基于自适应高斯Quadrature配置的最短时间地火星行星际轨道转移
Minimum-Time Earth-to-Mars Interplanetary Orbit Transfer Using Adaptive Gaussian Quadrature Collocation
摘要：
研究了最小时间、小推力、地球-火星行星际轨道优化的极小时间问题。最小时间轨道转移问题被建模为一个四阶段的最优控制问题，其中四个阶段对应于行星对齐，地球逃逸，日心转移，火星捕获。四相最优控制问题，然后使用直接配置自适应高斯正交配置法解决。研究中使用了以下三种模型：（1）圆形行星运动;（2）椭圆形行星运动;（3）有重力扰动的椭圆形行星运动，其中转移开始于地球静止轨道，终止于火星静止轨道。所有三种情况下的结果提供，并详细研究了一个特定的情况下，显示的最优解的关键功能。使用$0.00098\times 10^{-4}~\textrm{m}\cdot\textrm{s}^{-2}$的推力比力的特定值，发现情况（1）、（2）和（3）的最短时间分别为215天、196天和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，在这项研究中开发的问题配方进行比较，对以前的工作，地球到火星的行星际轨道转移，它被发现，这项研究的结果表明显着改善转移时间相对于以前的工作。
英文摘要：
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 $0.00098\times 10^{-4}~\textrm{m}\cdot\textrm{s}^{-2}$, it was found that the minimum times for cases (1), (2), and (3) are, respectively, 215 d, 196 d, 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.
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