Station-Keeping Techniques for Sidereal Resonant Tulip-Shaped Three-Body Orbits

Many pumpkin-shaped three-body orbits, 1:1 sidereal-resonant members of the tulip-shaped family, offer continuous lunar visibility, zero lunar occultations, and repeating ground tracks; properties attractive for cislunar SSA, PNT, and communication missions. Although dynamically unstable, these orbits can be maintained through targeted station-keeping. This study evaluates two complementary strategies using high-fidelity Monte Carlo simulation informed by monodromy-based stability analysis. The Principal Stretching Direction Control (PSDC) method, which corrects drift along the dominant unstable Floquet mode, achieves annual delta-v below 15 m/s while preserving geometric fidelity to a reference ephemeris. A reference-free eccentricity-control method provides robustness under degraded navigation or autonomy constraints, maintaining higher-petal families with annual $\Delta V$ below 110 m/s. Both methods demonstrate multi-year viability, and their performance aligns with pre-computed analytic station-keeping bounds. These results establish pumpkin-shaped orbits as practical, controllable candidates for future lunar infrastructure and persistent cislunar operations.