pytransform3d.transformations.transform_from_transform_log

pytransform3d.transformations.transform_from_transform_log(transform_log)

Compute transformation from matrix logarithm of transformation.

Exponential map.

\[\exp: \left[ \mathcal{S} \right] \theta \in se(3) \rightarrow \boldsymbol{T} \in SE(3)\]

\[\begin{split}\exp([\mathcal{S}]\theta) = \exp\left(\left(\begin{array}{cc} \left[\hat{\boldsymbol{\omega}}\right] & \boldsymbol{v}\\ \boldsymbol{0} & 0 \end{array}\right)\theta\right) = \left(\begin{array}{cc} Exp(\hat{\boldsymbol{\omega}} \theta) & \boldsymbol{J}(\theta)\boldsymbol{v}\theta\\ \boldsymbol{0} & 1 \end{array}\right),\end{split}\]

where \(\boldsymbol{J}(\theta)\) is the left Jacobian of \(SO(3)\) (see left_jacobian_SO3()).

Parameters:

transform_logarray-like, shape (4, 4)

Matrix logarithm of transformation matrix: [S] * theta.

Returns:

A2Barray, shape (4, 4)

Transform from frame A to frame B