بهینه‌سازی انتقال مداری چندضربه‏ ای با استفاده از روش شبه ‌نیوتن

نوع مقاله: مقالة‌ تحقیقی‌ (پژوهشی‌)

نویسندگان

1 دانشگاه صنعتی شریف، تهران، ایران

2 دانشکده مهندسی هوافضا، دانشگاه صنعتی شریف

3 استاد دانشگاه صنعتی شریف

4 پژوهشکده سامانه های ماهواره، پژوهشگاه فضایی ایران، تهران، ایران

چکیده

در این مقاله روشی جامع برای دست‌یابی به مسیرهای انتقال مداری بهینه بین دو مدار بیضوی غیرصفحه‏ای با استفاده از چند ضربه بر مبنای تکه مسیرهای لمبرت متوالی ارائه شده است. هدف، دست‌یابی به این مسیرها همراه با حداقل میزان مصرف سوخت است. از قابلیت‏های این روش پیشنهادی می‌توان به توانایی پیاده‏سازی برای تعداد دلخواه ضربه، تنوع مشخصات مدار ابتدایی و انتهایی و پوشش تمامی مسیرهای امکان‌پذیر قابل دست‌یابی به مدار هدف اشاره کرد. تعداد ضربه‏ها به عنوان ورودی مسئله لحاظ شده و مکان و زمان اعمال ضربه به عنوان متغیرهای بهینه‏سازی درنظر گرفته شده‌است. با توجه به زیادبودن تعداد متغیرهای بهینه‏سازی، از روش حل شبه‏ نیوتن جهت افزایش سرعت بهینه‏سازی کمک گرفته شده است. در راستای اعتبارسنجی روش پیشنهادی، ابتدا یک مسئلة انتقال مداری بین دو مدار دایروی بررسی شده و همگرایی حل حاصله به حل مسئله هاهمن نشان داده شده است. سپس، کارآیی روش پیشنهادی در مانورهای ملاقات و انتقال مداری نیز بررسی و نشان داده شده است.

کلیدواژه‌ها


عنوان مقاله [English]

Optimal Multiple-Impulse Orbit Transfer Utilizing Pseudo-Newton Method

نویسندگان [English]

  • Maryam Kiani 1
  • Amir Shakouri 2
  • S.H Pourtakdoust 3
  • Mohammad Sayanjali 4
1 Sharif university of technology, Tehran, Iran
2 Department of Aerospace Engineering, Sharif University of Technology
3 Department of Aerospace Engineering, Sharif University of Technology
4 Space System Research center, Iran Space Center, Tehran, Iran
چکیده [English]

A new strategy is presented for the optimal transfer of non-coplanar elliptical orbits based on sequential multi-Lambert trajectories. The proposed method tries to minimize the control effort during the orbit transfer. The main advantages of the proposed method include transfer between arbitrary initial and final orbits, utilizing desired number of impulses, and covering all possible transfer trajectories to achieve the target. The position and time instant of impulses are considered as the design variables which determine utilizing the well-known optimization method of pseudo-Newton. Performance of the proposed method is investigated and verified through some numerical simulations. It is also shown that the proposed method converges to the celebrated Hahmann’s maneuver in transfer between two coplanar orbital orbits.

کلیدواژه‌ها [English]

  • Orbital maneuver
  • Multiple-impulse maneuver
  • optimization
  • Pseudo-Newton method

[1]   Hohmann, W. and Ozaki, S., “The Attainability of Heavenly Bodies,” NASA Technical Translation F-44, Washington, DC, 1960.

[2]  Lion, P. M. and Handelsman, H., “Primer Vector on Fixed-Time Impulsive Trajectories,” AIAA Journal, Vol. 6, No. 1, 1968, pp. 127-132.

[3]  Prussing, J. E. andChiu, J. H., “Optimal Multiple-Impulse Time-Fixed Rendezvous Between Circular Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 9, No. 1, 1986, pp. 17-22.

[4]  Lawden, D. F., “Optimal Transfer Between Coplanar Elliptical Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 12, No. 3, 1992, pp. 788-791.

