A two-impulse method for stabilizing the spacecraft relative motion with respect to a periodic trajectory

The article presents an analytical method for computing a two-impulse control law that stabilizes the spacecraft relative motion with respect to an invariant set. The invariant set contains the states belonging to a desired periodic relative trajectory and is described using linear equations. The two impulses are computed analytically based on the prediction of the evolution of the relative trajectory. Closed-loop tests are conducted using the non-linear relative dynamics, for different eccentricities of the reference orbit and for different levels of navigation uncertainty. Encouraging results are obtained using a control strategy that requires very few computational effort.