›› 2012, Vol. 32 ›› Issue (4): 22-27.doi: 10.3780/j.issn.1000-758X.2012.04.004

• 研究探讨 • 上一篇    下一篇

大范围运动柔性航天器的递推有限段法分析

李文龙, 余正宁, 师鹏, 赵育善   

  1. (北京航空航天大学宇航学院,北京 100191)
  • 收稿日期:2011-06-22 修回日期:2011-10-18 出版日期:2012-08-25 发布日期:2012-08-25
  • 作者简介:李文龙 1988年生,2009年毕业于北京航空航天大学飞行器设计专业,现为北京航空航天大学博士研究生。研究方向为航天器动力学与控制。
  • 基金资助:

    中央高校基本科研业务费专项资金(YWF-10-02-091)资助项目

Recursive Finite Segment Method Analysis of Flexible Spacecraft Undergoing Large Overall Motions

Li Wenlong, Yu Zhengning, Shi Peng, Zhao Yushan   

  1. (School of Astronautics, Behang University, Beijing 100191)
  • Received:2011-06-22 Revised:2011-10-18 Online:2012-08-25 Published:2012-08-25

摘要: 采用有限段法对做大范围运动柔性航天器建模时,针对传统方法求解计算效率低的问题,提出将有限段法与空间算子代数理论结合的高效处理方法。首先采用有限段法对柔性部件进行离散,将系统构造成为带关节柔性的多刚体系统,然后采用空间算子代数理论建立递推动力学方程,保证了分段引入大量广义坐标的情况下计算量仅呈线性增长,很好地克服了分段后系统运算量急剧增长的问题。最后给出双柔性杆机械臂系统的仿真算例,分别采用空间算子代数算法(SOA)与牛顿欧拉法(NE)建模,数值仿真结果表明采用SOA法与NE法建模所得计算结果完全一致。对比两种方法计算时间表明,SOA法计算量与系统自由度呈线性关系,且远小于牛顿欧拉法,仿真结果证实了本文方法的可行性和有效性。

关键词: 空间算子代数, 有限段法, 动力学方程, 柔性航天器

Abstract: The number of freedom degree of flexible spacecraft undergoing large overall motions would increase largely if the finite segment method was adopted, so the traditional methods would be inefficient. A more efficient way was proposed by combining the finite segment method and the spatial operator algebra theory. Firstly, the flexible components were divided into several rigid bodies, so the original system turned to be a rigid multi-body with flexible joints. Then, the spatial operator algebra (SOA) theory based recursive kinetic equation of motion was established. Finally,a numerical example of two flexible link manipulators was presented. The simulation results are quite consistent when the problem was solved by the SOA method as well as the Newton Euler method. The computation time indicates that it increases linearly with the number of DOF by spatial operator algebra theory, and much fewer than that of the Newton Euler method. Results confirm the validation and efficiency of this method.

Key words: Spatial operator algebra, Finite segment method, Kinetic equation, Flexible spacecraft