3.1 Specifying a Robot’s Configuration
A robot’s configuration must completely define the position of every point in the system. A Robot’s configuration space is the space of all possible configurations. A Robot’s workspace is the space of all possible spaces the robot’s end effector (or body for mobile robots) can occupy.
3.2 Obstacles and the Configuration Space
The relationship between the Configuration Space and the Workspace is not always obvious. This section highlights some ways to visualize workspace vs configuration space.
3.3 The Dimension of the Configuration Space
Explores the relationship between Degrees of Freedom and Constraints.
3.4 The Topology of the Configuration Space
Defines Homeomorphisms and Diffeomorphisms, defines a Manifold and Differentiable Manifold. I would describe this section as containing the meat of this chapter.
3.5 Embeddings of Manifolds in Rn
Describes the utility of Matrix representations for Configurations, Frames of Reference, and Transformations.