I've come across the abbreviation SE several times recently. I know it has to do with the pose of the robot, and the degrees of freedom. Most recently I found it on page 8 of this paper:

D. Kragic and H. I. Christensen, “Survey on visual servoing for manipulation,” Royal Institute of Technology (KTH), Stockholm, Sweden, Tech. Rep. ISRN KTH/NA/P-02/01-SE, CVAP259, 2002.


In that context, SE means "Special Euclidean" group, e.g. SE(3)* which is shorthand for "the special Euclidean group of rigid body displacements in three-dimensions".

*Planning Algorithms, Steven M LaValle 2012-04-20

  • $\begingroup$ Unfortunately, the links are not valid anymore, next time you can cite the paper by title, author, and maybe publisher/year. $\endgroup$
    – Elod
    Apr 13 '21 at 10:07

It is a mathematical concept call the "Special Euclidean" group. Roughly, it is a combination of a rotation and translation. You'll also frequently see SO3, which is the special orthogonal group which means rotations.


$SE(3)$ is the representation for both translation and rotation in 3D space, whereas $SO(3)$ is only the representation for rotations. $\mathbb{R}^3$ is for translations in 3D space.

If you only consider 2-dimentional space, then you can simply change 3 to 2, i.e., $SE(2)$, $SO(2)$, $\mathbb{R}^2$.

I wouldn't worry too much about it. You can just consider these as mathematical notations.


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