Fast Cooperative Close-Range Satellite Formation Trajectory Optimization Using Finite Fourier Series Method

Close-range satellite collision-free formation flying is critical for future space missions that are equipped with electric, low-thrust propulsion systems. This paper employs the Finite Fourier Series (FFS) approximation method to rapidly generate the low-thrust, collision-free trajectories for the reconfiguration of three-satellite configurations. Results demonstrate that the FFS method can quickly produce suitable initial near-optimal feasible trajectories. This capability is crucial for the rapid feasibility evaluation of numerous mission scenarios during the initial design phase. Our results indicate that the proposed method can rapidly generate appropriate initial flight paths, which is crucial for fast satellite formation reconfiguration. Moreover, these initial solutions can significantly accelerate the solution of formation reconfiguration problems that are solved using direct optimization methods.