回転とポーズの固有構造：共通点と特異点
On the Eigenstructure of Rotations and Poses: Commonalities and Peculiarities
回転とポーズの行列表現（SO(3), SE(3), Ad(SE(3))）の固有構造を完全に特徴付け、回転とポーズの類似点と相違点を明らかにした論文。
著者: Gabriele M T D'Eleuterio, Timothy D Barfoot
分類: cs.RO
原文アブストラクト
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.
