INTRODUCTION Robotics is concerned with the generation of computer-controlled motions of physical objects in a wide variety of settings. Because physical objects define spatial distributions in 3-space, geometric representations and computations play an important role in robotics. As a result the field is a significant source of practical problems for computational geometry. There are substantial differences, however, in the ways researchers in robotics and in computational geometry address related problems. Robotics researchers are mostly interested in developing methods that work well in practice and can be combined into integrated systems. Unlike researchers in computational geometry, they often pay little attention to the underlying combinatorial and complexity issues. This difference in approach will pervade this chapter. In Section 41.1 we survey basic definitions and problems in robot kinematics. Part manipulation is discussed in Section 41.2 with emphasis on part grasping, fi