Stationkeeping controllers for Earth–Moon L1 and L2 libration points halo orbits

This paper considers the dynamics of the circular restricted three-body problem (CRTBP) for the Earth–Moon system designing stationkeeping controllers at periodic orbits. Taking into account the L1 and L2 equilibrium points in this dynamics, it is constructed a family of periodic orbits in the vicinity of these libration points, called halo orbits. The orbits are constructed using an analytical approach as a first guess with a numerical method in addition, in order to correct the linear approximation procedure. Withal the stability of these libration points, trajectories are analyzed and proved to be unstable; a spacecraft moving near these points must use some correction maneuver to remain close to the nominal orbit. Two types of controllers are proposed for stationkeeping maneuvers performed by low-thrust power-limited propulsion system. The first controller is based on the linear quadratic regulator (LQR) and the second one is based on the nonlinear feedback control which uses the state-dependent Riccati equation control (SDRE). Finally, a parameters comparison analysis is performed taking into account different values of the weight matrices for both controllers at both halo orbits.