Fast initial design of low-thrust multiple gravity-assist three-dimensional trajectories based on the Bezier shape-based method

Abstract

In deep space exploration, the application of low-thrust propulsion technology and multiple gravity-assist technology will greatly improve the scope of spacecraft exploration but will significantly increase the difficulty of trajectory design. This study proposes a fast initial design method of low-thrust trajectories, which reasonably combines low-thrust propulsion and multiple gravity-assist technology. In this paper, the Bezier shape-based method is combined with the gravity-assist algorithm to obtain a fast algorithm for calculating the low-thrust multiple gravity-assist transfer trajectories. For the design of the Jupiter rendezvous trajectories, the feasibility of the proposed method is proved by comparing several calculation examples with and without gravity assistance. In order to prove the effectiveness of the proposed method, it is compared with the finite Fourier series (FFS) shape-based method. The simulation results show that the proposed method can use shorter computation time to obtain transfer trajectories with smaller velocity increments than the FFS shape-based method. In order to prove the superiority of the proposed method, the results obtained by the proposed method are used as initial values for further optimization of the Gauss pseudospectral method (GPM). The simulation results show that the difference between the performance indexes of the Bezier method and the GPM is only about 2%, while the Bezier method only uses approximately 2% of the computation time of the GPM. The method described in this paper is significant for obtaining a feasible initial solution quickly for a large number of design cases.