3次元姿勢の微分計算入門
A Primer on the Differential Calculus of 3D Orientations
3次元姿勢の扱いを抽象化し、座標変換と指数写像に基づく表現非依存で最小な微分を導入することで、最適化問題の定式化を容易にする手法を解説した入門文書。
著者: Michael Bloesch, Hannes Sommer, Tristan Laidlow, Michael Burri, Gabriel Nuetzi, Péter Fankhauser, Dario Bellicoso, Christian Gehring, Stefan Leutenegger, Marco Hutter, Roland Siegwart
分類: cs.RO
原文アブストラクト
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal solutions. The existence of many different conventions further complicates this issue, especially when interfacing multiple differing implementations. This document discusses an alternative approach which makes use of a more abstract notion of 3D orientations. The relative orientation between two coordinate systems is primarily identified by the coordinate mapping it induces. This is combined with the standard exponential map in order to introduce representation-independent and minimal differentials, which are very convenient in optimization based methods.
