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Control of Nonprehensile Manipulation

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Control Problems in Robotics

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 4))

Abstract

Nonprehensile manipulation is the process of manipulating a part without a form- or force-closure grasp. Without such a grasp, the part is free to roll, slide, or break contact with the robot(s) manipulating it. Controlling the motion of a part using nonprehensile manipulation becomes the challenging problem of controlling a dynamic system with equations of motion incorporating the robot and part geometry, friction and restitution laws, and changing dynamics due to changing contact states. Drawing from the work of others and our own previous work, in this paper we pose several open problems in the control of nonprehensile manipulation.

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References

  1. S. Akella, W. Huang, K. M. Lynch, and M. T. Mason. Parts feeding on a conveyor with a one joint robot. Algorithmica, 26(3):313–344, March-April 2000.

    Google Scholar 

  2. J. C. Alexander and J. H. Maddocks. On the kinematics of wheeled vehicles. The International Journal of Robotics Research, 8(5):15–27, October 1989.

    Google Scholar 

  3. K. F. Böhringer and H. Choset, editors. Distributed Manipulation. Kluwer, 2000.

    Google Scholar 

  4. K. F. Böhringer, B. R. Donald, L. E. Kavraki, and F. Lamiraux. A distributed, universal device for planar parts feeding: unique part orientation in programmable force fields. In Distributed Manipulation, pages 1–28. Kluwer, 2000.

    Google Scholar 

  5. R. W. Brockett and L. Dai. Nonholonomic kinematics and the role of elliptic functions in constructive controllability. In Z. Li and J. Canny, editors, Nonholonomic Motion Planning. Kluwer Academic, 1993.

    Google Scholar 

  6. B. Brogliato and A. Zavala-Rio. On the control of complementary-slackness juggling mechanical systems. IEEE Transactions on Automatic Control, 45(2):235–246, February 2000.

    Google Scholar 

  7. M. Bühler and D. E. Koditschek. From stable to chaotic juggling: Theory, simulation, and experiments. In IEEE International Conference on Robotics and Automation, pages 1976–1981, Cincinnati, OH, 1990.

    Google Scholar 

  8. M. Bühler, D. E. Koditschek, and P. J. Kindlmann. Planning and control of a juggling robot. International Journal of Robotics Research, 13(2):101–118, 1994.

    Article  Google Scholar 

  9. F. Bullo, A. D. Lewis, and K. M. Lynch. Controllable kinematic reductions for mechanical systems: Concepts, computational tools, and examples. In 2002 International Symposium on the Mathematical Theory of Networks and Systems, August 2002.

    Google Scholar 

  10. F. Bullo and K. M. Lynch. Kinematic controllability for decoupled trajectory planning of underactuated mechanical systems. IEEE Transactions on Robotics and Automation, 17(4):402–412, August 2001.

    Google Scholar 

  11. R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Toward a dynamical pick and place. In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 2: 292–297, 1995.

    Google Scholar 

  12. P. Choudhury and K. M. Lynch. Rolling manipulation with a single control. International Journal of Robotics Research, 2002. To appear.

    Google Scholar 

  13. B. R. Donald, J. Jennings, and D. Rus. Algorithmic Foundations of Robotics (WAFR), chapter Information invariants for distributed manipulation, pages 431–459. A.K. Peters, Ltd, Wellesley, MA, 1995.

    Google Scholar 

  14. M. A. Erdmann. Understanding action and sensing by designing action-based sensors. International Journal of Robotics Research, 14(5):483–509, October 1995.

    Google Scholar 

  15. B. Goodwine and J. W. Burdick. Controllability of kinematic control systems on stratified configuration spaces. IEEE Trans. on Automatic Control, 46(3):358–368, 2000.

    Article  MathSciNet  Google Scholar 

  16. G. W. Haynes and H. Hermes. Nonlinear controllability via Lie theory. SIAM Journal on Control, 8(4):450–460, November 1970.

    Google Scholar 

  17. Y. Jia and M. Erdmann. Observing pose and motion through contact. In IEEE International Conference on Robotics and Automation, pages 723–729, 1998.

    Google Scholar 

  18. V. Jurdjevic. Geometric Control Theory. Cambridge University Press, 1997.

    Google Scholar 

  19. A. D. Lewis. When is a mechanical control system kinematic? In IEEE Conference on Decision and Control, pages 1162–1167, December 1999.

    Google Scholar 

  20. A. D. Lewis and R. M. Murray. Configuration controllability of simple mechanical control systems. SIAM Journal on Control and Optimization, 35(3):766–790, May 1997.

    Google Scholar 

  21. K. Lian, L. Wang, and L. Fu. Controllability of spacecraft systems in a central gravitational field. IEEE Transactions on Automatic Control, 39(12):2426–2440, December 1994.

    Google Scholar 

  22. J. Luntz and W. Messner. Closed-loop stability of distributed manipulation. In Proc. American Control Conference (ACC), 2000.

    Google Scholar 

  23. J. Luntz, W. Messner, and H Choset. Velocity field design for parcel manipulation on the modular distributed manipulation system. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), 1999.

