傾斜回転と傾斜位相空間
Tilt Rotations and the Tilt Phase Space
3D物体のバランス解析に有用な「傾斜回転」を厳密に定義し、複数のパラメータ化と可換な加法が定義できる傾斜位相空間の性質を解析した。
著者: Philipp Allgeuer, Sven Behnke
分類: cs.RO
原文アブストラクト
In this paper, the intuitive idea of tilt is formalised into the rigorous concept of tilt rotations. This is motivated by the high relevance that pure tilt rotations have in the analysis of balancing bodies in 3D, and their applicability to the analysis of certain types of contacts. The notion of a 'tilt rotation' is first precisely defined, before multiple parameterisations thereof are presented for mathematical analysis. It is demonstrated how such rotations can be represented in the so-called tilt phase space, which as a vector space allows for a meaningful definition of commutative addition. The properties of both tilt rotations and the tilt phase space are also extensively explored, including in the areas of spherical linear interpolation, rotational velocities, rotation composition and rotation decomposition.
