`pytransform3d.transformations`.left_jacobian_SE3¶

pytransform3d.transformations.left_jacobian_SE3(Stheta)[source]¶

Left Jacobian of SE(3).

$\boldsymbol{\mathcal{J}} = \left( \begin{array}{cc} \boldsymbol{J} & \boldsymbol{0}\\ \boldsymbol{Q} & \boldsymbol{J} \end{array} \right),$

where $\boldsymbol{J}$ is the left Jacobian of SO(3) and $\boldsymbol{Q}$ is given by Barfoot and Furgale (see reference below).

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.

Returns:

pytransform3d.transformations.left_jacobian_SE3¶