[5]  Taur, D. R., Coverstone-Carroll, V. and J. E. Prussing, "Optimal Impulsive Time-Fixed Orbital Rendezvous and Interception with Path Constraints," Journal of Guidance, Control, and Dynamics, Vol. 18, No. 1, 1995, pp. 54-60.

[6]  Wenzel, R. S. and Prussing, J. E., "Preliminary Study of Optimal Thrust-Limited Path-Constrained Maneuvers," Journal of Guidance, Control, and Dynamics, Vol. 19, No. 6, 1996, pp. 1303-1309.

[7]  Kim, Y. H., and Spencer, D. B., "Optimal Spacecraft Rendezvous Using Genetic Algorithms," Journal of Spacecraft and Rockets, Vol. 39, No. 6, 2002, pp. 859-865.

[8]  Pontani, M., Ghosh, P., and Conway, B. A., "Particle Swarm Optimization of Multiple-Burn Rendezvous Trajectories," Journal of Guidance, Control, and Dynamics, Vol. 35, No. 4, 2012, pp. 1192-1207.

[9]  Shakouri, A., Trajectory Shaping of Orbital Maneuver in Presence of Uncertainty, M.Sc. Thesis, Sharif University of Technology, 2017.

[10] Navabi, M. andSanatifar, M., “Optimal Impulsive Maneuver Between Elliptical Coplanar-Noncoaxial Orbits,” Journal of Space Science and Technology (JSST), Vol. 3, No., 12, 2010, pp. 67-74.

[11] Navabi, M. and Sanatifar, M., “Optimal Impulsive Orbital 3D Maneuver with or without Time Constraints,” Amirkabir Journal of Mechanical Engineering, Vol. 44, No. 53, 2012, pp. 53-69.

[12] Curtis, H. D.,Orbital Mechanics for Students,3rd Ed., Butterworth-Heinemann, Boston, 2014.

[13] Prussing, J. E., “A Class of Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions,” Journal of the Astronautical Sciences, Vol. 48, No. 2, 2000, pp. 131-148.

[14] Shen, H. J., and Tsiotras, P., “Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions,” Journal of Guidance, Control, and Dynamics, Vol. 26, No. 1, 2003, pp. 50-61.

[15] Zhang, G., and Mortari, D., “Constrained Multiple-Revolution Lambert's Problem,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 6, 2010, pp. 1779-1786.

[16] Engels, R., and Junkins, J., “The Gravity-Perturbed Lambert Problem: A KS Variation of Parameters Approach,” Celestial Mechanics, Vol. 24, No. 3, 1981, pp. 3-21.

[17] Kechichian, J. A., “The Algorithm of the Two-Impulse Time-Fixed Noncoplanar Rendezvous with Drag and Oblateness Effects,” Journal of the Astronautical Sciences, Vol. 46, No. 1, 1998, pp. 47-64.

[18] Schumacher, P. W., Sabol C., Higginson C. C., and Alfriend K. T., “Uncertain Lambert Problem,” Journal of Guidance, Control, and Dynamics, Vol. 38, No. 9, 2015, pp. 1573-1584.

[19] Abdelkhalik, O., and Mortari, D., “N-Impulse Orbit Transfer Using Genetic Algorithms,” Journal of Spacecraft and Rockets, Vol. 44, No. 2, 2007, pp. 456-460.

[20] Bryson, A. E., HoY. C., Applied Optimal Control,Hemisphere Publishing Corporation, London, 1975.

[21] Kelley, C. T.,Iterative Methods for Optimization,SIAM, Philadelphia,1999.

[22] Nocedal, J. and Wright, S. J., Numerical Optimization,Springer, New York, 2006.

[23] Davidon, W. C., “Variable Metric Method for Minimization,” SIAM Journal of Optimization, Vol. 1, No. 1, 1991, pp. 1-17.

[24] Fletcher, R.,Practical Methods of Optimization,John Wiley & Sons,Chichester,1987.

[25] Broyden, C. G., “A Class of Methods for Solving Nonlinear Simultaneous Equations,” Mathematics of Computation, Vol. 19, No. 92, 1965, pp. 577-593.

[26] Byrd R. H., “Analysis of a Symmetric Rank-One Trust Region Method,” SIAM Journal of Optimization, Vol. 6, No. 4, 1996, pp. 1025-1039.