Advertisement

Automation and Remote Control

, Volume 68, Issue 8, pp 1372–1390 | Cite as

Optimization of interorbital three-dimensional transfer trajectories for stage spacecraft

  • I. S. Grigor’ev
  • I. A. Danilina
Topical Issue

Abstract

Problems of three-dimensional trajectory optimization of transfers for stage spacecraft and spacecraft with auxiliary fuel tank (AFT) from the low circuit orbit of the Earth’s artificial satellite (EAS) into the geostationary orbit and optimization problems of fuel distribution in stages or tanks are solved. Control of spacecraft motion is conducted by jet engines of bounded thrust; stage engines can have different characteristics, i.e., thrust-to-weight ratio and specific thrust. The used stage or auxiliary fuel tank is detached on the passive segment. Detachment is considered to be instantaneous, if the spacecraft position and velocity do not change at the detachment instant and the mass decreases in jumping mode. The mass of detached tanks is considered proportionate to the mass of consumed fuel; the mass of engine and auxiliary constructions, to thrust-to-weight ratio. The useful mass of the spacecraft with the limited time of transfer is maximized. The considered problems are intricate nonlinear optimal control problems with discontinuous phase variables. They are formalized as optimal control problems by a union of dynamic systems and are solved on the basis of the corresponding principle of the maximum. In this paper, boundary-value problems of the principle of the maximum are numerically solved by the shooting method. The choice of computing schemes of the shooting method and solution to systems of nonlinear equations is conducted by using a series of auxiliary problems.

PACS numbers

02.60.Pn 45.80.+r 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Grigor’ev, I.S. and Danilina, I.A., Optimization of Interorbital Three-dimensional Transfer Trajectories for Spacecraft of Different-Design, in IV Polyakhovskie chteniya: izbrannye trudy (IV Polyakhovskie Readings: Selected Works), St. Peteresburg: VVM, 2006, pp. 241–250.Google Scholar
  2. 2.
    Grodzovskii, G.L., Ivanov, Yu.N., and Tokarev, V.V., Mekhanika kosmicheskogo poleta. Problemy optimizatsii (Mechanics of Space Flight. Optimization Problems), Moscow: Nauka, 1975.Google Scholar
  3. 3.
    Vorob’ev, L.M., K teorii poleta reaktivnykh apparatov (On the Theory of Jet Craft), Moscow: Mashinostroenie, 1979.Google Scholar
  4. 4.
    Grigor’ev, I.S., Grigor’ev, K.G., and Petrikova, Yu.D., About the Quickest Maneuvers of Spacecraft with Jet Engines of Large Bounded Thrust in the Gravitational Field in the Vacuum, Kosm. Issled., 2000, vol. 38, no. 2, pp. 171–192.Google Scholar
  5. 5.
    Grigor’ev, I.S. and Grigor’ev, K.G., On Conditions of the Principle of the Maximum in Problems of Optimal Control for the Aggregate of Dynamic Systems and Their Applications to Solving Problems of Spacecraft-Motion Optimal Control, Kosm. Issled., 2003, vol. 41, no. 3, pp. 307–331.Google Scholar
  6. 6.
    Grigor’ev, I.S., Investigation of Optimal Tranfser Trajectories of Spacecraft with the Jet Engine of Large Bounded Thrust between the Earth and the Moon, Cand. Sc. (Phys.-Math.) Dissertation, Mosk. Gos. Univ., 1996.Google Scholar
  7. 7.
    Grigor’ev, I.S. and Grigor’ev, K.G., Problems of Transfer Trajectory Optimization for Spacecraft with the Jet Engine of Large Thrust in the Arbitrary Gravitational Field in the Vaccum. Their Solving in the Pulse Formulation, Kosm. Issled., 2002, vol. 40, no. 1, pp. 88–111.Google Scholar
  8. 8.
    Spravochnoe rukovodstvo po nebesnoi mekhanike i actrodinamike (Handbook on Celestial Mechanics and Astrodynamics), Duboshin, G.N., Ed., Moscow: Nauka, 1976.Google Scholar
  9. 9.
    Grigor’ev, I.S. and Grigor’ev, K.G., On Using the Solutions to Problems of Spacecraft-Trajectory Optimization in the Pulse Formulation while Solving Problems of Optimal Trajectory Control for Spacecraft with the Jet Engine of Bounded Thrust. I, Kosm. Issled., 2007, vol. 45, no. 4, pp. 358–366.Google Scholar
  10. 10.
    Ryzhov, S.Yu., Grigor’ev, I.S., and Egorov, V.A., Optimization of Spacecraft Many-Revolution Orbit Tranfsers, Preprint of Keldysh Institute for Applied Mathematics, Russ. Acad. Sci., Moscow, 2005, no. 63 (available at http://www.keldysh.ru/papers/2005/source/prep2005_63.zip).
  11. 11.
    Grigor’ev, I.S. and Ryzhov, S.Yu., On Solving Problems of Optimization of Spacecraft Many-Revolution Orbit Transfers, Kosm. Issled., 2006, vol. 44, no. 3, pp. 272–280.Google Scholar
  12. 12.
    Grigor’ev, K.G. and Grigor’ev, I.S., Investigation of Optimal Three-dimensional Trajectories of Transfers for Spacecraft with Jet Engines of Large Bounded Thrust between Orbits of the Earth and Moon’s Artificial Satellites, Kosm. Issled., 1997, vol. 35, no. 1, pp. 52–75.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • I. S. Grigor’ev
    • 1
  • I. A. Danilina
    • 2
  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Tsiolkovsky State Aviation Technological UniversityMoscowRussia

Personalised recommendations