2. Defining the Problem

For simplicity reasons I will from now on use the term 'robot' for the object whose motion is to be planned rather than speaking about abstract entities, but depending on the application you have in mind you may freely substitute 'sprite', 'spaceship', 'car' and many more. They all fit in the same framework:

The last point already describes the problem discussed in this article:

Given a certain set C (derived from a robot's dof), a subset Cfree of C, a start configuration qstart and a goal configuration qgoal (both elements of Cfree), compute a path within Cfree that connects qstart with qgoal.