Contact Juggling of a Disk With a Disk-Shaped Manipulator

In this paper, we present a feedback controller that enables contact juggling manipulation of a disk with a disk-shaped manipulator, called the mobile 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 hand moves with a full three degrees of freedom in a vertical plane. The proposed controller drives the object to follow a desired trajectory through rolling interaction with the hand. Based on the mathematical model of the system, dynamic feedback linearization is used in the design of the controller. The performance of the controller is demonstrated through simulations considering disturbances and uncertainties.

[1]  Timothy Bretl,et al.  Approximate steering of a plate-ball system under bounded model perturbation using ensemble control , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[2]  Naoji Shiroma,et al.  The roles of shape and motion in dynamic manipulation: the butterfly example , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[3]  Kevin C. Craig,et al.  Mechatronic design of a ball-on-plate balancing system , 2002 .

[4]  Yusie Rizal,et al.  Visual Servoing Tracking Control of a Ball and Plate System: Design, Implementation and Experimental Validation , 2013 .

[5]  Aaron M. Dollar,et al.  On dexterity and dexterous manipulation , 2011, 2011 15th International Conference on Advanced Robotics (ICAR).

[6]  Naif B. Almutairi,et al.  On the sliding mode control of a Ball on a Beam system , 2009 .

[7]  R. Mukherjee,et al.  Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem , 2002 .

[8]  Andrew R. Teel,et al.  Semi-global stabilization of the `ball and beam' using `output' feedback , 1993, 1993 American Control Conference.

[9]  Kevin M. Lynch,et al.  Rolling manipulation control of the disk-on-disk on a two-link arm , 2016, 2016 IEEE International Conference on Mechatronics and Automation.

[10]  Kevin M. Lynch,et al.  Control of Nonprehensile Manipulation , 2003, Control Problems in Robotics.

[11]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[12]  Ranjan Mukherjee,et al.  Exponential stabilization of the rolling sphere , 2004, Autom..

[13]  Kevin M. Lynch,et al.  Control of Nonprehensile Rolling Manipulation: Balancing a Disk on a Disk , 2013, IEEE Trans. Robotics.

[14]  P. Kokotovic,et al.  Nonlinear control via approximate input-output linearization: the ball and beam example , 1992 .

[15]  Zexiang Li,et al.  Motion of two rigid bodies with rolling constraint , 1990, IEEE Trans. Robotics Autom..

[16]  Leonid B. Freidovich,et al.  Case study in non-prehensile manipulation: planning and orbital stabilization of one-directional rollings for the “Butterfly” robot , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[17]  Marilena Vendittelli,et al.  A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism , 2005, IEEE Transactions on Robotics.

[18]  P. Kokotovic,et al.  Global asymptotic stabilization of the ball-and-beam system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[19]  Hiroyuki Ichihara,et al.  I-PD controller design based on generalized KYP lemma for ball and plate system , 2013, 2013 European Control Conference (ECC).

[20]  Vincenzo Lippiello,et al.  Passivity-Based Control for a Rolling-Balancing System: The Nonprehensile Disk-on-Disk , 2017, IEEE Transactions on Control Systems Technology.

[21]  Suguru Arimoto,et al.  Dynamic object manipulation using a virtual frame by a triple soft-fingered robotic hand , 2010, 2010 IEEE International Conference on Robotics and Automation.

[22]  Kevin M. Lynch,et al.  Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments , 1999, Int. J. Robotics Res..

[23]  Vincenzo Lippiello,et al.  The Effect of Shapes in Input-State Linearization for Stabilization of Nonprehensile Planar Rolling Dynamic Manipulation , 2016, IEEE Robotics and Automation Letters.

[24]  Alberto Rodriguez,et al.  Optimal shape and motion planning for dynamic planar manipulation , 2018, Auton. Robots.

[25]  Giuseppe Oriolo,et al.  ENERGY-BASED CONTROL OF THE BUTTERFLY ROBOT , 2006 .

[26]  Thomas Parisini,et al.  Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System , 2009, IEEE Transactions on Automatic Control.

[27]  Shigeyuki Hosoe,et al.  Motion Planning Algorithms for a Rolling Sphere With Limited Contact Area , 2008, IEEE Transactions on Robotics.