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Optimal Control of Retrieval of a Tethered Subsatellite

  • Alois Steindl
  • Wolfgang Steiner
  • Hans Troger
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)

Abstract

The most important and complicated operations during a tethered satellite system mission are deployment and retrieval of a subsatellite from or to a space ship. The deployment process has been treated in [15]. In this paper retrieval is considered. We restrict to the practically important case that the system is moving on a circular Keplerian orbit around the Earth. The main problem during retrieval is that it results in an unstable motion concerning the radial relative equilibrium which is stable for a tether of constant length. The uncontrolled retrieval results in a strong oscillatory motion. Hence for the practically useful retrieval of a subsatellite this process must be controlled. We propose an optimal control strategy using the Maximum Principle to achieve a force controlled retrieval of the tethered subsatellite from the radial relative equilibrium position far away from the space ship to the radial relative equilibrium position close to the space ship.

Key words

Time optimal control maximum principle Pontrijagin space pendulum 

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References

  1. [1]
    E.M. Abdel-Rahman and A.H. Nayfeh, ‘Pendulation reduction in boom cranes using cable length manipulation’, Nonlinear Dynamics, 27, 255–269, 2002.CrossRefzbMATHGoogle Scholar
  2. [2]
    P. Bainum and V.K. Kumar, ‘Optimal control of the shuttle-tethered-subsatellite system’, Acta Astronautica, 7, 1333–1348, 1980.CrossRefzbMATHGoogle Scholar
  3. [3]
    B. Barkow, A. Steindl, H. Troger and G. Wiedermann, ‘Some methods of controlling the deployment of a tethered satellite’, Int. J. Vibration and Control, 9, 187–208, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    T. Beardsley, ‘The way to go in Space’, Scientific American, pp. 40–77 February 1999.Google Scholar
  5. [5]
    V.V. Beletsky and E.M. Levin, ‘Dynamics of space tether systems’, Advances of the Astronautical Sciences, 83, 1993.Google Scholar
  6. [6]
    F.L. Chernousko, ‘Dynamics of retrieval of a space tethered system’, J. Appl. Maths. Mechs, 59, 165–173, 1995.zbMATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    R.P. Hoyt, R.L. Forward, G.D. Nordley and C.W. Uphoff, ‘Rapid interplanetary tether transport systems’, IAF-99-A.5.10, 50th IAF Congress Amsterdam, 31 pages, 1999.Google Scholar
  8. [8]
    M. Krupa, A. Kuhn, W. Poth, M. Schagerl, A. Steindl, W. Steiner, H. Troger and G. Wiedermann, ‘Tethered satellite systems: A new concept of space flight’, Eur J. Mech. A/Solids 19, S145–S164, 2000.Google Scholar
  9. [9]
    M. Krupa, M. Schagerl, A. Steindl and H. Troger, ‘Stability of relative equilibria. Part I: Comparison of four methods”, Meccanica 35, 325–351, 2001.MathSciNetCrossRefGoogle Scholar
  10. [10]
    M. Krupa, A. Steindl and H. Troger, ‘Stability of relative equilibria. Part II: Dumbell satellites’, Meccanica 35, 353–371, 2001.MathSciNetCrossRefGoogle Scholar
  11. [11]
    A.K. Misra and V.J. Modi, ‘Deployment and retrieval of shuttle supported tethered satellites’, J. Guidance and Control, 5, 278–285, 1982.CrossRefzbMATHGoogle Scholar
  12. [12]
    ‘Proceedings of the fourth international conference on tethers in space’, Science and Technology Corporation, Hampton, VA, 1995.Google Scholar
  13. [13]
    W. Steiner, A. Steindl and H. Troger, ‘Dynamics of a space tethered satellite system with two rigid endbodies’, Science and Technology Corporation, Hampton, VA, in [12], 1367–1379, 1995.Google Scholar
  14. [14]
    W. Steiner, A. Steindl and H. Troger, ‘Center manifold approach to the control of a tethered satellite system,’ Applied Mathematics and Computation, 70, 315–327, 1995.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. Steindl and H. Troger, ‘Optimal control of deployment of a tethered subsatellite’, Nonlinear Dynamics, 31, 257–274, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    G. Wiedermann, M. Schagerl, A. Steindl and H. Troger, ‘Computation of force controlled deployment and retrieval of a tethered satellite system by the finite element method’, in Proceedings of ECCM’99, W. Wunderlich (ed.), pp. 410–429, 1999.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Alois Steindl
    • 1
  • Wolfgang Steiner
    • 2
  • Hans Troger
    • 1
  1. 1.Institutefor MechanicsVienna University of TechnologyVienna
  2. 2.Wels College of EngineeringWels

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