Advertisement

Solution of a Hard Flight Path Optimization Problem by Different Optimization Codes

  • K. Chudejl
  • Ch Biiskensl
  • T. Graf
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 21)

Abstract

Solar electric propulsion is the key technology to reduce propellant consumption for interplanetary missions. A number of studies of interplanetary and lunar missions are currently performed by the European Space Agency (ESA), which exploit the benefits of solar electric propulsion (e.g., [11,8]). Although solar electric propulsion has the disadvantage of low-thrust levels the high specific impulse leads to considerable reduction of propellant mass and therefore to an increase in payload mass. Trajectory optimization problems with solar electric propulsion are known to be extremly difficult (e.g., [3]). They have in the past been successfully solved by indirect methods while direct methods usually failed. Nevertheless the sophistication of direct solution methods has also permanently increased

The interesting question is: Can low-thrust missions be solved today by direct methods? How precise are these solutions compared with an indirect solution? What time and requirements does it take for a successful solution?

A detailed numerical comparison of the direct solution code NUDOCCCS (Büskens [11]) and the indirect multiple shooting code MUMUS (Hiltmann [7]) is presented for a reference problem (a low thrust orbital transfer problem of a LISA spacecraft with constraints on the solar aspect angle) from [11]

Keywords

Optimal Control Problem Reference Problem Lunar Mission Propellant Mass Direct Solution Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Battin, R. H. (1987) An Introduction to the Mathematics and Methods of Astrodynamics, American Institute of Aeronautics and Astronautics, New YorkzbMATHGoogle Scholar
  2. 2.
    Betts, J. T. (1998) Survey of Numerical Methods for Trajectory Optimization. Journal of Guidance, Control, and Dynamics, 21, 193–207zbMATHCrossRefGoogle Scholar
  3. 3.
    Bulirsch, R., Callies, R. (1992) Optimal Trajectories for a Multiple Rendezvous Mission to Asteroids. Acta Astronautica, 26, 587–597CrossRefGoogle Scholar
  4. 4.
    Büskens, C. (1998) Optimierungmethoden und Sensitivitätsanalyse für optimale Steuerprozesse mit Steuer-und Zustands-Beschränkungen. Dissertation, Universität MünsterGoogle Scholar
  5. 5.
    Chudej, K. (2000) Effiziente Lösung zustandsbeschränkter Optimalsteuerungsaufgaben. Habilitationsschrift, Universität BayreuthGoogle Scholar
  6. 6.
    Graf, T. (2001) Flugbahnoptimierung eines Niedrig-Schub Raumfahrzeugs. Diplomarbeit, Lehrstuhl für Ingenieurmathematik, Universität BayreuthGoogle Scholar
  7. 7.
    Hiltmann, P., Chudej, K., Breitner, M. (1993) Eine modifizierte Mehrzielmethode zur Lösung von Mehrpunkt-Randwertproblemen, Benutzeranleitung. Report No. 14, Sonderforschungsbereich 255 Transatmosphärische Flugsysteme, Lehrstuhl für Höhere Mathematik und Numerische Mathematik, Technische Universität MünchenGoogle Scholar
  8. 8.
    Jehn, R., Hechler, M., Rodriguez-Canabal, J., Schoenmaekers, J., Cano, J. L. (2000) Trajectory Optimisation for ESA Low-Thrust Interplanetary and Lunar Missions. CNES Workshop on Low-Thrust Trajectory Optimisation, ToulouseGoogle Scholar
  9. 9.
    Pesch, H. J. (1994) A Practical Guide to the Solution of Real-Life Optimal Control Problems. Control and Cybernetics, 23, 7–60MathSciNetzbMATHGoogle Scholar
  10. 10.
    von Stryk, O. (1993) Numerical solution of optimal control problems by direct collocation. In: R. Bulirsch, et al (Eds.) Optimal Control — Calculus of Variations, Optimal Control Theory and Numerical Methods, ISNM 111, Birkhäuser, Basel, 129–143Google Scholar
  11. 11.
    Vasile, M., Jehn, R. (1999) Low Thrust Orbital Transfer for a LISA Spacecraft With Constraints on the Solar Aspect Angle. MAS Working Paper No. 424, ESOC DarmstadtGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • K. Chudejl
    • 1
  • Ch Biiskensl
    • 1
  • T. Graf
    • 2
  1. 1.Lehrstuhl für IngenieurmathematikUniversität BayreuthBayreuth
  2. 2.Lehrstuhl für Angewandte MathematikUniversität BayreuthBayreuth

Personalised recommendations