四元数在水下航行体运动建模中的应用

摘要

This paper focuses on a particular type of Autonomous Underwater Vehicle(AUV)that uses the Control Moment Gyros(CMGs)for attitude control. It is noticed that the AUV may have a large attitude angle,and as a result,a proper motion model must be established to avoid the attitude description matrix singularity. To do so,the four-parameter approach is applied to establish the kinematics equation,and the relationship between four-parameter and Euler's angle is then given. When constructing the dynamics equation,the AUV is regarded as a multi-rigid-body system consisting of the AUV itself and CMGs, while Euler's angle is replaced by four-parameter. For validation,the motion model is simulated by the Runge-Kutta method. The results show that the model effectively avoids the singularity.%针对一类以控制力矩陀螺（CMG）为姿态控制执行机构的水下航行体，考虑到其大角度机动时姿态描述矩阵可能会出现奇异的问题，建立了与其相适应的运动模型。首先，通过引入四元数来建立运动学方程，并给出四元数与欧拉角之间的关系。随后，在建立动力学方程时，将水下航行体视为由水下航行体和CMG组成的多刚体系统，并使用四元数来代替动力学方程中的欧拉角项。最后，使用龙格库塔法对所建立的模型进行仿真。仿真结果表明，所建立的模型能有效避免使用欧拉角方法建立模型时所产生的奇异问题。