نویسندگان

دانشگاه صنعتی امیرکبیر

چکیده

در مقالة حاضر، رویکرد جدیدی برای حل مسئلة انتقال مداری بهینه با تراست کم پیشنهاد می‌شود. در این رویکرد، مسئلة بهینه‌سازی مسیر انتقال مداری بهینه، با المان‌های مداری اعتدالی اصلاح‌شده تعریف می‌گردد. برای حل این مسئله، از روش هم‌نشانی مستقیم که یک روش عددی کارا برای حل مسائل کنترل بهینه است، استفاده می‌شود. با استفاده از این روش، مسئلة بهینه‌سازی مسیر به‌طور کامل گسسته شده و تبدیل به یک مسئلة برنامه‌ریزی غیرخطی می‌شود. این مسئلة گسسته که تعداد بسیار زیادی متغیر دارد، با یک حل‌کنندة برنامه‌ریزی غیرخطی قدرتمند به نام IPOPTحل می‌شود. در نهایت، مقادیر بهینة حالت و کنترل برای انتقال مداری بهینه با حداقل مصرف سوخت به‌دست می‌آیند.

کلیدواژه‌ها

عنوان مقاله [English]

Optimal Low Thrust Orbit Transfer Using Direct Collocation Method

نویسندگان [English]

  • R. Jamilnia
  • A. Naghash

چکیده [English]

In this paper, a new approach is proposed for solving the problem of optimal low thrust orbit transfer. In this approach, the problem of trajectory optimization of optimal orbit transfer is defined by modified equinoctial orbital elements. For solving this problem, direct collocation method, that is an efficient numerical method for solving optimal control problems, is used. By using this method, the problem of trajectory optimization is fully discretized and converted to a nonlinear programming problem. This discrete problem with large numbers of variables and constraints is solved by a powerful nonlinear programming solver (IPOPT). Finally, optimal state and control variables are achieved for optimal orbit transfer with minimum fuel consumption.

کلیدواژه‌ها [English]

  • Low thrust orbit transfer
  • Modified equinoctial orbital elements
  • Trajectory Optimization
  • Optimal control
  • Direct collocation method
  • Nonlinear Programming
[1] Kechichian, J. A., "Optimal low-thrust transfer using variable bounded thrust", Acta Astronautica, Vol. 36, No. 7, pp. 357-365, 1995.
[2] Guelman, M., "Earth to Moon transfer with a limited power engine", American Institute of Aeronautics and Astronautics, AIAA/AAS Astrodynamics Specialist Conference, Scottsdale, Arizona, 1994.
[3] Guelman, M. "Earth to Moon transfer with a limited power engine", Journal of Guidance, Control and Dynamics,  Vol.18, No 5, pp. 1133–1138, 1995.
[4] Oberle, H. J. and Taubert, K., "Existence and multiple solutions of the minimum-fuel orbit transfer problem", Journal of Optimization Theory and Applications, Vol. 95, No 2, pp. 243–262, 1997.
[5] Nah, R. S. and Vadali, S. R., "Fuel-optimal low-thrust three-dimensional Earth-Mars trajectories", Journal of Guidance, Control, and Dynamics,  Vol. 24, No. 6, pp. 1100–1107, 2001.
[6] Colasurdo, G. and Casalino, L. "Optimal low-thrust maneuvers in presence of Earth shadow", American Institute of Aeronautics and Astronautics, AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Rhode Island, 2004.
[7] Pourtakdoust, S. H. and Jalali, M. A., "Thrust Limited Optimal Three Dimensional Spacecraft Trajectories", International Journal of Engineering, Vol.14, No. 1, pp. 81-90.
[8] Betts, J. T., "Using sparse nonlinear programming to compute low thrust orbit transfers", The Journal of the Astronautical Sciences,  Vo. 41, pp. 349-371, 1993.
[9] Betts, J. T., "Survey of numerical methods for trajectory optimization", Journal of Guidance, Control, and Dynamics, Vol. 21, pp. 193-207, 1998.
[10] Betts, J. T., "Very low thrust trajectory optimization", in High Performance Scientific and Engineering Computing, Proceedings of the International FORTWIHR Conference on HPSEC, Munich, 1998.
[11] Betts, J. T., "Very low thrust trajectory optimization using a direct SQP method", Journal of Computational and Applied Mathematics, 120, pp. 27-40, 2000.
[12] Zondervan, K. P., Wood, L. J. and Caughey, T. K., "Optimal low-thrust, three-burn orbit transfers with large plane changes", The Journal of the Astronautical Sciences, Vol. 32, No.4, pp. 407–428, 1984.
[13] Kluever, C. A. and Pierson, B. L., "Optimal low-thrust Earth-Moon transfers with a switching function", The Journal of the Astronautical Sciences, Vol. 42, No. 3, pp. 269–284, 1994.
[14] Schoenmaekers, J. ,Horas, D. and Pulido, J. A., "SMART-1 with solar electric propulsion to the Moon", In Proceedings of the 16th International Symposium on Space Flight Dynamics, California, pp. 114-120, 2001.
[15] Walker, M., Ireland, B. and Owens, J., "A set of modified equinoctial orbit elements", Journal of Celestial Mechanics, Vol. 36, pp. 409-419, 1985.
[16] Betts, J. T., "Survey of numerical methods for trajectory optimization", Journal of Guidance, Control, and Dynamics, Vol. 21, No.2, pp. 193–207, 1998.
[17] Betts, J. T., "Practical methods for optimal control using nonlinear programming", Society for Industrial and Applied Mathematics, 2001.
[18] VonStryk, O. and Bulirsch, R., "Direct and indirect methods for trajectory optimization", Annals of Opera-tions Research, Vol. 37, pp. 357-373, 1992.
[19] Wächter, A., Introduction to IPOPT, Carnegie Mellon University, 2008.
[20] Wächter, A. and Biegler, L. T., "On the implement-ation of an interior-point filter line-search algorithm for large-scale nonlinear programming", Journal of Mathematical Programming, Vol. 106, No. 1, pp. 25–57, 2006.
[21] Wächter, A., An interior point algorithm for large scale nonlinear optimization with applications in process engineering, PhD thesis, Carnegie Mellon University, Pennsylvania, 2002.