Control of Nonprehensile Rolling Manipulation: Balancing a Disk on a Disk

This paper presents feedback stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We show that it is possible to stabilize the object at the upright position, while the hand or object rotates to a specific orientation or spins at a constant velocity. We use full-state feedback linearization to derive control laws. We present simulation as well as experimental results demonstrating the controllers.