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# IMU: What is the "w" in the IMU data

Hello there, i use the Gazebo IMU-Plugin to generate sensor data of an IMU for my robot. An IMU message looks like the following:

orientation:
x: -9.881865455454e-324
y: -9.881865455454e-324
z: 8.8755655245457e-17
w: 1.0
orientation_covariance ...

I understand the x,y,z koordinates, but what does that "w" mean?

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It's the fourth component of a quaternion. (You don't have to fully understand the math behind it, it's roughly a rotation axis and a corresponding rotation angle around this axis). See also: tf2/quaternions

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Just as a clarification: @vonunwerth: the entire orientation field is a Quaternion.

( 2018-09-04 02:06:33 -0600 )edit

Quaternion is a type of mathematical notation. It is not the same thing as a vector, but similar concepts can be expressed with it. You can imagine it like a Struct or a data type that has 4 variables, one of them has the name "w".

this YouTube video explains the concept of a quaternion in a visual way.

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Answers above may have explained it well. But as an addition: x, y, z over there are not coordinates of some point, they are stating the axis of rotation. A quaternion := (x, y, z, w), in which (x, y, z) is scaled with sin(theta/2), and w := cos(theta/2), in which theta is the angle of rotation.

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Last updated: Feb 18 '20