4 Robot Motion Fundamentals 1: Geometry

In the previous chapter we concluded the big picture overview of robotics. In this chapter we start to zoom in on specific parts of the robot system. We stated before that robots are programmable general purpose machines that directly interact with the real world to perform tasks in it. A less complete, but still illustrative description depicts robots as general purpose motion machines. Motion is the topic of this and the next chapters. In other words, we focus our attention on the acting part.^[118] At the same time, the concepts that you will learn here, together with their concrete realizations and the mathematics behind them, are also important in other parts.

4.1 Objects in Space

4.2 Coordinate Transformations

4.3 Common Geometry Representations

4.3.1 Vectors

4.3.2 Matrices

4.3.3 Homogenous Coordinates

4.3.4 Quaternions

4.3.5 Shapes

4.4 Practical Advice

4.5 Exercises on Geometry

4.6 Summary