基于高斯伪光谱的星际小推力转移轨道快速优化  

Fast Optimization of Interplanetary Low-Thrust Transfer Trajectory Based on Gauss Pseudospectral Algorithm

作　　者：尚海滨[1] 崔平远[1] 徐瑞[1] 乔栋[1] 

机构地区：[1]北京理工大学深空探测技术研究所,北京100081

出　　处：《宇航学报》2010年第4期1005-1011,共7页Journal of Astronautics

基　　金：国家自然科学基金(10832004);国家863项目(2009AA7035060C);高等学校博士学科点专项科研基金(20091101120003)

摘　　要：针对星际小推力转移轨道优化问题,给出了一种基于高斯伪光谱配点的快速优化算法。首先,基于归一化的改进春分点根数建立了星际小推力转移轨道的优化模型;然后,采用高斯伪光谱配点策略对优化模型进行离散化处理,推力方向限制和天体星历分别作为路径约束和事件约束,将轨道优化问题转化为一个大规模多约束参数优化问题;在此基础上,基于高斯伪光谱的配点特性,推导出性能指标和约束方程的解析雅可比矩阵,保证了雅可比矩阵计算的准确性和效率;最后,以利用太阳能电推进探测火星和水星为例,对所给算法进行了数值验证。数值结果表明:高斯伪光谱方法可有效用于星际小推力轨道的优化问题,并且与数值差分相比,解析的雅可比矩阵算法可提高计算效率67.78%。In this paper,we have proposed a fast gauss pseudospectral approach for optimization of interplanetary low-thrust transfer trajectory.First,the optimization model of interplanetary low-thrust trajectory was established using modified equinoctial elements.Then,through parameterizing the optimization model by gauss pseudospectral strategy,the low-thrust trajectory optimization problem was translated into a large-scale parameters optimization problem with multi-constraints,in which the thrust direction and planetary ephemeris constrains were treated as path and event constraints respectively.Furthermore,in order to improve the efficiency and precision,the analytical jacobian matrix of performance index and constraints equations were derived.Taking the Mars and Mercury mission as the examples,the proposed gauss pseudospectral approach was validated.The numerical result demonstrates that,comparing to traditional numerical algorithm,the computation efficiency can be improved 67.78% using analytic jacobian matrix.

关 键 词：小推力 星际转移 快速优化 高斯伪光谱 雅可比矩阵 

分 类 号：V41[航空宇航科学与技术—航空宇航推进理论与工程]