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.

中文翻译：

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基于贝塞尔形状法的低推力多重重力辅助三维轨迹快速初始设计

摘要 在深空探测中，低推力推进技术和多重重力辅助技术的应用将大大提高航天器探测范围，但会显着增加轨迹设计难度。本研究提出了一种将低推力推进和多重重力辅助技术合理结合的低推力轨迹快速初始设计方法。本文将基于贝塞尔形状的方法与重力辅助算法相结合，得到了一种计算低推力多重重力辅助转移轨迹的快速算法。对于木星交会轨迹的设计，通过对比几个有重力辅助和无重力辅助的计算实例，证明了该方法的可行性。为了证明所提出方法的有效性，它与基于有限傅里叶级数 (FFS) 的基于形状的方法进行了比较。仿真结果表明，与FFS基于形状的方法相比，所提出的方法可以使用更短的计算时间来获得速度增量更小的传递轨迹。为了证明所提方法的优越性，将所提方法得到的结果作为初始值，进一步优化高斯伪谱法(GPM)。仿真结果表明，Bezier 方法与 GPM 的性能指标差异仅为 2% 左右，而 Bezier 方法仅使用 GPM 计算时间的 2% 左右。本文描述的方法对于大量设计案例快速获得可行的初始解决方案具有重要意义。