quat2euler

Quaternion to Euler angles transformation.

Transforms a normalised quaternion \(\chi\longrightarrow[\phi, \theta, \psi]\) to roll, pitch and yaw angles respectively.

The transformation is valid away from the singularity present at:

\[\Delta = \frac{1}{2}\]

where \(\Delta = q_0 q_2 - q_1 q_3\).

The transformation is carried out as follows:

\[\begin{split}\psi &= \arctan{\left(2\frac{q_0q_3+q_1q_2}{1-2(q_2^2+q_3^2)}\right)} \\ \theta &= \arcsin(2\Delta) \\ \phi &= \arctan\left(2\frac{q_0q_1 + q_2q_3}{1-2(q_1^2+q_2^2)}\right)\end{split}\]

param quat:

Normalised quaternion.

type quat:

np.ndarray

returns:

Array containing the Euler angles \([\phi, \theta, \psi]\) for roll, pitch and yaw, respectively.

rtype:

np.ndarray

References

Blanco, J.L. - A tutorial on SE(3) transformation parameterizations and on-manifold optimization. Technical Report 012010. ETS Ingenieria Informatica. Universidad de Malaga. 2013.