Optimization Design of Cislunar Navigation Constellation with Orbital Period Resonance for On-orbit Servicing

A hierarchical optimization framework integrating clustering and particle swarm algorithms is proposed to address challenges in cislunar navigation constellation design，including high-dimensional variables and extensive parameter spaces. The methodology leverages a periodic resonant orbit repository constructed from multiple families of three-body periodic orbits in cislunar space. Optimal constellation configurations are identified through a three-stage hierarchical clustering algorithm，prioritizing average dilution of precision（DOP）as the primary metric and coverage ratio as secondary. Final parameters are refined via satellite augmentation strategies and phase optimization. Targeting medium-Earth orbits （12 000～20 000 km）and high-Earth orbits（36 000 km radius），simulation results demonstrate that a 6-satellite constellation combining L2 north/south near-rectilinear Halo orbits（NRHOs）with L4/L5 planar orbits achieves optimal performance，characterized by a normalized baseline period of 1. 635 24，resonance ratio of 1∶2∶4∶4，average DOP of 9. 282 2，and 100% four-satellite coverage. This approach validates the feasibility of cislunar constellations for high-precision navigation in medium-high Earth orbits，offering a reference for future cislunar navigation system design.