Difference between revisions of "Roll-Pitch-Yaw"
From Robotics
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[[File:rpy-car.png|right|350px]] | [[File:rpy-car.png|right|350px]] | ||
| − | The roll, pitch and yaw angles are three angles defined in regard of [[Three-Angle Representations|absolute transformation]] to describe the orientation of an object, generally vehicles, in three-dimensional space. In the following the common convention will be used, so the three angles can be described as follows: | + | The roll, pitch and yaw angles are three angles defined in regard of [[Three-Angle Representations|absolute transformation]] to describe the orientation of an object, generally vehicles, in three-dimensional space. In the following the common convention will be used, so the three angles can be described as follows (in the order they are applied): |
* '''Yaw''': Rotation around the vertical axis of the object or vehicle, respectively | * '''Yaw''': Rotation around the vertical axis of the object or vehicle, respectively | ||
* '''Pitch''': Rotation around the lateral axis | * '''Pitch''': Rotation around the lateral axis | ||
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So the roll-pitch-yaw representation of the orientation is defined as follows: | So the roll-pitch-yaw representation of the orientation is defined as follows: | ||
:<math> | :<math> | ||
| − | RPY(\phi,\theta,\psi)=Rot(x,\phi)Rot(y,\theta)Rot(z,\psi) | + | \begin{align} |
| + | RPY(\phi,\theta,\psi)&=Rot(x,\phi)Rot(y,\theta)Rot(z,\psi) \\ | ||
| + | &= | ||
| + | \left[\begin{array}{cccc} | ||
| + | \cos{\psi}\cos{\theta} & -\cos{\theta}\sin{\phi} & \sin{\theta} & 0\\ | ||
| + | \cos{\psi}\sin{\phi}+\cos{\phi}\sin{\psi}\sin{\theta} & \cos{\phi}\cos{\psi}-\sin{\phi}\sin{\psi}\sin{\theta} & -\cos{\theta}sin{\psi} & 0\\ | ||
| + | \sin{\phi}\sin{\psi}-\cos{\phi}\cos{\psi}\sin{\theta} & \cos{\psi}\sin{\phi}\sin{\theta} & \cos{\psi}\cos{\theta} & 0\\ | ||
| + | 0 & 0 & 0 & 1 | ||
| + | \end{array}\right] | ||
| + | \end{align} | ||
</math> | </math> | ||
Revision as of 13:27, 7 May 2015
| ← Back: Three-Angle Representations | Overview: Three-Angle Representations | Next: Euler angles → |
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 the following the common convention will be used, so the three angles can be described as follows (in the order they are applied):
- 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:
![\begin{align}
RPY(\phi,\theta,\psi)&=Rot(x,\phi)Rot(y,\theta)Rot(z,\psi) \\
&=
\left[\begin{array}{cccc}
\cos{\psi}\cos{\theta} & -\cos{\theta}\sin{\phi} & \sin{\theta} & 0\\
\cos{\psi}\sin{\phi}+\cos{\phi}\sin{\psi}\sin{\theta} & \cos{\phi}\cos{\psi}-\sin{\phi}\sin{\psi}\sin{\theta} & -\cos{\theta}sin{\psi} & 0\\
\sin{\phi}\sin{\psi}-\cos{\phi}\cos{\psi}\sin{\theta} & \cos{\psi}\sin{\phi}\sin{\theta} & \cos{\psi}\cos{\theta} & 0\\
0 & 0 & 0 & 1
\end{array}\right]
\end{align}](/wiki/robotics/images/math/b/3/0/b30b4dbf95117448f1f3db0f1ed58380.png)
