A micro Lie theory for state estimation in robotics001

[A micro Lie theory for state estimation in robotics] (https://arxiv.org/pdf/1812.01537.pdf)​

视觉SLAM论文list添加链接描述

Abstract 摘要

A Lie group is an old mathematical abstract objectdating back to the XIX century,
李群是一个古老的数学抽象，可以追溯到十九世纪，

when mathematician Sophus Lie laid the foundations of the theory of continuous transformation groups.
当时数学家 Sophus Lie 奠定了连续变换群理论的基础。

Its influence has spread over diverse areas of science and technology many years later.
许多年后，它的影响力已经蔓延到科学和技术的各个领域。

In robotics, we are recently experiencing an important trend in its usage, at least in the fields of
estimation, and particularly in motion estimation for navigation.

在机器人技术中，我们最近正在经历一个重要的使用趋势，至少在以下领域
估计，特别是在导航的运动估计中。

Yet for a vast majority of roboticians, Lie groups are highly
abstract constructions and therefore difficult to understand and
to use.
然而对于绝大多数机器人专家来说，李群是高度抽象的结构，因此难以理解和使用。

In estimation for robotics it is often not necessary to exploit
the full capacity of the theory, and therefore an effort of selection
of materials is required.
在机器人技术使用估计时，通常不需要利用全部理论的能力，因此需要选择材料的能力。

In this paper, we will walk through the
most basic principles of the Lie theory, with the aim of conveying
clear and useful ideas, and leave a significant corpus of the Lie
theory behind.
在本文中，我们将介绍Lie 理论的最基本原理，旨在传达清晰而有用的想法，
并留下一个重要的Lie语料库(corpus)背后的理论。

Even with this mutilation, the material included
here has proven to be extremely useful in modern estimation
algorithms for robotics, especially in the fields of SLAM, visual
odometry, and the like.
即使有这种残缺，包括材料里的(算法)被证明是非常有用的现代机器人学的算法，特别是在SLAM、视觉里程计之类的。

Alongside this micro Lie theory, we provide a chapter with a few application examples, and a vast reference of formulas for the major Lie groups used in robotics, including most
Jacobian matrices and the way to easily manipulate them. We
also present a new C++ template-only library implementing all
the functionality described here.
除了这个micro Lie 理论，我们还提供了一章一些应用实例和大量公式参考用于机器人的主要Lie群，
包括雅可比矩阵及其易于操作的方法。
我们还提供了一个新的C++模板库，实现了所有的这里描述的功能。