
2 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
چکیده [English]

In this study, a new approach is proposed to design low-thrust trajectory in the preliminary design phase for GEO to Halo transfer in the three-body problem. In this method, the approximate and near optimal trajectory is conducted through guessing thrust angles. In this approach, the in-plane and out of plane thrust angles are considered as finite Fourier series with unknown coefficients. The coefficients are calculated by an optimization algorithm with the aim of minimizing mission duration. Since the number of the trajectory revolutions is unknown, this parameter is also considered as a discrete decision variable of optimization algorithm. Due to the existence of continues and discrete decision variables, discrete particle swarm optimization algorithm is employed to solve the problem. The advantages of this method include: simplicity of execution and low volume of mathematical computation, considering satellite mass, do not assume special restriction for thrust angle such as tangential thrust and determination the near optimal mission duration. . In order to evaluate the proposed method, Trajectory design of GEO to Halo is performed for several level of thrust. Results indicate that this approach determines the number of trajectory revolutions, fuel consumed, near optimal duration and trajectory of the mission with high accuracy.

کلیدواژه‌ها [English]

  • Low thrust trajectory design
  • three-body problem
  • preliminary design phase
  • approximate and near optimal solution
  • discrete particle swarm optimization algorithm

مراجع

[1]   M. D. Rayman, P. Varghese, D. H. Lehman, and L. L. Livesay, Results from the Deep Space 1 technology validation mission, Acta Astronautica, Vol. 47, No. 2, pp. 475–487, 2000.
[2]   K. Komurasaki, An overview of electric propulsion activities, In 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2003.
[3]   B. H. Foing et al., ESA’s SMART-1 mission launched to the MOON: Technology and science goals, Science and Technology Series, Vol. 108, No. 11, pp. 3–14, 2004.
[4]   C. R. Hargraves and S. W. Paris, Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, pp. 338–342, 1987.
[5]   P. J. Enright and B. A. Conway, Discrete approximations to optimal trajectories using direct transcription and nonlinear programming, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 4, pp. 994–1002, 1992.
[6]   J. A. Kechichian, Optimal low-earth-orbit-geostationary-earth-orbit intermediate acceleration orbit transfer, Journal of Guidance, Control, and Dynamics, Vol. 20, No. 4, pp. 803–811, 1997.
[7]   J. T. Betts, Survey of numerical methods for trajectory optimization, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, pp. 193–207, 1998.
[8]   C. L. Ranieri and C. A. Ocampo, Indirect optimization of three-dimensional finite-burning interplanetary transfers including spiral dynamics, Journal of Guidance, Control, and Dynamics, Vol. 32, No. 2, pp. 445–455, 2009.
[9]   J. T. Betts, Very low-thrust trajectory optimization using a direct SQP method, Journal of Computational and Applied Mathematics, Vol. 120, No. 1, pp. 27–40, 2000.
[10] R. Falck and J. Dankanich, Optimization of low-thrust spiral trajectories by collocation, in AIAA/AAS Astrodynamics Specialist Conference,  p. 4423, 2012.
[11] L. Mazzini, Finite thrust orbital transfers, Acta Astronautica, Vol. 100, pp. 107–128, 2014.
[12] S. Li, Y. Zhu, and Y. Wang, Rapid design and optimization of low-thrust rendezvous/ interception trajectory for asteroid deflection missions, Advances in Space Research, Vol. 53, No. 4, pp. 696–707, 2014.
[13] C. Sun, J. Yuan, and Q. Fang, Continuous low thrust trajectory optimization for preliminary design, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 230, No. 5, pp. 921–933, 2016.
[14] A. E. Petropoulos and J. M. Longuski, Automated design of low-thrust gravity-assist trajectories, In AIAA/AAS Astrodynamics Specialist Conference, Vol. 4033, pp. 157–166, 2000.
