姿态运动的Rodrigues参数描述

Attitude representation using rodrigues parameter

详细介绍了刚体姿态运动的Rodrigues参数描述,指出了Rodrigues参数的许多新特性,定义了Ro drigues参数的乘法及相关的代数运算,给出了坐标变换的Rodrigues参数乘法描述,推导了Rodrigues参数描述的姿态运动学微分方程及逆运动方程,并给出了Rodrigues参数与其他常用姿态描述之间的转换公式。文中指出用Ro drigues参数描述姿态转动具有简洁、直观的优点,而且Rodrigues参数描述的微分方程结构简洁、无多余的约束,其计算效率优于当前广泛应用的四元数方法。文末介绍了Rodrigues参数在弹道导弹捷联姿态实时解算中的应用,基于Rodrigues参数的捷联姿态算法在计算精度、内存消耗上均优于目前弹上计算机使用的四元数递推算法,且计算量仅相当于后者的一半。

This paper gives detail discussion of attitude representation using Rodrigues parameters.Many new attractive properties of Rodrigues parameters are presented.A special algebra of Rodrigues parameters is defined for better description of attitude motion and coordinate transformation.A simple derivation of Rodrigues parameters based attitude kinematics equation and inverse kinematics equation is presented.The relationship of Rodrigues parameters with other attitude representation,such as Euler angle,quaternion and direction cosine matrix are also provided.We point out that attitude representation using Rodrigues parameters has the advantage of simple and clear geometric interpretation,and that the Rodrigues parameters based attitude kinematics equation has simple mathematic structure and is more efficient than widely used quaternion based kinematics equation.At last,we discussed the application of Rodrigues parameters in real time attitude calculation of strapdown ballistic missile.The computational burden of Rodrigues parameters based strapdown attitude algorithm is only half of currently used quaternion based algorithm,while has better precision and less memory consumption.