Orientation parametrisations
Parents:
rotations-so3-group-index
,
quaternion index
,
probabilistic models-for-imu
See also:
Rotation error representation
Source: MKok 2017 , markley-2014
Orientation parametrisations
- Note: CCW rotation of a vector $x_v$ to $x_u$ corresponds to a CW rotation of the CS $v$ to CS $u$ (see also active/passive transformations ).
- Rotations are a member of SO(3)
| rotation matrix | unique description of orientation |
|---|---|
| Euler axis/angle Rotation vector | not unique, due to wrapping |
| Euler angles | not unique, due to wrapping and gimbal lock |
| Unit quaternions | not unique, -q and q depict the same orientationProof: http://math.stackexchange.com/questions/2016282/negative-quaternion |
| Gibbs / Rodrigues parameter | infinite for 180 degree rotations, but 1:1 mapping between itself and unit quaternions |