Autonomous regulation of spacecraft motion about unstable periodic orbits using impulsive maneuvers

This paper presents a control method for autonomous regulation of spacecraft motion about unstable periodic orbits by occasional impulsive maneuvers. In this method, the impulsive maneuver to be applied at each prescribed time is obtained by modulating the difference between the actual state and the reference state of the motion at the time. The method is based on that of Generalized Sampled-data Hold Function (GSHF) control which is known to be useful in stabilizing motion about unstable periodic orbits using continuous maneuvers. A formula for impulsive maneuvers is obtained so that the impulsive maneuvers mimic the efficacy of a stabilizing GSHF controller. The method is applied to a halo orbit spacecraft in the Hill's circular three-body problem as an illustration.