Authors

Diana Serra, Joel Ferguson, Fabio Ruggiero, Andrea Siniscalco, Antoine Petit, Vincenzo Lippiello, Bruno Siciliano

Abstract

A method to reconfigure in a nonprehensile way the pose (position and orientation) of a sphere rolling on a plate is proposed in this letter. The nonholonomic nature of the task is first solved at a planning level, where a geometric technique is employed to derive a Cartesian path to steer the sphere towards the arbitrarily desired pose. Then, an integral passivity-based control is designed to track the planned trajectory. The port-Hamiltonian formalism is employed to model the whole dynamics. Two approaches to move the plate are addressed in this paper, showing that only one of them allows the full controllability of the system. A humanoid-like robot is employed to bolster the proposed method experimentally.

Citation

  • Journal: 2018 26th Mediterranean Conference on Control and Automation (MED)
  • Year: 2018
  • Volume:
  • Issue:
  • Pages: 13–20
  • Publisher: IEEE
  • DOI: 10.1109/med.2018.8442769

BibTeX

@inproceedings{Serra_2018,
  title={{On the Experiments About the Nonprehensile Reconfiguration of a Rolling Sphere on a Plate}},
  DOI={10.1109/med.2018.8442769},
  booktitle={{2018 26th Mediterranean Conference on Control and Automation (MED)}},
  publisher={IEEE},
  author={Serra, Diana and Ferguson, Joel and Ruggiero, Fabio and Siniscalco, Andrea and Petit, Antoine and Lippiello, Vincenzo and Siciliano, Bruno},
  year={2018},
  pages={13--20}
}

