4.1.2 Manifolds

In motion planning, efforts are made to ensure that the resulting configuration space has nice properties that reflect the true structure of the space of transformations. One important kind of topological space, which is general enough to include most of the configuration spaces considered in Part II, is called a manifold. Intuitively, a manifold can be considered as a ``nice'' topological space that behaves at every point like our intuitive notion of a surface.