3D Rigid Body Motion

In the last lecture, we explained the framework and content of visual SLAM. This lecture will introduce one of the fundamental problems of visual SLAM: How to describe a rigid body’s motion in three-dimensional space? Intuitively, we certainly know that this consists of one rotation plus one translation. The translation part does not really have any problems, but the rotation part is questionable. We will introduce the meaning of rotation matrices, quaternions, Euler angles and how they are computed and transformed. In the practice section, we will introduce one of the widely used linear algebra libraries: Eigen. It provides a C++ matrix calculation, and its geometry module also provides the necessary data structures and operations, like quaternions. Eigen is heavily optimized, but there are still some special issues to be discussed about its usage. We will leave it to the practice part.