1/theta missing when computing G-1 ? (python & matlab)

[louisdehaybe]

Hello,

In the book, page 106, they provide the analytical expression for G^-1, that is being use to calculate the log_SE3 . In particular, the experssion begins by 1/theta * Identity + ....

However, in both matlab and python versions of the code, the function MatrixLog6 begins by eye(3) + ... , so there is not the 1/theta in the code.

Is there an error, or do I miss something ?

Thanks !

[HuanWeng]

Thank you and good catch! However the function outputs correctly. No error there.

The discrepancy between the algorithm in the book and code is due to a small trick used in the code. MatrixLog6() outputs $[{\cal S}]\theta$, the top right $3\times3$ submatrix of which is $v\theta = \theta G^{-1}(\theta)p = (\theta G^{-1}(\theta))p$. Multiplying $\theta$ and $G^{-1}$ together at first reduces some unnecessary computation.