pytransform3d.transformations.transform_from_exponential_coordinates#
- pytransform3d.transformations.transform_from_exponential_coordinates(Stheta, check=True)[source]#
Compute transformation matrix from exponential coordinates.
Exponential map.
\[Exp: \mathcal{S} \theta \in \mathbb{R}^6 \rightarrow \boldsymbol{T} \in SE(3)\]\[\begin{split}Exp(\mathcal{S}\theta) = Exp\left(\left(\begin{array}{c} \hat{\boldsymbol{\omega}}\\ \boldsymbol{v} \end{array}\right)\theta\right) = \exp(\left[\mathcal{S}\right] \theta) = \left(\begin{array}{cc} Exp(\hat{\boldsymbol{\omega}} \theta) & \boldsymbol{J}(\theta)\boldsymbol{v}\theta\\ \boldsymbol{0} & 1 \end{array}\right),\end{split}\]where \(\boldsymbol{J}(\theta)\) is the left Jacobian of \(SO(3)\) (see
left_jacobian_SO3()).- Parameters:
- Sthetaarray-like, shape (6,)
Exponential coordinates of transformation: S * theta = (omega_1, omega_2, omega_3, v_1, v_2, v_3) * theta, where S is the screw axis, the first 3 components are related to rotation and the last 3 components are related to translation. Theta is the rotation angle and h * theta the translation.
- checkbool, optional (default: True)
Check if exponential coordinates are valid
- Returns:
- A2Barray, shape (4, 4)
Transformation matrix from frame A to frame B
