大范围运动柔性航天器的递推有限段法分析

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

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。

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.