Fast Cooperative Trajectory Optimization for Close-Range Satellite Formation Using Bezier Shape-Based Method

Close-range formation flying of multiple satellites is an important technology for future space missions, where formation reconfiguration is a very important field and needs to design suitable flight paths and consider the risk of collisions between satellites. This paper uses the Bezier shape-based (SB) method to rapidly generate the low-thrust collision-avoidance flight paths in the formation reconfiguration. The reconfiguration process of two satellite formations is considered and compared with the finite Fourier series (FFS) method. The simulation results show that the Bezier method spends less computation time to obtain better performance index than the FFS method. In order to verify the applicability of the results obtained by the Bezier method to a direct solver, the results are applied to the Gauss pseudospectral method (GPM) solver as an initial guess. The results show that the Bezier method can take a short time to design suitable initial collision-avoidance flight paths for an direct optimization solver. This is very important for the rapid feasibility evaluation of numerous flight scenarios at the stage of initial mission design and onboard flight paths generation.