论文标题
关于旋转和姿势的特征结构：共同和特殊性
On the Eigenstructure of Rotations and Poses: Commonalities and Peculiarities
论文作者
论文摘要
在许多科学和工程领域，例如机器人技术，航空航天，计算机视觉和图形，旋转和姿势无处不在。在本文中，我们根据其矩阵谎言组表示的特征结构提供了旋转和姿势的完整表征，因此（3），SE（3）和AD（SE（SE（3）））。姿势表示的特征成分表明，它们可以被施放成与旋转非常相似的形式，尽管前者的结构可能会根据所涉及的翻译和旋转的相对性质而变化。理解这些重要数量的特征结构本身就是值得的，但是要欣赏诸如旋转和姿势以及雅各布人的计算的最小多项式等实用结果也是必不可少的。此外，我们可以说，主轴的姿势与主轴轮换的方式几乎相同。
Rotations and poses are ubiquitous throughout many fields of science and engineering such as robotics, aerospace, computer vision and graphics. In this paper, we provide a complete characterization of rotations and poses in terms of the eigenstructure of their matrix Lie group representations, SO(3), SE(3) and Ad(SE(3)). An eigendecomposition of the pose representations reveals that they can be cast into a form very similar to that of rotations although the structure of the former can vary depending on the relative nature of the translation and rotation involved. Understanding the eigenstructure of these important quantities has merit in and of itself but it is also essential to appreciating such practical results as the minimal polynomial for rotations and poses and the calculation of Jacobians; moreover, we can speak of a principal-axis pose in much the same manner that we can of a principal-axis rotation.