Download the bib file

References

  • Brockett, R. W. & Dai, L. Non-holonomic Kinematics and the Role of Elliptic Functions in Constructive Controllability. Nonholonomic Motion Planning 1–21 (1993) doi:10.1007/978-1-4615-3176-0_1 – 10.1007/978-1-4615-3176-0_1
  • Huynh, D. Q. Metrics for 3D Rotations: Comparison and Analysis. J Math Imaging Vis 35, 155–164 (2009) – 10.1007/s10851-009-0161-2
  • Marchand, E., Spindler, F. & Chaumette, F. ViSP for visual servoing: a generic software platform with a wide class of robot control skills. IEEE Robot. Automat. Mag. 12, 40–52 (2005) – 10.1109/mra.2005.1577023
  • Bouthemy, P. A maximum likelihood framework for determining moving edges. IEEE Trans. Pattern Anal. Machine Intell. 11, 499–511 (1989) – 10.1109/34.24782
  • Bullo, F. & Lewis, A. D. Kinematic controllability and motion planning for the snakeboard. IEEE Trans. Robot. Automat. 19, 494–498 (2003) – 10.1109/tra.2003.810236
  • Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10, 432–450 (2004) – 10.3166/ejc.10.432-450
  • Bloch, A. M., Reyhanoglu, M. & McClamroch, N. H. Control and stabilization of nonholonomic dynamic systems. IEEE Trans. Automat. Contr. 37, 1746–1757 (1992) – 10.1109/9.173144
  • Ferguson, J., Donaire, A. & Middleton, R. H. Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Trans. Automat. Contr. 62, 5947–5953 (2017) – 10.1109/tac.2017.2700995
  • Montana, D. J. The Kinematics of Contact and Grasp. The International Journal of Robotics Research 7, 17–32 (1988) – 10.1177/027836498800700302
  • murray, A Mathematical Introduction to Robotic Manipulation (1994)
  • Jurdjevic, V. The geometry of the plate-ball problem. Arch. Rational Mech. Anal. 124, 305–328 (1993) – 10.1007/bf00375605
  • Becker, A. & Bretl, T. Approximate steering of a plate-ball system under bounded model perturbation using ensemble control. 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems 5353–5359 (2012) doi:10.1109/iros.2012.6385722 – 10.1109/iros.2012.6385722
  • Bicchi, A. & Sorrentino, R. Dexterous manipulation through rolling. Proceedings of 1995 IEEE International Conference on Robotics and Automation vol. 1 452–457 – 10.1109/robot.1995.525325
  • Bicchi, A., Marigo, A. & Prattichizzo, D. Dexterity through rolling: manipulation of unknown objects. Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C) vol. 2 1583–1588 – 10.1109/robot.1999.772585
  • Marigo, A. & Bicchi, A. Rolling bodies with regular surface: controllability theory and applications. IEEE Trans. Automat. Contr. 45, 1586–1599 (2000) – 10.1109/9.880610
  • lee, Basketball robot: Ball on plate with pure haptic information. IEEE International Conference on Robotics and Automation (2008)
  • Choudhury, P. & Lynch, K. M. Rolling Manipulation with a Single Control. The International Journal of Robotics Research 21, 475–487 (2002) – 10.1177/027836402761393342
  • Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
  • Lynch, K. M., Shiroma, N., Arai, H. & Tanie, K. The roles of shape and motion in dynamic manipulation: the butterfly example. Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146) vol. 3 1958–1963 – 10.1109/robot.1998.680600
  • siciliano, Robotics Modelling Planning and Control (2009)
  • serra, Time-optimal paths for a robotic batting task. Springer Lecture Notes in Electrical Engineering (2017)
  • Serra, D., Satici, A. C., Ruggiero, F., Lippiello, V. & Siciliano, B. An Optimal Trajectory Planner for a Robotic Batting Task: The Table Tennis Example. Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics 90–101 (2016) doi:10.5220/0005982000900101 – 10.5220/0005982000900101
  • Ruggiero, F. et al. Nonprehensile Manipulation of Deformable Objects: Achievements and Perspectives from the Robotic Dynamic Manipulation Project. IEEE Robot. Automat. Mag. 25, 83–92 (2018) – 10.1109/mra.2017.2781306
  • serra, Robot control for nonprehensile dynamic manipulation tasks. International Conference on Informatics in Control Automation and Robotics Doctoral Consortium (2016)
  • serra, A nonlinear least squares approach for nonprehensile dual-hand robotic ball juggling. World Congress Int Federation Automat Contr (2017)
  • Ruggiero, F., Lippiello, V. & Siciliano, B. Nonprehensile Dynamic Manipulation: A Survey. IEEE Robot. Autom. Lett. 3, 1711–1718 (2018) – 10.1109/lra.2018.2801939
  • Mason, M. T. & Lynch, K. M. Dynamic manipulation. Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS ’93) vol. 1 152–159 – 10.1109/iros.1993.583093
  • Lynch, K. M. & Mason, M. T. Dynamic Nonprehensile Manipulation: Controllability, Planning, and Experiments. int j robot res 18, 64–92 (1999) – 10.1177/02783649922066079
  • Harada, K. & Kaneko, M. Rolling based manipulation under neighborhood equilibrium. Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164) vol. 3 2492–2498 – 10.1109/robot.2001.932997
  • cui, A coordinate-free approach to instantaneous kinematics of two rigid objects with rolling contact and its implications for trajectory planning. IEEE International Conference on Robotics and Automation (2009)
  • Harada, K. & Kaneko, M. Neighborhood equilibrium grasp for multiple objects. Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065) vol. 3 2159–2164 – 10.1109/robot.2000.846348
  • Oriolo, G. & Vendittelli, M. A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism. IEEE Trans. Robot. 21, 162–175 (2005) – 10.1109/tro.2004.839231
  • Date, H., Sampei, M., Ishikawa, M. & Koga, M. Simultaneous Control of Position and Orientation for Ball-Plate Manipulation Problem Based on Time-State Control Form. IEEE Trans. Robot. Automat. 20, 465–479 (2004) – 10.1109/tra.2004.825267
  • Casagrande, D., Astolfi, A. & Parisini, T. Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System. IEEE Trans. Automat. Contr. 54, 1881–1886 (2009) – 10.1109/tac.2009.2020670
  • Das, T. & Mukherjee, R. Exponential stabilization of the rolling sphere. Automatica 40, 1877–1889 (2004) – 10.1016/j.automatica.2004.06.003