Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

da Silva Fernandes, Sandro; Golfetto, Wander Almodovar

doi:https://doi.org/10.1155/2007/59372

Mathematical Problems in Engineering

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Dynamics and Control in Sciences and Engineering

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Volume 2007 | Article ID 059372 | https://doi.org/10.1155/2007/59372

Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

Sandro da Silva Fernandes¹and Wander Almodovar Golfetto²

Academic Editor: José Manoel Balthazar

Received22 Sept 2006

Revised18 Apr 2007

Accepted20 May 2007

Published12 Jul 2007

Abstract

A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

References

J.-P. Marec, Optimal Space Trajectories, Elsevier, New York, NY, USA, 1979.
View at: Zentralblatt MATH
V. Coverstone-Carroll and S. N. Williams, “Optimal low thrust trajectories using differential inclusion concepts,” Journal of the Astronautical Sciences, vol. 42, no. 4, pp. 379–393, 1994.
View at: Google Scholar
J. A. Kechichian, “Optimal low-thrust rendezvous using equinoctial orbit elements,” Acta Astronautica, vol. 38, no. 1, pp. 1–14, 1996.
View at: Publisher Site | Google Scholar
J. A. Kechichian, “Reformulation of Edelbaum's low-thrust transfer problem using optimal control theory,” Journal of Guidance, Control, and Dynamics, vol. 20, no. 5, pp. 988–994, 1997.
View at: Google Scholar | Zentralblatt MATH
J. A. Kechichian, “Orbit raising with low-thrust tangential acceleration in presence of earth shadow,” Journal of Spacecraft and Rockets, vol. 35, no. 4, pp. 516–525, 1998.
View at: Google Scholar
C. A. Kluever and S. R. Oleson, “A direct approach for computing near-optimal low-thrust transfers,” in AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, Idaho, USA, August 1997, AAS paper 97-717.
View at: Google Scholar
A. A. Sukhanov and A. F. B. A. Prado, “Constant tangential low-thrust trajectories near an oblate planet,” Journal of Guidance, Control, and Dynamics, vol. 24, no. 4, pp. 723–731, 2001.
View at: Google Scholar
V. Coverstone-Carroll, J. W. Hartmann, and W. J. Mason, “Optimal multi-objective low-thrust spacecraft trajectories,” Computer Methods in Applied Mechanics and Engineering, vol. 186, no. 2–4, pp. 387–402, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
M. Vasile, F. B. Zazzera, R. Jehn, and G. Janin, “Optimal interplanetary trajectories using a combination of low-thrust and gravity assist manoeuvres,” in Proceedings of the 51st International Astronautical Congress (IAF '00), Rio de Janeiro, Brazil, October 2000, IAF-00-A.5.07.
View at: Google Scholar
G. D. Racca, “New challenges to trajectory design by the use of electric propulsion and other new means of wandering in the solar system,” Celestial Mechanics & Dynamical Astronomy, vol. 85, no. 1, pp. 1–24, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
T. N. Edelbaum, “Optimum power-limited orbit transfer in strong gravity fields,” AIAA Journal, vol. 3, no. 5, pp. 921–925, 1965.
View at: Google Scholar | MathSciNet
J.-P. Marec and N. X. Vinh, “Optimal low-thrust, limited power transfers between arbitrary elliptical orbits,” Acta Astronautica, vol. 4, no. 5-6, pp. 511–540, 1977.
View at: Publisher Site | Google Scholar
C. M. Hassig, K. D. Mease, and N. X. Vinh, “Minimum-fuel power-limited transfer between coplanar elliptical orbits,” Acta Astronautica, vol. 29, no. 1, pp. 1–15, 1993.
View at: Publisher Site | Google Scholar
S. Geffroy and R. Epenoy, “Optimal low-thrust transfers with constraints—generalization of averaging techniques,” Acta Astronautica, vol. 41, no. 3, pp. 133–149, 1997.
View at: Publisher Site | Google Scholar
B. N. Kiforenko, “Optimal low-thrust orbital transfers in a central gravity field,” International Applied Mechanics, vol. 41, no. 11, pp. 1211–1238, 2005.
View at: Publisher Site | Google Scholar
J. V. Breakwell, J. L. Speyer, and A. E. Bryson Jr., “Optimization and control of nonlinear systems using the second variation,” SIAM Journal on Control and Optimization, vol. 1, no. 2, pp. 193–223, 1963.
View at: Publisher Site | Google Scholar | Zentralblatt MATH
A. G. Longmuir and E. V. Bohn, “Second-variation methods in dynamic optimization,” Journal of Optimization Theory and Applications, vol. 3, no. 3, pp. 164–173, 1969.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
J.-P. Marec, Transferts Optimaux Entre Orbites Elliptiques Proches, ONERA, Châtillon, France, 1967.
S. da Silva Fernandes and W. A. Golfetto, “Numerical computation of optimal low-thrust limited-power trajectories—transfers between coplanar circular orbits,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 27, no. 2, pp. 178–185, 2005.
View at: Publisher Site | Google Scholar
S. da Silva Fernandes and W. A. Golfetto, “Computation of optimal low-thrust limited-power trajectories through an algorithm based on gradient techniques,” in Proceedings of the 3rd Brazilian Conference on Dynamics, Control and Their Applications, pp. 789–796, São Paulo, Brazil, 2004, CD-ROM.
View at: Google Scholar
A. E. Bryson Jr. and Y. C. Ho, Applied Optimal Control, John Wiley & Sons, New York, NY, USA, 1975.
View at: MathSciNet
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New York, NY, USA, 1962.
View at: Zentralblatt MATH | MathSciNet
T. Bullock and G. Franklin, “A second-order feedback method for optimal control computations,” IEEE Transactions on Automatic Control, vol. 12, no. 6, pp. 666–673, 1967.
View at: Publisher Site | Google Scholar
S. da Silva Fernandes, “A note on the solution of the coast-arc problem,” Acta Astronautica, vol. 45, no. 1, pp. 53–57, 1999.
View at: Publisher Site | Google Scholar
S. da Silva Fernandes, “Generalized canonical systems applications to optimal trajectory analysis,” Journal of Guidance, Control, and Dynamics, vol. 22, no. 6, pp. 918–921, 1999.
View at: Google Scholar
F. W. Gobetz, “A linear theory of optimum low-thrust rendez-vous trajectories,” The Journal of the Astronautical Sciences, vol. 12, no. 3, pp. 69–76, 1965.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2007 Sandro da Silva Fernandes and Wander Almodovar Golfetto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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