We are interested in using low degree-of-freedom robots to perform complex tasks by not grasping (nonprehensile manipulation). By not grasping, the robot can use gravitational, centrifugal, and Coriolis forces as virtual motors to control more degrees-of-freedom of the part. The extra motion freedoms of the part are exhibited as rolling, slipping, and free flight. This paper describes controllability, planning, and implementation of planar dynamic nonprehensile manipulation. We show that almost any planar object is controllable by point contact, and the controlling robot requires only two degrees-of-freedom (a point translating in the plane). We then focus on a one joint manipulator (with a two-dimensional state space) and show that even this simplest of robots, by using slipping and rolling, can control a planar object to a fulldimensional subset of its six-dimensional state space. We have developed a one joint robot to perform a variety of dynamic tasks, including snatching an object from a table, rolling an object on the surface of the arm, and throwing and catching. Nonlinear optimization is used to plan robot trajectories that achieve the desired object motion via coupling forces through the nonprehensile contact. 1
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