Two dimensional transformations and its application to vehicle motion control and analysis

The authors propose a new 2-D transformation group in order to represent positioning of rigid body vehicles working in a plane. This group is a variation of the 3-D homogeneous transformation group. The relationship between this transformation group and the group of all invertible 4×4 matrices is discussed. One of the advantages of this formulation is that the orientation of the vehicle is explicitly given, rather than by its trigonometric function values. This group theory is applied to describe the motion of vehicles and odometry error analysis for vehicles