In order to aid our discussion, we will first give a few definitions:

• Free Space & Forbidden Space – Free space is the space which is not occupied by obstacles. This corresponds to the white areas in the above diagram. Forbidden space is the space occupied by obstacles, and it corresponds to the black areas in the above diagram.

• Work Space & Configuration Space – The following figures best illustrates the differences between work space and configuration space.

Although our discussion is focused on point robots, it is useful to understand how polygonal robots spell out the difference between work space and configuration space. Suppose that we have a point robot, then this point can move freely in our free space without intersecting with our obstacles. For a polygonal robot, if its reference point trespass certain points in the space, the robot will intersect with one of the obstacles.  These points are in the shaded area in the figure above, and are relative the reference point of the robot. The configuration space is the free space without these gray areas. The work space include these gray areas, and is the space that the polygonal robot will reach by moving around. In most cases, we make the natural assumption that the point robot is the reference point of a polygonal robot.