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A New Mixed Iterative Algorithm to Solve the Fuel-Optimal Linear Impulsive Rendezvous Problem

Author

Listed:
  • D. Arzelier

    (CNRS, LAAS
    Université de Toulouse, LAAS)

  • C. Louembet

    (CNRS, LAAS
    Université de Toulouse, LAAS)

  • A. Rondepierre

    (IMT)

  • M. Kara-Zaitri

    (CNRS, LAAS
    Université de Toulouse, LAAS)

Abstract

The optimal fuel impulsive time-fixed rendezvous problem is reviewed. In a linear setting, it may be reformulated as a non-convex polynomial optimization problem for a pre-specified fixed number of velocity increments. Relying on variational results previously published in the literature, an improved mixed iterative algorithm is defined to address the issue of optimization over the number of impulses. Revisiting the primer vector theory, it combines variational tests with sophisticated numerical tools from algebraic geometry to solve polynomial necessary and sufficient conditions of optimality. Numerical examples under circular and elliptic assumptions show that this algorithm is efficient and can be integrated into a rendezvous planning tool.

Suggested Citation

  • D. Arzelier & C. Louembet & A. Rondepierre & M. Kara-Zaitri, 2013. "A New Mixed Iterative Algorithm to Solve the Fuel-Optimal Linear Impulsive Rendezvous Problem," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 210-230, October.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:1:d:10.1007_s10957-013-0282-z
    DOI: 10.1007/s10957-013-0282-z
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    Cited by:

    1. Efstathios Bakolas, 2019. "On the Computation of Sparse Solutions to the Controllability Problem for Discrete-Time Linear Systems," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 292-316, October.

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