Abstract
A task of a pair formation flying satellites optimal relative motion control is described. It is presented as a Lagrange problem of satellite relative motion by the criterion of the control acceleration minimization. The сontrol acceleration term corresponds to the term of a fuel flow or a satellite specific impulse. On the basis of a Hill-Clohessy-Wiltshire equation a mathematical model of the relative motion of a pair of satellites is obtained. One satellite is controlled and another is noncontrolled. Analytical description of such relative motion is presented. The optimization criterion considers control acceleration minimization with fixed boundary conditions and a fixed time interval. The system of Euler-Lagrange equations is obtained as a necessary condition for the extremum existence. An analytical solution for the Lagrange problem is obtained. Relative motion simulation for given examples is performed. The example studies relative motion by distance, relative attitude and lateral deviation parametres and four time intervals, corresponding to half orbit length, one, two and four orbit length. The correlation of optimization criterion value and duration of the maneuver is determined. Direct dependence between duration of maneuvers, control acceleration magnitude and control acceleration costs is presented. Correlation between duration of maneuvers and shape of the optimal trajectory is studied. Practical application of this paper results is discussed. An algorithm of a formation flying relative motion control is provided. The algorithm includes stages of an initial relative position definition, the required relative position and duration of a maneuver definition, constants of integration evaluation, optimal control acceleration synthesis.
Published Version
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