Kinematics is the study of the geometry of motion. Kinematic modelling therefore enjoys a particularly distinguished role as one of the most important analytical tools of mobile robotics. We use kinematics to model the gross motion of the robot body as well as the internal motions of mechanisms associated with suspension, steering, propulsion, implements, and sensors. Kinematic models are employed offline for such diverse purposes as design, analysis, and visualization. Such models are also used online on computers used to interface to robots or on the computers on the robot. Many kinematic models are based on matrices and we will need a few advanced topics on matrices for a few other purposes, so matrices are reviewed first. The tools developed in this section will be used throughout the rest of the book.

Conventions and Definitions

This chapter will present some aspects of notation that will be unfamiliar to most readers who have not studied advanced dynamics. We do not need advanced dynamics in this book but we do need precise notation. We also need notations powerful enough to handle many concepts from dynamics rather than just homogeneous coordinates applied to points and vectors in space. For these reasons, we will depart from the conventions of many other robotics books and use the notations of physics rather than those of computer graphics. The reader is advised to skim this subchapter first up to Figure 2.7 and the commentary afterward. With that context, a second reading would be more illuminating.