This paper presents a method to use the Bezier curve to rapidly generate three-dimensional low-thrust trajectories, which can provide a suitable initial approximation to be used for more accurate trajectory optimal control tools. Two missions, from Earth to Mars and the asteroid Dionysus, are considered to evaluate the performance of the method. In order to verify the advantages of this method, it is compared with the finite Fourier series method. Numerical results show that the Bezier method can get better performance index in shorter computation time compared with the finite Fourier series method. The applicability of the solution obtained by Bezier method is evaluated by introducing the obtained solution into the Gauss pseudospectral method as an initial guess. The simulation results show that the Bezier method can rapidly generate a very suitable three-dimensional initial trajectory for the optimal solver. This is very important for rapid evaluation of the feasibility of a large number of low-thrust flight schemes in the preliminary mission design stage.

中文翻译：

---

基于贝塞尔曲线整形方法的低推力轨迹初始设计

本文提出了一种利用贝塞尔曲线快速生成三维低推力轨迹的方法，该方法可以提供一个合适的初始近似值，以用于更精确的轨迹优化控制工具。考虑从地球到火星和小行星狄俄尼索斯的两个任务来评估该方法的性能。为了验证该方法的优点，将其与有限傅立叶级数法进行比较。数值结果表明，与有限傅里叶级数方法相比，贝塞尔方法可以在更短的计算时间内获得更好的性能指标。Bezier方法得到的解的适用性是通过将得到的解作为初始猜测引入到高斯伪谱方法中来评价的。仿真结果表明，Bezier 方法可以快速生成非常适合最优求解器的三维初始轨迹。这对于在任务初步设计阶段快速评估大量低推力飞行方案的可行性非常重要。