The set of all transformations in \(n\) dimensional Euclidean space which preserve the Euclidean distance between all points once applied.

The case \(n=3\) is used to represent rigid body transformations. Namely, let \(T = \begin{bmatrix} R & p\\ \textbf{0} & 1 \end{bmatrix}\) where \(R\) is from SO(n) with \(n=3\), \(p \in \mathbb{R}^3\), \(\textbf{0}\) is a row vector of zeros and 1 is simply the scalar. All possible matrices \(T\) define \(SE(3)\), and is closed under matrix multiplication. In the context of robotics they are called homogeneous transforms, and are often used to:




Lynch, Kevin M., and Frank C. Park. 2017. Modern Robotics: Mechanics, Planning, and Control. 1st ed. USA: Cambridge University Press.

Author: Nazaal

Created: 2022-03-13 Sun 21:44