Collocation of geostationary satellites using convex optimization

Abstract

A method is developed to calculate station-keeping maneuvers for a fleet of satellites collocated in a geostationary slot. The method is enabled by linear time-varying formulation of the dynamics in terms of non-singular orbital elements. A leader-follower control hierarchy is used, so that the motion of the follower satellites is controlled relative to the leader. Key objectives of the station-keeping problem are a minimization of propellant consumption, using a limited number of maneuvers, while guaranteeing safe separation between the satellites. The method is applied in a realistic simulation scenario, including orbit determination, actuation and modeling errors. The method is demonstrated to work for an inhomogeneous fleet of four satellites with a maneuver cycle of one week. It is then demonstrated that by reducing the maneuver cycle duration to one day, it is possible to collocate 16 satellites in a single slot, without penalties on propellant consumption.