Inter-orbital Spacecraft Transfer Optimization: Choosing Initial Approximations Based on Correlation Analysis of Key Parameters

Cover Page

Cite item

Full Text

Abstract

This paper presents a new approach to choosing initial approximations in inter-orbital transfer optimization problems for a spacecraft with a chemical booster and fixed thrust. The approach involves correlations between the values of key problem parameters. It is implemented using numerical methods, mathematical modeling, and programming. Relevant publications on the subject area (methods for finding initial approximations in optimization problems) are systematically studied and several mathematical relationships are identified. As a result, laws are specified to facilitate the choice of initial approximations in order to ensure convergence and achieve the optimum. The results of a computational experiment confirm the applicability and effectiveness of this approach in typical optimization problems (an optimal spacecraft trajectory design between near-Earth orbits as one example).

About the authors

E. V Savvina

Email: petrakowae@mail.ru

References

  1. Bard, Y. Nonlinear Parameter Estimation. – New York & London: Academic Press edition. – 1979. – 349 p.
  2. Kitrell, J.R., Mezaki, R., and Watson, C.C. Estimation of parameters for nonlinear least squares analysis // Industrial & Engineering Chemistry. – 1965. – Vol. 57. – P. 18–27.
  3. Wu, D., Cheng, L., Gong, S., and Baoyin, H. Approximate time-optimal low-thrust rendezvous solutions between circular orbits // Aerospace Science and Technology. – 2022. – Vol. 131, Part A. – Art. No. 108011.
  4. Петухов В.Г. Оптимизация межпланетных траекторий космических аппаратов с идеально-регулируемым двигателем методом продолжения. Космические исследования. – 2008. – Т. 46. – № 3. – С. 224–237. [Petukhov, V.G. Optimization of interplanetary trajectories of spacecraft with a ideally regulated engine by the continuation method. – Space Studies. – 2008. – Vol. 46, no. 3. – P. 224–237. (In Russian)]
  5. Hofmann, C., and Topputo, F. Embedded Homotopy for Convex Low-Thrust Trajectory Optimization with Operational Constraints // Proceedings of 2022 AAS/AIAA Astrodynamics Specialist Conference. – Charlotte, NC, USA, 2022. – P. 1–16.
  6. Jiang, F., Baoyin, F. and Li, J. Practical Techniques for Low-Thrust Trajectory Optimization with Homotopic Approach // Journal of Guidance, Control and Dynamics. – 2012. – Vol. 35, no. 1. – P. 245–258.
  7. Wu, D., Wu, C., Lin, F., et al. Analytical Costate Estimation by a Reference Trajectory-Based Least-Squares Method // Journal of Guidance, Control and Dynamics. 2022. – Vol. 45. – P. 1–9.
  8. Wu, D., Wu, Ch., Lin, F., and Baoyin, H. An Atlas of Optimal Low-Thrust Rephasing Solutions in Circular Orbit // arXiv:2209.07418v1. – 2022. – doi: 10.48550/arXiv.2209.07418.
  9. Саввина Е.В. построение траектории перелета космического аппарата между околоземными эллиптическими орбитами методом перебора значений параметров внутри сетки данных // Проблемы управления. – 2023. – № 2. – С. 65–74. [Savvina, E.V. Inter-orbital Spacecraft Transfer: Trajectory Design by Iterating Parameter Values within a Data Grid // Control Sciences. – 2023. – No. 2. – Р. 56–63]
  10. Mathcad: Math Software for Engineering Calculations. – URL: https://www.mathcad.com (дата обращения 15 мая 2023 г.) [Accessed May 15, 2023]
  11. PythonTM. – URL: https://www.python.org (дата обращения 15 мая 2023 г.) [Accessed May 15, 2023]
  12. Shapiro, S.S., Wilk M.B. An Analysis of Variance Test for Normality (Complete Samples) // Biometrika. – 1965. – Vol. 52, no. 3/4. – P. 591–611.]
  13. Mohd Razali, N. and Yap, B.W. Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests // J. Stat. Model. Analytics. – 2011. – Vol. 2, no. 1. –P. 20–33.
  14. Rahman, M. and Zakkula, G. A modification of the test of Shapiro and Wilk for normality // Journal of Applied Statistics. – 1997. – Vol. 24. – P. 219–236.
  15. Simard, R.J., and L'Ecuyer, P. Computing the Two-Sided Kolmogorov-Smirnov Distribution // Journal of Statistical Software. – 2011. – Vol. 39. – P. 1–18.
  16. Кобзарь А.И. Прикладная математическая статистика. Для инженеров и научных работников. – М.: ФИЗМАТЛИТ, 2006. [Kobzar', A.I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov. – M.: FIZMATLIT, 2006. (In Russian)]
  17. Афифи А., Эйзен С. Статистический анализ: подход с использованием ЭВМ; перевод с английского И.С. Енюкова, И.Д. Новикова; под редакцией Г.П. Башарина. – М.: Мир, 1982. [Afifi, A.A. and Azen, S.P. Statistical analysis: A computer oriented approach. – London, N.Y.: Academic Press Inc. Publ., 1979.]

Supplementary files

Supplementary Files
Action
1. JATS XML
Download


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).