A Note on a Geometrical Method to Solve Spacecraft Formation Flying Control

Spacecraft formation flying is becoming more important since the use of multiple satellites has been demonstrated to be cost-effective. In some applications, the spacecraft need to satisfy certain geometrical constraints; e. g. regarding formation pointing. In this paper an efficient method has been devised that minimises the variation of orbital elements to achieve the requested states. The positions that minimise displacement from a reference plane are computed, and the compatible velocities that reduce shape and plane variation for all S/C are evaluated. This allows to find optimal values for a TPBVP. The algorithm has been applied to close-range GEO formations.