Control of Underactuated Manipulation by Real-Time Nonlinear Optimization

  • Kevin M. Lynch
  • Craig K. Black

Abstract

Underactuated manipulation is the process of controlling a large number of object degrees-of-freedom with fewer robot degrees-of-freedom. The challenge is to derive motion planners and feedback controllers to control underactuated manipulation. In this paper we study the use of real-time nonlinear optimization for motion planning and feedback control of planar batting manipulation with a one joint robot. We study two tasks: cyclic juggling of a disk, and control of a disk from one six-dimensional state to another by a sequence of three bats. We show analytically and experimentally that the juggling controller yields a stable limit cycle with a large basin of attraction. The experimental results for state-to-state control are less successful and indicate that more accurate modeling of the impact and flight dynamics are required.

Keywords

Manifold Rubber Assure Lution Verse 

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References

  1. [1]
    D. E. Koditschek. Robot assembly: Another source of nonholonomic control problems. In American Control Conference, pages 1627–1632, 1991.Google Scholar
  2. [2]
    P. Ferbach and J.-F. Rit. Planning nonholonomic motions for manipulated objects. In IEEE International Conference on Robotics and Automation, pages 2935–2942, 1996.CrossRefGoogle Scholar
  3. [3]
    A. Bicchi and K. Y. Goldberg. Minimalism in robot manipulation. In Lecture Notes, Workshop in 1996 IEEE International Conference on Robotics and Automation, 1996.Google Scholar
  4. [4]
    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.CrossRefGoogle Scholar
  5. [5]
    K. M. Lynch and M. T. Mason. Dynamic nonprehensile manipulation: Controllability, planning, and experiments. International Journal of Robotics Research, 18 (1): 64–92, Jan. 1999.CrossRefGoogle Scholar
  6. [6]
    S. Akella, W. Huang, K. M. Lynch, and M. T. Mason. Parts feeding on a conveyor with a one joint robot. Algorithmica, to appear.Google Scholar
  7. [7]
    I. Kolmanovsky and N. H. McClamroch. Developments in nonholonomic control problems. IEEE Control Systems Magazine, pages 20–36, Dec. 1995.Google Scholar
  8. [8]
    J. T. Wen. Control of nonholonomic systems. In W. S. Levine, editor, The Control Handbook, pages 1359–1368. CRC Press, 1996.Google Scholar
  9. [9]
    E. Sontag. Gradient techniques for systems with no drift: A classical idea revisited. In IEEE International Conference on Decision and Control, pages 2706–2711, 1993.Google Scholar
  10. [10]
    H. Sussmann. A continuation method for nonholonomic path-finding problems. In IEEE International Conference on Decision and Control, pages 2718–2723, 1993.Google Scholar
  11. [11]
    A. W. Divelbiss and J. Wen. A global approach to nonholonomic motion planning. In IEEE International Conference on Decision and Control, pages 1597–1602, 1992.Google Scholar
  12. [12]
    C. Fernandes, L. Gurvits, and Z. Li. Near-optimal nonholonomic motion planning for a system of coupled rigid bodies. IEEE Transactions on Automatic Control, 30 (3): 450–463, Mar. 1994.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    F. Lizarralde, J. T. Wen, and L. Hsu. Feedback stabilization of nonlinear systems: a path space iteration approach. In IEEE International Conference on Decision and Control, pages 4022–4023, 1998.Google Scholar
  14. [14]
    N. B. Zumel and M. A. Erdmann. Balancing of a planar bouncing object. In IEEE International Conference on Robotics and Automation, pages 2949–2954, San Diego, CA, 1994.Google Scholar
  15. [15]
    Y. Wang and M. T. Mason. Two-dimensional rigid-body collisions with friction. ASME Journal of Applied Mechanics, 59: 635–641, Sept. 1992.CrossRefMATHGoogle Scholar
  16. [16]
    C. K. Black. Planning and control of planar batting using nonlinear optimization. Master’s thesis, Northwestern University, Department of Mechanical Engineering, Nov. 1998.Google Scholar
  17. [17]
    K. Kosuge, K. Fureta, and T. Yokoyama. Virtual internal model following control of robot arms. In IEEE International Conference on Robotics and Automation, pages 1549–1554, 1987.Google Scholar
  18. [18]
    G. Zeglin and B. Brown. Control of a bow leg hopping robot. In IEEE International Conference on Robotics and Automation, pages 793–798, 1998.Google Scholar

Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Kevin M. Lynch
    • 1
  • Craig K. Black
    • 1
  1. 1.Dept. of Mechanical EngineringNorthwestern UniversityEvanstonUSA

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