Robust adaptive strategy for stationkeeping of Halo orbit

This paper deals with the stationkeeping strategy for Halo orbit at the Libration Point L₁ in the Sun-Earth/Moon system. To understand the stability of Halo orbit generating from Circular Restricted Three Body Problem (CR3BP), the Floquet Multiplier is calculated from the Poincaré Mapping defined by the selected nominal orbit. To ascertain the mis-modeled accelerations, the Spatial Bi-Circular Model (SBCM) is used to model the Sun-Earth/Moon system instead of the Ephemeris Model, because there is an analytic expression for the former. Furthermore, SBCM is precise enough to validate the effectiveness of stationkeeping controller. The Hamiltonian dynamics of SBCM in Syzygy Frame of Sun-Earth/Moon system is derived. The alternating gravitation, which caused by the Moon and will make the spacecraft away from the nominal trajectory, is proved to be the small perturbation. Thus, the controller is designed just based on CR3BP without any information on disturbance. The standard algorithm of backstepping control is used to design the initial controller, and then a robustly adaptive controller is achieved after some modifications. The controller designed is proved to have asymptotic stability and the ability of estimating the spacecraft mass and the upper-bound of the disturbance on-linely. Simulation results confirm the validity of the controller proposed.