配点法和网格细化技术用于非光滑轨迹优化  

Application of Local Collocation Method and Mesh Refinement to Non-Smooth Trajectory Optimization

作　　者：赵吉松[1,2] 谷良贤[2] 佘文学 

机构地区：[1]北京空天技术研究所,北京100074 [2]西北工业大学航天学院,西安710072

出　　处：《宇航学报》2013年第11期1442-1450,共9页Journal of Astronautics

基　　金：西北工业大学博士论文创新基金(CX200902)

摘　　要：针对非光滑轨迹优化问题,采用局部配点法开发出通用的轨迹优化方法(考虑NLP的规范化处理、稀疏特性和数值微分算法等),从细化效率、易用性和适应性等角度对基于数据压缩原理的网格细化技术进行改进,发展出通用的非光滑轨迹优化方法。采用典型的非光滑轨迹优化算例对方法进行了验证,结果表明:(1)所述方法能够以较少的离散节点高精度、快速求解非光滑轨迹优化问题,在轨迹变化平坦区域采用较稀的网格,在轨迹变化剧烈区域加密网格;(2)采用控制变量作为网格细化函数能够捕捉到状态变量的剧烈变化特性;(3)采用局部配点法优化轨迹时,在非光滑区域应该加密网格而不宜分段优化。Abstract： A general non-smooth trajectory optimization approach is developed in the present paper. The mesh refinement procedure based on data compress for dyadic grids is improved to increase efficiency, usability, and flexibility, and is then combined with the local collocation method which takes advantage of scaling, sparsity and numerical differentiation of NLP. Numerical examples of several challenging non-smooth trajectory optimization （ including bang-bang control and so on ） demonstrate that： （1） the approach solves non-smooth trajectory optimization rapidly with high accuracy, and captures non-smooth regions exactly with density mesh; （2） the approach captures non-smooth regions of states although the mesh is refined according to controls ; （3） for the local collocation method, it is better to refine the mesh rather than divide the non-smooth trajectory into multiple segments.

关 键 词：非光滑轨迹 优化 配点法 网格细化 

分 类 号：V412[航空宇航科学与技术—航空宇航推进理论与工程]