### This chapter covers

- Kinematics: Trajectories and the conversion between joint and task space

- Analytical and numerical approaches to kinematics

- Differentiation and integration as essential mathematical tools

While the previous chapter on geometry laid the foundation for robot motion, nothing actually moved yet. In this chapter, we will set things into motion. Motion at its core is the change of geometry, especially poses, over time. We need a formalism that allows us to concisely describe change (over time). Calculus provides us with the required mathematical tools to model change in our robot software. Thus, you will become familiar with concepts from calculus, *derivatives* and *integrals*, throughout the chapter.

The goal of this chapter is to give you a solid basic understanding of the topics mentioned. When finishing the chapter you will have gained the *general* knowledge and skills in calculus and kinematics. This enables you to work with and learn more about the kinematics of *specific* robots in later chapters. The following two chapters on dynamics and control take a similar approach: Solid overview up front, details and refinements later on, e.g. when discussing specific robot applications.

The previous chapter was all about working with objects in space. This chapter is all about the motion of these objects.