Collocation of Geostationary Satellites Using Convex Optimization

A method is developed to determine station-keeping maneuvers for a fleet of satellites collocated in a geostationary slot. The method is enabled by a linear time-varying formulation of the satellite orbit dynamics in terms of nonsingular orbital elements. A leader–follower control hierarchy is used, such that the motion of the follower satellites is controlled relative to the leader. Key objectives of the station-keeping method are to minimize propellant consumption and to limit the number of maneuvers while guaranteeing safe separation between the satellites. The method is applied in a realistic simulation scenario, including orbit determination, as well as actuation and modeling errors. The method is demonstrated to work for a fleet of four satellites with differences in mass, surface area, and propulsion system for a maneuver cycle of one week. It is then demonstrated that, by reducing the maneuver cycle duration to one day, the method allows collocation of 16 satellites in a single slot, without penalties on propellant consumption.