Station-keeping and formation flying based on nonlinear output regulation theory

Station-keeping and formation flying along a libration point orbit in the circular restricted three-body problem are considered. In order to deal with the relative motion with respect to a reference trajectory, this paper extends our previous study which derives the station-keeping controller based on the output regulation theory. First the reference orbit of the chief satellite is represented as the output of an autonomous system called exosystem, assuming the reference orbit is given by a truncated Fourier series. For the formation flying, the relative trajectory of the deputy satellite with respect to the chief satellite is also represented by the output of an exosystem. Then the reference signal to be asymptotically tracked for the formation flying is obtained by the superposition of the two exosystems. The proposed controllers are applied and verified for the station-keeping and formation flying along a periodic orbit of the Sun-Earth L₂ point.