The problem of minimum-time, low-thrust, Earth-to-Mars interplanetary orbital trajectory optimization is considered. The minimum-time orbital transfer problem is modeled as a four-phase optimal control problem where the four phases correspond to planetary alignment, Earth escape, heliocentric transfer, and Mars capture. The four-phase optimal control problem is then solved using a direct collocation adaptive Gaussian quadrature collocation method. The following three models are used in the study: 1) circular planetary motion, 2) elliptic planetary motion, and 3) elliptic planetary motion with gravity perturbations, where the transfer begins in a geostationary orbit and terminates in a Mars-stationary orbit. Results for all three cases are provided, and one particular case is studied in detail to show the key features of the optimal solutions. Using the particular value thrust specific force of $9.8\times {10}^{-4}\mathrm{m}\cdot {\mathrm{s}}^{-2}$, it was found that the minimum times for cases 1, 2, and 3 are, respectively, 215, 196, and 198 d with departure dates, respectively, of 1 July 2020, 30 June 2020, and 28 June 2020. Finally, the problem formulation developed in this study is compared against prior work on an Earth-to-Mars interplanetary orbit transfer where it is found that the results of this research show significant improvement in transfer time relative to the prior work.

考虑了最短时间、低推力、地球到火星的行星际轨道轨迹优化问题。最小时间轨道转移问题被建模为四阶段最优控制问题，其中四个阶段对应于行星对齐、地球逃逸、日心转移和火星捕获。然后使用直接搭配自适应高斯正交搭配方法解决四相最优控制问题。研究中使用了以下三个模型：1) 圆形行星运动，2) 椭圆行星运动，以及 3) 具有重力扰动的椭圆行星运动，其中转移从地球静止轨道开始，终止于火星静止轨道。提供了所有三种情况的结果，并详细研究了一种特殊情况以显示最佳解决方案的关键特征。$9.8\times {10}^{-4}\mathrm{米}\cdot {\mathrm{秒}}^{-2}$，发现案例 1、2 和 3 的最短时间分别为 215、196 和 198 天，出发日期分别为 2020 年 7 月 1 日、2020 年 6 月 30 日和 2020 年 6 月 28 日。最后，将本研究中提出的问题公式与先前关于地球到火星行星际轨道转移的工作进行比较，发现本研究的结果表明，与先前的工作相比，转移时间有显着改善。