Davis, Jeremy John (2010-08). Constellation Reconfiguration: Tools and Analysis. Doctoral Dissertation. Thesis uri icon

abstract

  • Constellation reconfi guration consists of transforming an initial constellation of satellites into some final constellation of satellites to maintain system optimality. Constellations with phased deployment, changing mission requirements, or satellite failures would all benefi t from reconfi guration capability. The constellation reconfiguration problem can be broken into two broad sub-problems: constellation design and constellation transfer. Both are complicated and combinatorial in nature and require new, more efficient methods. Having reviewed existing constellation design frameworks, a new framework, the Elliptical Flower Constellations (EFCs), has been developed that offers improved performance over traditional methods. To assist in rapidly analyzing constellation designs, a new method for orbit propagation based on a sequential solution of Kepler's equation is presented. The constellation transfer problem requires an optimal assignment of satellites in the initial orbit to slots in the final orbit based on optimal orbit transfers between them. A new method for approximately solving the optimal two-impulse orbit transfer with fixed end-points, the so-called minimum Delta v Lambert's problem, is developed that requires the solution of a 4th order polynomial, as opposed to the 6th or higher order polynomials or iterative techniques of existing methods. The recently developed Learning Approach to sampling optimization is applied to the particular problem of general orbit transfer between two generic orbits, with several enhancements specifi c to this problem that improve its performance. The constellation transfer problem is then posed as a Linear Assignment Problem and solved using the auction algorithm once the orbit transfers have been computed. Constellations designed for global navigation satellite systems and for global communications demonstrate signifi cant improvements through the use of the EFC framework over existing methods. An end-to-end example of constellation recon figuration for a constellation with changing regional coverage requirements shows the effectiveness of the constellation transfer methods.
  • Constellation reconfi guration consists of transforming an initial constellation

    of satellites into some final constellation of satellites to maintain system optimality.

    Constellations with phased deployment, changing mission requirements, or satellite

    failures would all benefi t from reconfi guration capability. The constellation reconfiguration problem can be broken into two broad sub-problems: constellation design

    and constellation transfer. Both are complicated and combinatorial in nature and

    require new, more efficient methods. Having reviewed existing constellation design

    frameworks, a new framework, the Elliptical Flower Constellations (EFCs), has been

    developed that offers improved performance over traditional methods. To assist in

    rapidly analyzing constellation designs, a new method for orbit propagation based

    on a sequential solution of Kepler's equation is presented. The constellation transfer

    problem requires an optimal assignment of satellites in the initial orbit to slots in

    the final orbit based on optimal orbit transfers between them. A new method for

    approximately solving the optimal two-impulse orbit transfer with fixed end-points,

    the so-called minimum Delta v Lambert's problem, is developed that requires the solution

    of a 4th order polynomial, as opposed to the 6th or higher order polynomials or

    iterative techniques of existing methods. The recently developed Learning Approach

    to sampling optimization is applied to the particular problem of general orbit transfer between two generic orbits, with several enhancements specifi c to this problem that

    improve its performance. The constellation transfer problem is then posed as a Linear

    Assignment Problem and solved using the auction algorithm once the orbit transfers

    have been computed. Constellations designed for global navigation satellite systems

    and for global communications demonstrate signifi cant improvements through the use

    of the EFC framework over existing methods. An end-to-end example of constellation

    recon figuration for a constellation with changing regional coverage requirements

    shows the effectiveness of the constellation transfer methods.

publication date

  • August 2010