Six-degree-of-freedom motion state prediction of spacecraft near the libration point of Earth-Moon system based on Koopman operator

Attitude-orbit maintenance, fuel optimization, and collision avoidance of the libration point spacecraft all rely on the effective prediction of their motion states. However, the instability and orbit-attitude coupling in the three-body problem pose significant challenges to state prediction. To address the need for six-degree-of-freedom motion state prediction of large spacecraft near the libration point, a linear predictor construction method based on the Koopman operator is proposed. First, a circular restricted three-body orbit-attitude motion model for large spacecraft near the libration point is established. Then, based on the theory of the Koopman operator, the motion of the spacecraft near the libration point is sampled, and a six-degree-of-freedom linear predictor for the spacecraft's motion state is constructed. Finally, the effectiveness of the predictor is analyzed in different regions of the near-rectilinear Halo orbit using simulation data. The simulation results show that the Koopman operator-based predictor outperforms the prediction method based on the local linearization of the periodic solution in both orbital motion and attitude motion prediction. Moreover, despite the strong instability in the perilune region, the proposed predictor can still provide reasonable predictions of the motion state.