Abstract: To address the inefficiency of traditional indirect and direct methods in designing low-thrust fuel optimal rendezvous trajectories under gravity-assist maneuvers, a rapid trajectory optimization algorithm based on finite Fourier series shaping is proposed. This method transformes the trajectory optimization design into a low-computation nonlinear programming problem that adheres to thrust and gravity-assist constraints under analytically satisfying boundary conditions, thereby significantly enhancing solution efficiency. Additionally, a feasible range estimation strategy for the number of trajectory revolutions is proposed to overcome the limitation that the optimality of shape-based method influenced by the flight revolution; however, the current determination of flight revolution still relies on empirical trial and error. Moreover, to address the challenge of accurately approximating complex low-thrust trajectories under multiple gravity-assist using shape-based method, the overall iterative optimization and segmented optimization strategy are proposed. The feasibility and efficiency of the proposed method and its corresponding strategies are demonstrated by comparing simulation results with and without gravity-assist design, as well as single and multiple gravity-assist designs. The results show that, without relying on any prior information, the proposed method can design reasonable three-dimensional low-thrust rendezvous trajectories within seconds, and reasonable three-dimensional low-thrust single or multiple gravity-assist rendezvous trajectories within tens of seconds.

Key words: low-thrust trajectory design, gravity assist, finite Fourier series, shape-based, fuel optimal, nonlinear programming