pytransform3d.transformations.left_jacobian_SE3

pytransform3d.transformations.left_jacobian_SE3(Stheta)

Left Jacobian of SE(3).

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

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:

Jarray, shape (6, 6)

Jacobian of SE(3).

See also

left_jacobian_SE3_series

Left Jacobian of SE(3) at theta from Taylor series.

left_jacobian_SE3_inv

Left inverse Jacobian of SE(3).

References

[1]

Barfoot, T. D., Furgale, P. T. (2014). Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems. IEEE Transactions on Robotics, 30(3), pp. 679-693, doi: 10.1109/TRO.2014.2298059.