This section presents an overview of manipulation planning; the concepts explained here are mainly due to [16,17]. Returning to Example 7.2, imagine that the robot must carry a key that is so large that it changes the connectivity of . For the manipulation planning problem, the robot is called a manipulator, which interacts with a part. In some configurations it is able to grasp the part and move it to other locations in the environment. The manipulation task usually requires moving the part to a specified location in , without particular regard as to how the manipulator can accomplish the task. The model considered here greatly simplifies the problems of grasping, stability, friction, mechanics, and uncertainties and instead focuses on the geometric aspects (some of these issues will be addressed in Section 12.5). For a thorough introduction to these other important aspects of manipulation planning, see ; see also Sections 13.1.3 and 12.5.