Formation flight control for modeling interferometric aperture planes

Current restrictions on monolithic telescope aperture size have made it necessary for distributed systems of satellites to increase resolution of distant objects utilizing infrared interferometry. Based on linearized relative equations of motion near the L₂ libration point of the Circular Restricted Three-Body Problem (CR3BP), a state feedback control method is developed to track a reference position to maintain several craft in a planar formation relative to a hub craft. The hub's motion using linearized equation relative to the libration point is found and used for determining the pointing error due to the hub motion. Wide ranges of pointing angles for the aperture configuration are simulated that are useful in estimating station keeping fuel consumption and attainable targeting for interferometric observations. A halo orbit was produced using linearized analytical equations that served as a reference orbit for the formation. A geometrical relation was developed that gave an estimate of the maximum pointing error accumulated by the formation's movement along the reference orbit The relative positions of the satellites composing the aperture plane stabilize to the appropriate reference position in a few seconds and remain fixed for the observation period of 5-10 days. Control acceleration levels varied according to the distance from the hub craft, with the effort increasing with the distance from the hub craft. The range of the control efforts (ΔV's) to keep the formation fixed for an observation period ranged from approximately 1 m/s to 4.5 m/s for each satellite. This type of analysis is useful for mission planning because it enables the propellant cost estimates over a range of pointing directions to the astronomical objects that are to be observed.