Classification of Effective Cislunar Periodic Orbits for Lunar Navigation Constellation with Launch-Count Considerations

This study investigates the structure of the solution space in lunar navigation constellation design by formulating it as a multi-objective optimization problem based on periodic orbits in the Circular Restricted Three-Body Problem (CR3BP). The design space includes various periodic orbits based on CR3BP, with a focus on those accessible via lunar swing-by maneuvers to enable low-$\Delta V$ orbit insertion. Three objective functions are considered: navigation accuracy, quantified by Geometric Dilution of Precision (GDOP); orbit insertion cost, represented by total Delta-V; and communication performance, characterized by transmission power. The NSGA-II algorithm is employed as an analysis tool to examine how different user scenarios—namely, a static user on the lunar south pole and a dynamic user in Near Rectilinear Halo Orbit (NRHO)—affect the geometry of feasible solutions. The results show that the structure of trade-offs and achievable configurations vary significantly depending on user location and motion. South pole users benefit from orbit diversity and high-gain antennas to reduce both GDOP and Delta-V. In contrast, NRHO users require broader beam coverage and higher transmission power to maintain continuous links. By incorporating orbit insertion efforts into the analysis of CR3BP-based constellations, this study reveals the importance of user-specific constraints and dynamical accessibility in shaping the design space.