[15] A. E. Petropoulos and J. M. Longuski, A shape-based algorithm for the automated design of low-thrust, gravity-assist trajectories, dvances in the Astronautical Sciences, Vol. 109, No. 5, pp. 2321–2336, 2002.
[16] B. J. Wall and B. A. Conway,  Shape-based approach to low-thrust rendezvous trajectory design, Journal of Guidance, Control, and Dynamics, Vol. 32, No. 1, pp. 95–102, 2009.
[17] B. J. Wall,  Shape-based approximation method for low-thrust trajectory optimization, In AIAA/AAS Astrodynamics Specialist Conference and Exhibit, pp. 18–21, 2008.
[18] D. Wang, G. Zhang, and X. Cao, Modified inverse-polynomial shaping approach with thrust and radius constraints, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 229, No. 13, pp. 2506–2518, 2015.
[19] D. M. Novak and M. Vasile, Improved shaping approach to the preliminary design of low-thrust trajectories, Journal of Guidance, Control, and Dynamics, Vol. 34, No. 1, pp. 128–147, 2011.
[20] C. Xie, G. Zhang, and Y. Zhang, Shaping approximation for low-thrust trajectories with large out-of-plane motion, Journal of Guidance, Control, and Dynamics, Vol. 39, No. 12, pp. 2776–2785, 2016.
[21] M. Vasile, P. De Pascale, and S. Casotto, On the optimality of a shape-based approach based on pseudo-equinoctial elements, Acta Astronautica, Vol. 61, No. 1–6, pp. 286–297, 2007.
[22] B. D. E. Vogeleer, Automatic and Fast Generation of Sub-optimal and Feasible Low-Thrust Trajectories Using a Method, TU Delft, Delft University of Technology, 2008.
[23] E. Taheri and O. Abdelkhalik, Shape based approximation of constrained low-thrust space trajectories using Fourier series, Journal of Spacecraft and Rockets, Vol. 49, No. 3, pp. 535–546, 2012.
[24] E. Taheri and O. Abdelkhalik, Fast initial trajectory design for low-thrust restricted-three-body problems, Journal of Guidance, Control, and Dynamics, Vol. 38, No. 11, pp. 2146–2160, 2015.
[25] E. Taheri and O. Abdelkhalik, Initial three-dimensional low-thrust trajectory design, Advances in Space Research, Vol. 57, No. 3, pp. 889–903, 2016.
[26] D. J. Gondelach and R. Noomen, “Hodographic-shaping method for low-thrust interplanetary trajectory design, Journal of Spacecraft and Rockets, Vol. 52, No. 3, pp. 728–738, 2015.
[27] K. Zeng, Y. Geng, B. Wu, and C. Xie, A novel shape-based approximation method for constrained low-thrust trajectory design, In AIAA/AAS Astrodynamics Specialist Conference, p. 5637, 2016.
[28] Z. Fan, M. Huo, N. Qi, C. Zhao, Z. Yu, and T. Lin, Initial design of low-thrust trajectories based on the Bezier curve-based shaping approach, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 234, No. 11, pp. 1825–1835, 2020.
[29] Z. Fan, M. Huo, J. Qi, and N. Qi, Fast initial design of low-thrust multiple gravity-assist three-dimensional trajectories based on the Bezier shape-based method, Acta Astronautica, Vol. 178, pp. 233–240, 2021.
[30] H. D. Curtis, Orbital Mechanics for Engineering Students. Butterworth-Heinemann, 2013.
[31] V. A. Chobotov, Orbital mechanics. American Institute of Aeronautics and Astronautics, 2002.
[32] J.-B. Caillau, B. Daoud, and J. Gergaud, Minimum fuel control of the planar circular restricted three-body problem, Celestial Mechanics and Dynamical Astronomy, Vol. 114, No. 1–2, pp. 137–150, 2012.
[33] D. E. Kirk, Optimal control theory: an introduction. Courier Corporation, 2004.
[34] Y.-X. Jin, H.-Z. Cheng, J. Yan, and L. Zhang, New discrete method for particle swarm optimization and its application in transmission network expansion planning, Electric Power Systems Research, Vol. 77, No. 3–4, pp. 227–233, 2007.
[35] T. Bäck, D. B. Fogel, and Z. Michalewicz, Handbook of evolutionary computation, Release, Vol. 97, No. 1, p. B1, 1997.
[36] C. Zhang, F. Topputo, F. Bernelli-Zazzera, and Y. S. Zhao, Low-thrust minimum-fuel optimization in the circular restricted three-body problem, Journal of Guidance, Control, and Dynamics, Vol. 38, No. 8, pp. 1501–1509, 2015.

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