Acknowledgments We Thank

based manipulation planning as a game with nature. Planning sequences of squeeze-grasps to orient and grasp polygonal objects. Grasping planar curved parts with a parallel-jaw gripper. We have considered the planar problem of determining the convex shape of a polygonal part from a sequence of measurements taken with a frictionless parallel-jaw gripper. We have derived both negative 25] and positive results. The negative results are related to the study of curves of constant width (Gleichdicke) in classical geometry, establishing a new link between computational geometry and robotics. The positive results are examples of sensor-based manipulation planning, but diier from previous work in that we use a frictionless gripper and give a computational analysis of the planning problem. The required hardware is inexpensive and well-known. This is consistent with our aim to develop new software for \old" hardware. Yap for rewarding discussions on this subject. We also thank the anonymous referees for their constructive criticism and useful suggestions. Application of random sampling to on-line algorithms in computational geometry. 21 q q q q q q q u u q q q q