论文标题
利用缩放常数以促进间接轨迹优化方法的收敛性
Exploiting Scaling Constants to Facilitate the Convergence of Indirect Trajectory Optimization Methods
论文作者
论文摘要
本说明会开发出易于适用的技术,以改善收敛性并减少间接低推力轨迹优化的计算时间,以解决燃油和时间优势问题。为了解决燃料最佳(FO)问题,基于能量最佳(EO)解决方案引入了一个正缩放系数 - $γ_{tr} $ - 为FO问题的开关功能建立了方便的配置文件。这否定了对随机猜测的需求,以初始化间接优化过程。同样,在解决时间优势(到)问题以将EO问题连接到TO时,引入了另一个缩放因子-Yβ$ - 。针对问题的开发方法对于GTOC11竞争至关重要。进行案例研究以验证TO和FO问题中的解决方案过程。对于地心的案例,还考虑了日食和$ J_2 $扰动的效果。示例表明,EO可以很好地猜测和FO问题,并且引入常数可以减少初始残差并改善收敛性。还表明,Lagrangian质量乘数的方程式对于FO和情况都可以忽略相关的边界条件,而不会影响最佳性。这种简化降低了问题维度并提高了效率。
This note develops easily applicable techniques that improve the convergence and reduce the computational time of indirect low thrust trajectory optimization when solving fuel- and time-optimal problems. For solving fuel optimal (FO) problems, a positive scaling factor -- $Γ_{TR}$ -- is introduced based on the energy optimal (EO) solution to establish a convenient profile for the switching function of the FO problem. This negates the need for random guesses to initialize the indirect optimization process. Similarly, another scaling factor-$β$-, is introduced when solving the time-optimal (TO) problem to connect the EO problem to the TO. The developed methodology for the TO problem was crucial for the GTOC11 competition. Case studies are conducted to validate the solution process in both TO and FO problems. For geocentric cases, the effect of eclipses and $J_2$ perturbations were also considered. The examples show that EO can provide a good guess for TO and FO problems and that introducing the constants can reduce the initial residuals and improve convergence. It is also shown that the equation for the Lagrangian multiplier of mass and the associated boundary condition can be ignored for both FO and TO cases without affecting optimality. This simplification reduces the problem dimensions and improves efficiency.