Proximity scenario design for geostationary rendezvous with collocated satellite avoidance

Abstract

Proximity operation is one of the prerequisites for in-orbit service or debris removal. Especially for objects in geostationary orbit (GEO), there are certain challenges in rendezvous and proximity operations, such as perturbed relative dynamics and constraints from collocated satellites. In this study, a novel optimization model is built to design the GEO proximity scenario, including the keeping points and durations of each phase. First, as a prerequisite of proximity scenario design, relative dynamics considering solar radiation pressure effects and the corresponding two-point boundary value problem are analytically solved. Second, the concept of passive safety performance is introduced. The safety constraints from both the target satellite and the collocated satellites are considered. The optimization model is then built, and an improved differential evolution optimization algorithm is employed to seek the solution with minimal velocity increment. The numerical examples indicate that a GEO proximity scenario can be stably and effectively designed by the presented method. Moreover, in the scenarios without a collocated satellite, with a static collocated satellite, and with dynamic collocated satellites, the optimized proximity scenarios remain passively safe. If any impulse in the scenario ceases, the resulting free drift trajectory would diverge from the target and the collocated satellites, maintaining the safety index and satisfying the given threshold.