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pmai merged 2 commits into from
Jul 11, 2025
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Add Tait-Bryan convention and quaternion formula to documentation #850

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d2f71df
Add Tait-Bryan conv. and quat formula
thomassedlmayer Jan 28, 2025
b993800
Fix doc formatting and reformulate
thomassedlmayer Apr 11, 2025
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Fix doc formatting and reformulate 
Signed-off-by: Thomas Sedlmayer <[email protected]>
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thomassedlmayer authored and pmai committed Jul 11, 2025
commit b993800e9d15efb3c0f53f858b80755a4a4e4dfb
4 changes: 2 additions & 2 deletions doc/usecases/transforming_coordinate_systems.adoc
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Expand Up @@ -71,7 +71,7 @@ Get Tait–Bryan angles from rotation matrix cite:[wiki_euler_angles]:
\phi = \arctan2(R_{23}/\cos(\theta),R_{33}/\cos(\theta))
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Note that OSI uses the following convention on choosing rotation axes for Tait-Bryan angles: *z-y'-x''* intrinsic rotations (equivalent to *x-y-z* extrinsic rotations); see cite:[tait_bryan_convention].
Note that OSI uses the following convention on choosing rotation axes for Tait-Bryan angles: **z-y'-x''** intrinsic rotations (equivalent to **x-y-z** extrinsic rotations); see cite:[tait_bryan_convention].

**Relative orientation**:

Expand All @@ -84,7 +84,7 @@ To transform from host vehicle coordinates into sensor coordinates and back use

**Converting orientation to quaternions**:

To transform OSI's orientation representation from Tait-Bryan angles to quaternions, the following formula can be used [cite:euler_to_quaternion]:
To convert OSI's orientation representation from Tait-Bryan angles to quaternions use the following formula cite:[euler_to_quaternion]. The resulting quaternion is equivalent to yaw (ψ), pitch (θ) and roll (ϕ) angles (**x-y-z** extrinsic rotations) or intrinsic Tait-Bryan angles following the **z-y'-x''** convention.

[latexmath]
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