Summary Lie algebra is useful in the SLAM problem. If the results of the map and pose are to be more accurate, an optimization problem is usually involved, and this optimization problem is often related to the solid body rotation or transformation matrix. But $SO(3)$ and $SE(3)$ do not satisfy Read more…
There are 3 categories of the most used methods to parameterize 3D solid body motion. i.e. matrix, quaternion and Lie group. Matrix Rotation $$ R=\begin{bmatrix} r_{11} &r_{12} &r_{13} \\ r_{21} &r_{22} &r_{23} \\ r_{31} &r_{32} &r_{33} \end{bmatrix}\in \mathbb{R^{3\times3}}, s.t. R~R^T=I, det(R)=1 $$ Transformation $$ T=\begin{bmatrix} R&t \\ 0^T&1 \end{bmatrix}\in \mathbb{R^{4\times4}} Read more…