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Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach

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  • A. Miele

    (Rice University)

  • M. Ciarcià

    (Rice University)

Abstract

In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [2008]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach. Specifically, we consider the relative motion between a target spacecraft in a circular orbit and a chaser spacecraft moving in its proximity as described by the Clohessy-Wiltshire equations. We consider the class of multiple-subarc trajectories characterized by constant thrust controls in each subarc. Under these conditions, the Clohessy-Wiltshire equations can be integrated in closed form and in turn this leads to optimization processes of the mathematical programming type. Within the above framework, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory.

Suggested Citation

  • A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 625-639, June.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:3:d:10.1007_s10957-008-9356-8
    DOI: 10.1007/s10957-008-9356-8
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    References listed on IDEAS

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    1. A. Miele & M. Ciarcià & M. W. Weeks, 2007. "Guidance Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 377-400, March.
    2. A. Miele & M. W. Weeks & M. Ciarcià, 2007. "Optimal Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 353-376, March.
    3. A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 593-624, June.
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