刚体姿态估计的类Rodrigues参数算法研究  

Rigid Body Attitude Estimation Algorithm Based on Similar Rodrigues Parameter

作　　者：杨永[1] 张根宝[1] 宁小磊[2] 陈连华[2] 

机构地区：[1]陕西科技大学电气与信息工程学院,陕西西安710021 [2]第二炮兵工程学院,陕西西安710025

出　　处：《上海航天》2011年第4期27-32,共6页Aerospace Shanghai

摘　　要：针对Rodrigues参数描述刚体姿态运动时的缺陷,提出了一种类Rodrigues参数的姿态估计算法,从定义上避免了Rodrigues参数和修正Rodrigues参数在π,-π,2π,-2π时的奇异性。推导了类Rodrigues参数描述的姿态运动学微分方程,给出了坐标变换的类Rodrigues参数描述,讨论了类Rodrigues的性质和运算,证明了类Rodrigues参数描述姿态的唯一性,并导出了类Rodrigues参数与其他常用姿态描述间的转换公式。给出了用于捷联惯导的姿态解算中的类Rodrigues递推解法。在Matlab软件中对基于STK生成的某标准弹道轨迹的仿真结果表明:类Rodrigues参数的姿态估计算法不存在奇异,计算效率优于目前广泛应用的四元数方法,有一定的理论参考价值。In order to get rid of the limitation of Rodrigues parameter represents rigid body attitude, similar Rodrigues parameters were proposed for attitude determination in this paper, which would avoid singularity that appeared in Rodrigues parameters and modified Rodrigues parameters at π- π, 2π, -2π in definition. A simple derivation of similar Rodrigues parameters based attitude kinematics equation was presented. Coordinate transformation using similar Rodrigues parameters was given. The property and operation of similar Rodrigues parameters were discussed. The exclusion of attitude representation based on similar Rodrigues parameters was proved. The relationship of similar Rodrigues parameters with other attitude representation, such as Euler angle, quaternion, rotation vector and direction cosine matrix were also provided. A recursive solution of similar Rodrigues parameters was given to attitude algorithm to facilitate its application in SINS. The simulation results of some standard ballistic tracer which generated from STK in Matlab software showed that the attitude estimation algorithm using similar Rodrigues parameter could avoid the occurrence of singularity and was more efficient on calculations than widely used quaternion based kinematics equation, which was an important significance in theory and reference.

关 键 词：姿态估计 类Rodrigues参数 RODRIGUES参数 

分 类 号：V249.3[航空宇航科学与技术—飞行器设计]