brentyi
commented
4 months ago Actually, for SE(2) and SE(3), are you able to reuse/refactor the code for the "V" and "V_inv" matrices? https://github.com/brentyi/jaxlie/blob/84babf5c04ba6287cdec250ab1eed2f6d0a53988/jaxlie/_se2.py#L164-L175 https://github.com/brentyi/jaxlie/blob/84babf5c04ba6287cdec250ab1eed2f6d0a53988/jaxlie/_se3.py#L142-L159 https://github.com/brentyi/jaxlie/blob/84babf5c04ba6287cdec250ab1eed2f6d0a53988/jaxlie/_se2.py#L208-L221 https://github.com/brentyi/jaxlie/blob/84babf5c04ba6287cdec250ab1eed2f6d0a53988/jaxlie/_se3.py#L183-L205
These already seem to describe the parts of the left/right Jacobians that are the trickiest to compute.
simeon-ned
Reduce the size of following text, specifically do not use separate bullet for groups, just make list of them:"Thank you for providing that information. Based on the content you shared, I can summarize the key points:
This pull request adds analytical Jacobians for the logarithm (log) operation for all groups presented in
jaxlie. These Jacobians are also known as right inverse Jacobians. They represent the partial derivative of the log operation with respect to the group element:$$\text{Jlog}(T) = \frac{\partial \log_3(T)}{\partial T}$$
The implementation are based on derivations presented in the "micro Lie theory" paper, specifically equations 41c, 79, 126, 144, 163, and 179. Similar functionality is also implemented in established robotics libraries like Pinocchio, indicating the practical importance of these Jacobians in robotics applications.