Formation Control of Satellites Subject to Drag Variations and J2 Perturbations

The issue of controlling the relative position of satellites in formation has acquired increasing attention in recent years. Special challenge is the control of a low-Earth-orbit formation, where differences in Earth oblateness effects and different atmospheric drag cause a drift of the relative position. A method is developed to compensate for the secular combined effects of first-order gravitational perturbations (J 2 ) and atmospheric drag perturbations. The compensation is performed by impulsive velocity corrections. The velocity correction vector and the timing of the correction are determined such that the secular drifts of the relative nodal rate and of the relative mean latitude rate are set to values that cancel out future drifts due to drag for the next time interval. In addition, an optimality condition is developed such that this correction velocity is minimized. After the correction, the orbital element deviations are not set to zero, but rather to small acceptable values for which the in-plane and the out-of-plane relative drifts are small and bounded. The algorithms for the determination of the velocity correction are developed, and a numerical example is presented. The effects of measurement noise and drag uncertainty are discussed as well.