K. Uldall Kristiansen, P L Palmer & M Roberts
This paper develops a geometric and coordinate-independent approach to relative attitude dynamics. This setting is shown to be appropriate for the problem of optimal relative attitude control of spacecraft controlled with reaction wheels. In particular, within the linear approximation explicit analytic expressions are obtained for a fixed transfer time, minimum energy torque subject to specified relative attitude boundary conditions. The optimal torque is then applied to two different realistic formation flying mission scenarios where the range of validity of the linear approximation is also quantified. The results demonstrate an error of 10 for a net rotation of 25o. A feedback law is also suggested in which the optimal control is updated via measurements of the instantaneous attitude. In the second example this is shown to provide up to 55% improvement in accuracy just from one single update half way through the manoeuvre.
Paper: Relative Attitude