Roll-Pitch-Yaw

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The roll, pitch and yaw angles are three angles defined in regard of absolute transformation to describe the orientation of an object, generally vehicles, in three-dimensional space. In general the three angles can be described as follows:

• Yaw: Rotation around the vertical axis of the object or vehicle, respectively
• Pitch: Rotation around the lateral axis
• Roll: Rotation around the longitudinal axis (what is generally the movement axis of a vehicle)

There are different notations to define the axes of an object. Usually and in recent publications the vertical axis is the z-axis, the longitudal axis is x and then the lateral axis is the y-axis and directed to the left.

So the roll-pitch-yaw representation of the orientation is defined as follows:

$RPY(\phi,\theta,\psi)=Rot(x,\phi)Rot(y,\theta)Rot(z,\psi)$