Optimal Impulsive Formation Reconfiguration near Halo Orbits Using Geometric Configuration Invariants

This paper focuses on the relative motion and optimal impulsive formation reconfiguration near halo orbits. By applying the Floquet theorem, the time-varying system is simplified through a coordinate transformation, followed by the introduction of a geometric configuration invariant for the formation. This invariant provides a geometric interpretation, where general relative configurations are expressed as linear combinations of six fundamental components, scaled by the invariant. By leveraging the invariant's evolution under external orbital control, the reconfiguration trajectory is parameterized using a functional integral, reducing the complexity of trajectory planning to the selection of the invariant. Additionally, impulsive maneuvers are optimized with respect to the timing of impulses using the calculus of variations, minimizing the number of variables in the optimization process. This method provides a set of local optimal solutions, offering alternative impulsive sequences that can be used for rapid maneuver replanning with collision avoidance. Numerical results confirm the effectiveness and highlight the advantages of this reconfiguration optimization approach, particularly in leveraging geometric configuration invariants.