论文标题
态度控制问题和技术的观点
A perspective on Attitude Control Issues and Techniques
论文作者
论文摘要
本文回顾了刚体系统的态度控制问题，从刚体运动学的态度表示开始。高度冗余的旋转矩阵通过9个参数定义了全球和独特的态度取向，这是最基本的参数，而没有任何奇异性。最小的3参数Euler角或（修改的）Rodrigues参数既不定义态度取向，既没有在全球范围内也不唯一，但是前者表现出运动学的奇异性和gimbal锁，而后两个则表现出几何奇异性。曾经冗余的轴角或单位四元基因在全球范围内定义态度旋转，但并非使用4个参数，但前者不适合定义非常小或非常大的旋转，而后者尽管计算负担减少了，但后者显示出不愿意的现象。此外，我们探索了这些态度表示之间的关系，包括振荡锁，放松现象和一组零密集的Lebesgue度量的连接。根据态度表示，我们分析了不同的态度控制定律，几乎全球控制和全球态度控制，名义和一般鲁棒性以及技术工具。
This paper reviews the attitude control problems for rigid-body systems, starting from the attitude representation for rigid body kinematics. Highly redundant rotation matrix defines the attitude orientation globally and uniquely by 9 parameters, which is the most fundamental one, without any singularities; minimum 3-parameter Euler angles or (modified) Rodrigues parameters define the attitude orientation neither globally nor uniquely, but the former exhibits kinematical singularity and Gimbal lock, while the latter two exhibit geometrical singularity; once-redundant axis-angle or unit quaternion globally define the attitude rotation but not uniquely using 4 parameters, but the former is not appropriate to define very small or very large rotations, while the latter shows unwinding phenomenon despite of the reduced computation burden. In addition, we explore the relationships among those attitude representations, including the connections among Gimbal lock, unwinding phenomenon and a nowhere dense set of zero Lebesgue measure. Based on attitude representations, we analyze different attitude control laws, almost global control and global attitude control, nominal and general robustness, as well as the technique tools.
