Generation and stability analysis of long-term bounded spacecraft cluster orbits using Lagrangian Coherent Structures

The problem of initializing a naturally long-term bounded spacecraft cluster configuration that accounts for perturbations and minimizes collision risk is of great interest to the astrodynamics community. Recent studies have demonstrated that bounded relative motion in the zonal gravitational field exists but may extend up to hundreds of kilometers, beyond the requirements of cluster missions. To remedy this in a high-order gravitational field, even incorporating total perturbations, a novel Poincaré mapping is proposed by the kinematic features and Jacobi integrals of dynamics in Hamiltonian regular form. By reducing the search dimensions from six to two, the distribution of long-term bounded motion can be conveniently identified and extracted via the finite-time Lyapunov exponent and the Lagrangian Coherent Structures techniques. Utilizing the obtained distribution, a rapid initialization strategy for a long-term bounded cluster considering drift is provided by extending the system parameters. The optimization of collision risks in configurations is significantly enhanced through deep learning and geometric approximation methods, reducing time consumption by several orders of magnitude and greatly benefiting on-orbit cluster initialization and reconstruction missions. Numerical simulation results support the effectiveness of the proposed methods accounting for total perturbations over an extended period.