Skip to main content
Log in

Two Direct Low Thrust Trajectory Optimization Techniques

  • CONTROL SYSTEMS OF MOVING OBJECTS
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

Abstract

Direct low thrust trajectory optimization techniques that reduce the optimization problem in the class of continuous functions to a nonlinear programming problem are described. Two direct low thrust trajectory optimization methods are implemented; one of them is based on the optimization of thrust acceleration and the other optimizes the impulses approximating the thrust arcs. These methods are compared using a sample problem of transfer from Earth to Mars in terms of runtime, the number of iterations, and the size of the convergence domains. The computations are performed on a personal computer using MATLAB and on a multiprocessor computer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.

Similar content being viewed by others

REFERENCES

  1. N. A. Vazhenin, V. A. Obukhov, A. P. Plokhikh, and G. A. Popov, Electric Rocket Engines of Spacecraft and their Effect on Radio Systems of Space Communication (Fizmatlit, Moscow, 2012) [in Russian].

    Google Scholar 

  2. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Wiley, New York, 1962).

  3. D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction (Princeton Univ. Press, New Jersey, 2011).

    Book  MATH  Google Scholar 

  4. V. G. Petukhov, “Robust suboptimal feedback control for low-thrust transfer between noncoplanar elliptical and circular orbits,” Vestn. MAI 17 (3), 50–58 (2010).

  5. V. G. Petukhov, “Optimization of multi-orbit transfers between noncoplanar elliptic orbits,” Cosmic Res. 42, 250 (2004).

    Article  Google Scholar 

  6. M. S. Konstantinov, V. G. Petukhov, and M. Tein, Optimization of Heliocentric Flight Paths, 2nd ed. (Mosk. Aviats. Inst., Moscow, 2015) [in Russian].

    Google Scholar 

  7. B. Conway, Spacecraft Trajectory Optimization (Cambridge Univ. Press, New York, 2010).

    Book  Google Scholar 

  8. S. Tang and B. Conway, “Optimization of low-thrust interplanetary trajectories using collocation and nonlinear programming,” J. Guidance, Control, Dyn. 18, 599–604 (1995).

    Article  Google Scholar 

  9. C. Hargraves and S. Paris, “Direct trajectory optimization using nonlinear programming and collocation,” J. Guidance, Control, Dyn. 10, 338–342 (1987).

    Article  MATH  Google Scholar 

  10. F. Fahroo and I. Ross, “Direct trajectory optimization by a chebyshev pseudospectral method,” J. Guidance, Control, Dyn. 25, 160–166 (2002).

    Article  Google Scholar 

  11. J. Sims and S. Flanagan, “Preliminary design of low-thrust interplanetary missions,” in Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Girdwood, Alaska, USA, 1999, Paper AAS 99-338.

  12. V. V. Beletskii, “On the trajectories of space flight with a constant vector of jet acceleration,” Kosm. Issled. 2, 408–413 (1964).

    Google Scholar 

  13. G. Lantoine and R. Russell, “Complete closed-form solutions of the stark problem,” Celest. Mech. Dyn. Astron. 109, 333–366 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  14. F. Biscani and D. Izzo, “The stark problem in the weierstrassian formalism,” Mon. Not. R. Astron. Soc. 439, 810–822 (2014).

    Article  Google Scholar 

  15. E. Pellegrini, R. Russell, and V. Vittaldev, “F and G Taylor series solutions to the Stark and Kepler problems with sundman transformations,” Celest. Mech. Dyn. Astron. 118, 355–378 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  16. N. Hatten and R. Russell, “Comparison of three stark problem solution techniques for the bounded case,” Celest. Mech. Dyn. Astron. 121, 39–60 (2015).

    Article  Google Scholar 

  17. V. A. Il’in and G. E. Kuzmak, Optimal Transfer Orbits of Spacecraft with Large Thrust Engines (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

  18. JPL Planetary and Lunar Ephemerides. https://ssd.jpl.nasa.gov/?planet_eph_export. Accessed May 2, 2018.

  19. The Astronomical Almanac. http://asa.hmnao.com/SecK/Section_K.html. Accessed May 2, 2018.

  20. J. Nocedal and S. Wright, Numerical Optimization (Springer, New York, 2006).

    MATH  Google Scholar 

  21. UCSD/Stanford Optimization Software. https://ccom.ucsd.edu/textasciitilde optimizers/. Accessed May 2, 2018

  22. Computer Complex K-60. http://www.kiam.ru/MVS/resourses/k60.html. Accessed May 2, 2018.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Tselousova.

Additional information

Translated by A. Klimontovich

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Trofimov, S.P., Tselousova, A.A. & Shirobokov, M.G. Two Direct Low Thrust Trajectory Optimization Techniques. J. Comput. Syst. Sci. Int. 57, 989–1000 (2018). https://doi.org/10.1134/S1064230718060114

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064230718060114

Navigation