Optimal Floquet Stationkeeping under the Relative Dynamics of the Three-Body Problem

Deep space missions, and particularly cislunar endeavors, are becoming a major field of interest for the industry, including astrodynamics research community. While near-Earth missions may be completely covered by perturbed Keplerian dynamics, deep require different modeling approach, where multi-body gravitational interactions play role. To this end, Restricted Three-Body Problem stands out as an insightful first strategy early mission design purposes, retaining dynamical transport structures while still being relatively simple. Dynamical Systems Theory classical Hamiltonian Mechanics have proven themselves remarkable tools to analyze deep-space within context, with applications ranging from ballistic capture trajectory stationkeeping. In work, based on premise, derivation co-orbital dynamics between two spacecraft is introduced in detail. Thanks analytical numerical models derived, connections relative CR3BP problems shown exist, first-order linear solutions inherited normal form. The higher-order derived allow theoretical finding unveiling natural phase structures, periodic quasi-periodic orbital families, which further exploited general proximity operation applications. particular, novel reduced-order, optimal low-thrust stationkeeping controller Floquet space, hybridizing State Dependent Ricatti Equation (SDRE) Koopman control techniques efficient unstable manifold regulation. proposed algorithm demonstrated validated several end-to-end low-cost comparison against continuous algorithms presented literature also addressed reveal its enhanced performance. Finally, conclusions open lines discussed.