Section 4.2 defined , the manifold of robot transformations in the absence of any collision constraints. The current section removes from the configurations that either cause the robot to collide with obstacles or cause some specified links of the robot to collide with each other. The removed part of is referred to as the obstacle region. The leftover space is precisely what a solution path must traverse. A motion planning algorithm must find a path in the leftover space from an initial configuration to a goal configuration. Finally, after the models of Chapter 3 and the previous sections of this chapter, the motion planning problem can be precisely described.