Lie Groups and Lie Algebras in Robotics

In this lecture the group of rigid body motions is introduced via its representation on standard three dimensional Euclidian space. The relevance for robotics is that the links of a robot are usually modelled as rigid bodies. Moreover the payload of a robot is also usually a rigid body and hence much of robotics is concerned with understanding rigid transformations and sequences of these transformations. Chasles’s theorem is presented, that is: a general rigid body motion is a screw motion, a rotation about a line in space followed by a translation along the line.