论文标题
矩阵Lie Group $ SE_K（3）$的几何和运动学
The Geometry and Kinematics of the Matrix Lie Group $SE_K(3)$
论文作者
论文摘要
目前，国家估计对于机器人技术非常重要，基于不确定性表示的谎言组对于国家估计问题很自然。有必要充分利用基质谎言组的几何形状和运动学。因此，该注释首次对最近提出的矩阵lie组$ se_k（3）$提供了详细的推导，我们的结果扩展了Barfoot \ cite {Barfoot2017State}的结果。然后，我们描述了该组适合状态表示的情况。我们还基于MATLAB框架开发了代码，用于快速实施和测试。
Currently state estimation is very important for the robotics, and the uncertainty representation based Lie group is natural for the state estimation problem. It is necessary to exploit the geometry and kinematic of matrix Lie group sufficiently. Therefore, this note gives a detailed derivation of the recently proposed matrix Lie group $SE_K(3)$ for the first time, our results extend the results in Barfoot \cite{barfoot2017state}. Then we describe the situations where this group is suitable for state representation. We also have developed code based on Matlab framework for quickly implementing and testing.
