4.3 Configuration Space Obstacles

Section 4.2 defined ${\cal C}$, the manifold of robot transformations in the absence of any collision constraints. The current section removes from ${\cal C}$ 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 ${\cal C}$ 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.