    Google Scholar 

  24. J. Luntz, W. Messner, and H. Choset. Closed-loop distributed manipulation using discrete actuator arrays. In Workshop on the Algorithmic Foundations of Robotics (WAFR), 2000.

    Google Scholar 

  25. K. M. Lynch. Controllability of a planar body with unilateral thrusters. IEEE Transactions on Automatic Control, 44(6):1206–1211, June 1999.

    Google Scholar 

  26. K. M. Lynch. Locally controllable manipulation by stable pushing. IEEE Transactions on Robotics and Automation, 15(2):318–327, April 1999.

    Google Scholar 

  27. K. M. Lynch and C. K. Black. Recurrence, controllability, and stabilization of juggling. IEEE Transactions on Robotics and Automation, 17(2):113–124, April 2001.

    Google Scholar 

  28. K. M. Lynch and M. T. Mason. Stable pushing: Mechanics, controllability, and planning. International Journal of Robotics Research, 15(6):533–556, December 1996.

    Google Scholar 

  29. K. M. Lynch and M. T. Mason. Dynamic nonprehensile manipulation: Controllability, planning, and experiments. International Journal of Robotics Research, 18(1):64–92, January 1999.

    Google Scholar 

  30. K. M. Lynch, N. Shiroma, H. Arai, and K. Tanie. The roles of shape an motion in dynamic manipulation: The butterfly example. In IEEE International Conference on Robotics and Automation, pages 927–932, 1998.

    Google Scholar 

  31. A. Marigo and A. Bicchi. Rolling bodies with regular surface: Controllability theory and applications. IEEE Transactions on Automatic Control, 45(9):1586–1599, September 2000.

    Google Scholar 

  32. A. Marigo, M. Ceccarelli, S. Piccinocchi, and A. Bicchi. Planning motions of polyhedral parts by rolling. Algorithmica, 26:560–576, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  33. M. T. Mason. Mechanics of Robotic Manipulation. MIT Press, 2001.

    Google Scholar 

  34. T. D. Murphey. Control of Multiple Model Systems. PhD thesis, California Institute of Technology, May 2002.

    Google Scholar 

  35. T. D. Murphey and J. W. Burdick. Issues in controllability and motion planning for overconstrained wheeled vehicles. In Proc. Int. Conf. Math. Theory of Networks and Systems (MTNS), Perpignan, France, 2000.

    Google Scholar 

  36. T. D. Murphey and J. W. Burdick. On the stability and design of distributed systems. In Proc. IEEE Int. Conf. on Robotics and Automation, Seoul, Korea, 2001.

    Google Scholar 

  37. T. D. Murphey and J. W. Burdick. Global exponential stabilizability for distributed manipulation. In Proc. IEEE Int. Conf. on Robotics and Automation, Washington D.C., 2002.

    Google Scholar 

  38. F. Pfeiffer and C. Glocker. Multibody Dynamics with Unilateral Controls. Wiley, Chichester, 1996.

    Google Scholar 

  39. A. A. Rizzi and D. E. Koditschek. Progress in spatial robot juggling. In IEEE International Conference on Robotics and Automation, pages 775–780, Nice, France, 1992.

    Google Scholar 

  40. A. A. Rizzi and D. E. Koditschek. Further progress in robot juggling: The spatial two-juggle. In IEEE International Conference on Robotics and Automation, pages 3:919–924, Atlanta, GA, 1993.

    Google Scholar 

  41. M. W. Spong. Impact controllability of an air hockey puck. Systems and Control Letters, 42:333–345, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  42. A. Sudsang and L. Kavraki. A geometric approach to designing a programmable force field with a unique stable equilibrium for parts in the plane. In Proc. IEEE Int. Conf. Robotics and Automation, Seoul, Korea, 2001.

    Google Scholar 

  43. M. Zefran and J. W. Burdick. Stabilization of systems with changing dynamics. In Workshop on Hybrid systems: Computation and control, Berkeley, CA, 1998.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mechanical Engineering Dept., Northwestern University, Evanston, IL, 60208, USA

    Kevin M. Lynch & Todd D. Murphey

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  1. Kevin M. Lynch
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  2. Todd D. Murphey
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Editor information

Editors and Affiliations

  1. Centro Interdipartimentale di Ricerca, “Enrico Piaggio”, Università di Pisa, Via Diotisalvi, 2, 56100, Pisa, Italy

    Antonio Bicchi

  2. Dipartimento di Ingegneria dell’Informazione Facoltà di Ingegnerici, Università di Siena, Via Roma, 56, 53100, Siena, Italy

    Domenico Prattichizzo

  3. Centre for Autonomous Systems CVAP/NADA, Kungliga Tekniska Högskolan, 10044, Stockholm, Sweden

    Henrik Iskov Christensen

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© 2003 Springer-Verlag Berlin Heidelberg

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Lynch, K.M., Murphey, T.D. (2003). Control of Nonprehensile Manipulation. In: Bicchi, A., Prattichizzo, D., Christensen, H.I. (eds) Control Problems in Robotics. Springer Tracts in Advanced Robotics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36224-X_3

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  • DOI: https://doi.org/10.1007/3-540-36224-X_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00251-2

  • Online ISBN: 978-3-540-36224-1

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