Explicit form of station-keeping and formation flying controller for libration point orbits

A new station-keeping strategy based on nonlinear output regulation theory has been proposed for the periodic orbits in the circular restricted three-body problem. A Fourier series approximation was employed to generate the desired orbits, and then the output regulation theory for nonlinear systems was applied. The output regulation problem was solved in an analytical form. The proposed controller has been applied and verified in numerical simulations for the halo orbit of the sun–Earth L2 point. In the case that the reference orbit is the natural periodic orbit, the controller can approximate the optimal controller in the sense of minimizing the station-keeping cost. As an application of the proposed method, formation flying using circular orbits around the chief satellite has been worked out.