Design and continuation of nonlinear teardrop hovering formation along the near rectilinear Halo orbit

This short communication is devoted to the design and continuation of a teardrop hovering formation along the Near Rectilinear Halo orbit and provides further insights into future on-orbit services in the cislunar space. First, we extend the concept of the teardrop hovering formation to scenarios along the Near Rectilinear Halo orbit in the Earth-Moon circular restricted three-body problem. Then, we develop two methods for designing these formations based on the nonlinear model for relative motion. The first method addresses the design of the teardrop hovering formations with relatively short revisit distances, while the second method continues hovering trajectories from relatively short to relatively long revisit distances. New continuation method is developed to meet the design requirements of this new scenario. Specifically, this new continuation method refers to the new linear predictor applied to the continuation in a parameter that is part of the constraints. Simulation results verify the effectiveness of the proposed methods, and a near-natural teardrop hovering formation is achieved by considering the dynamical properties near the NRHO. Comparisons between design results obtained using linear and nonlinear models further strengthen the necessity of using the nonlinear model.