Difference between revisions of "Roll-Pitch-Yaw"
From Robotics
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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. | 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 | + | So the roll-pitch-yaw transformation matrix of the orientation is defined as follows: |
:<math> | :<math> | ||
\begin{align} | \begin{align} | ||
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\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\\ | \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\\ | \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> | ||
+ | |||
+ | <br/> | ||
+ | |||
+ | {{Example | ||
+ | |Title=Orientation of a car | ||
+ | |Contents=<br/> | ||
+ | Let the roll, pitch and yaw angles for a car be defined as follows: | ||
+ | :<math> | ||
+ | \begin{align} | ||
+ | &yaw: &\psi&=-&30^\circ \\ | ||
+ | &pitch: &\theta&=&20^\circ \\ | ||
+ | &roll: &\phi&=&35^\circ | ||
+ | \end{align} | ||
+ | </math> | ||
+ | Then the rotation matrix results as: | ||
+ | :<math> | ||
+ | \begin{align} | ||
+ | RPY(35^\circ,20^\circ,-30^\circ)&=Rot(x,35^\circ)Rot(y,20^\circ)Rot(z,-30^\circ) \\ | ||
+ | &= | ||
+ | \left[\begin{array}{cccc} | ||
+ | 0.7698 & -0.5390 & 0.3420 & 0\\ | ||
+ | 0.3566 & 0.8075 & 0.4698 & 0\\ | ||
+ | -0.5294 & -0.2397 & 0.8138 & 0\\ | ||
0 & 0 & 0 & 1 | 0 & 0 & 0 & 1 | ||
\end{array}\right] | \end{array}\right] | ||
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[[File:rpy-car-example.png|900px]] | [[File:rpy-car-example.png|900px]] | ||
+ | |||
+ | }} |
Revision as of 14:29, 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 transformation matrix of the orientation is defined as follows:
Example: Orientation of a car
Then the rotation matrix results as: |