Loosely Formation-Displaced Geostationary Orbit Optimization with Complex Hybrid Sail Propulsion

To explore the performance of hybrid sail and overcome the congestion of geostationary orbit, this work proposes a method intended to optimize the trajectories of the spacecraft formation and extend the concept of displaced geostationary orbit by loosening the relative distance and introducing a station-keeping box. The multispacecraft formation is a typical complex system with nonlinear dynamics, and the hybrid propulsion system introduces additional complexity. To solve this problem, suboptimal trajectories with constant relative distance constraints are first found with inverse methods, which were referred to as ideal displaced geostationary orbits. Then, the suboptimal trajectories are used as a first guess for a direct optimization algorithm based on Gauss pseudospectral algorithm, which loosens the relative distance constraints and allows the spacecraft to be placed anywhere inside the station-keeping box. The optimization results show that the loosely formation and station-keeping box can create more flexible trajectories and achieve higher efficiency of the hybrid sail propulsion system, which can save about 40% propellant consumption.