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首页> 外文期刊>Transactions of the Institute of Measurement and Control >Comparative study of attitude control methods based on Euler angles, quaternions, angle-axis pairs and orientation matrices
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Comparative study of attitude control methods based on Euler angles, quaternions, angle-axis pairs and orientation matrices

机译：基于欧拉角，四轴，角轴对和方向矩阵的姿态控制方法对比研究

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摘要

This paper presents a comparative study about the attitude control methods based on four commonly used error indicators, namely the triad of 3-2-1 deviational Euler angles, the error quaternion, the deviational angle-axis pair and the orientation error matrix. These error indicators are used here with the same backstepping control law to have a common basis of comparison. This control law makes the controller track a restoring angular velocity generated here specifically for each error indicator. This comparative study shows that all these error indicators can be used satisfactorily even in the critical orientations associated with them by taking special measures. For the deviational Euler angle triad, a critical orientation is a singularity, at which the angles become indefinite. Unless the vehicle is stationary, this indefiniteness is resolved here by applying L'Hopital's Rule on the angular velocity information. The Euler angle triad has also a multiplicity problem. It is solved here by using the novel criterion of minimal deviation angles. For the other error indicators, a critical orientation is an antipodal orientation, which is opposite to the desired one. In an antipodal orientation, the error quaternion and the deviational angle-axis pair cannot be determined through the customary formulas. They are determined here by using the novel specially introduced formulas. Besides, they may suffer from the unwinding phenomenon in an ordinary orientation. This phenomenon is prevented here by keeping the scalar part of the error quaternion non-negative and the deviation angle between 0 degrees and 180 degrees. For the orientation error matrix, a stationary and undisturbed antipodal orientation is an unstable equilibrium, in which the ordinary backstepping control law becomes ineffective for driving the system into action. This problem is solved here by adding an extra term to the ordinary backstepping control law.
机译：本文介绍了对基于四个常用误差指标的姿态控制方法的比较研究，即3-2-1偏差欧拉角，误差四元数，偏差角轴对和方向误差矩阵的三合会。这些错误指示器在这里使用相同的反向控制法具有共同的比较基础。该控制法使控制器跟踪专门针对每个错误指示器产生的恢复角速度。该比较研究表明，即使采取特殊措施，即使采用与其相关的临界取向，所有这些误差指标也可以令人满意地使用。对于偏差欧拉角三合会，临界取向是一个奇点，角度是无限期的。除非车辆是静止的，否则通过在角速度信息上应用L'Hopity的规则来解决这种无限度。欧拉角三合会也具有多重问题。通过使用最小偏差角的新标准来解决它。对于其他误差指示器，临界取向是一种反双向取向，其与所需的反向取向。在抗双向取向，误差四元数和偏差角轴对不能通过常规公式确定。通过使用新颖的专门介绍的公式来确定它们。此外，它们可能遭受普通定位的展开现象。这里通过将误差四元数的标量部分保持在0度和180度之间的偏差角来防止这种现象。对于定向误差矩阵，静止和未受干扰的反双向取向是一种不稳定的平衡，其中普通的反向控制法变得无效，使系统驱动到动作。通过向普通的反向控制法增加额外的术语来解决这个问题。

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