Like any field with a big body of knowledge, robotics has its own jargon that is ever evolving and takes practice to get used to. Also, some concepts are close to each other, yet different, and they tend to be more easily confused. The goal of this page is to act like a cheat sheet, stressing the differences between concepts and giving you the pointers to dig deeper.

This page is a stub! Shoot me an e-mail if you were you expecting to find something specific here and it's not.


  • Configuration: a vector \(\bfq\) of the configuration space, that is, a vector of generalized coordinates (a.k.a. joint coordinates) that characterizes the positions of all points in the multi-body model of our robot.

  • Orientation: the angular coordinates of a body in space. Not to be confused with a rotation, although there is an isomorphism between rotations and orientations (similarly to the isomorphism between positions and translations).

    • Euler angles: only three angles, but tricky to work with because of the gimbal lock and the many different conventions (intrinsic or extrinsic rotations? upward or downward z-axis?) In legged robotics, it is common to use the roll-pitch-yaw convention (intrinsic Z-Y-X, which is equivalent to extrinsic x-y-z: first roll around the fixed x-axis of the parent frame, then pitch around the fixed y-axis, then yaw around the fixed z-axis) with upward z-axis.
    • Unit quaternions: four numbers, better behaved than Euler angles with only one convention to figure out (are the coordinates ordered as \([w\ x\ y\ z]\) or \([x\ y\ z\ w]\)?).
    • Rotation matrices: nine numbers, no confusion regarding conventions, applies to position coordinates by direct matrix product.
  • Position: the linear coordinates \(\bfp \in \mathbb{R}^3\) of a body in space. Not to be confused with a translation, although there is an isomorphism between the Euclidean space \(\mathbb{R}^3\) and its translation group.

  • Rotation: a geometric transform \(\bfR \in SO(3)\) that acts on a rigid body.

  • Translation: a geometric transform in \(\mathbb{E}^3\) that acts on a rigid body.

© Stéphane Caron — Pages of this website are under the Creative Commons CC BY 4.0 license.