Fast and Accurate Numerical Integration of Relative Motion in Spacecraft Formation Flying

Abstract - The special perturbation method DROMO developed by Peláez in 2006 for the perturbed two-body problem is employed to propagate the relative motion in spacecraft formation flying, and the performance of the new method, named DROMO-FF, is analyzed. DROMO is a very fast and accurate regularized method which involves a set of seven integrals of the pure Keplerian motion whose physical meaning is described in the paper. We propose to propagate the absolute motion of N spacecraft simultaneously by using DROMO with the introduction of new dependent variables, necessary for the synchronization, and to determine the relative dynamics by differentiating the absolute states. After investigating the influence on the performance due to the numerical integration of the new variables, we show that DROMO-FF is significantly more accurate than Cowell’s method for the same computing time, or equivalently, faster for the same accuracy. A second approach to propagate relative motion wherein linearization is performed with respect to the formation baricenter is presented and compared to DROMO-FF. It is shown that for closed formations round-off does not affect the accuracy of DROMO-FF.