Closed-loop Control of a Nonprehensile Manipulation System Inspired by the Pizza-Peel Mechanism

A nonprehensile manipulation system consisting of a dexterous plate (e.g., a peel) which is intended to induce a rotating movement on a disk (e.g., a pizza) is studied. A dynamic model based on the Euler-Lagrange equations is first derived. Then, a controllability analysis of this model is carried out, which shows some intrinsic limitations of the proposed system. Later, a closed-loop control strategy is proposed to induce the desired rotating speed in the disk, while maintaining the position of both the disk and the plate as close to zero as possible. A stability analysis is performed to show the boundedness of all the states, the oscillatory response of all of them, and the maximum amplitude of these oscillations. A numerical simulation is employed to verify the proposed controller and the predicted behavior found in the stability analysis.