Modeling and Control of Two Manipulators Handling a Flexible Beam

This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Authors:

• Amer S. Al-Yahmadi
• T.C. Hsia

Keywords:

• Sliding mode control
• cooperative manipulators.

References:

[1] S. Schneider, "Experiments in the dynamic and strategic control of
cooperating manipulators," PhD Thesis, Stanford 1989.
[2] Michael A. Unseren, "A review of a method for dynamic load
distribution, dynamical modeling, and explicit internal force control
when two manipulators mutually lift and transport a rigid body object,"
IEEE International Conference on Robotics and Automation Tutorial T2
- Modeling and Control of Multi-arm Robot Systems, Albuquerque, New
Mexico, April 1997.
[3] Masaru Uchiyama, " Multi-Arm Robot Systems, A survey , " IEEE
International Conference on Robotics and Automation Tutorial T2 -
Modeling and Control of Multi-arm Robot Systems, Albuquerque, New
Mexico, April 1997.
[4] Guanfeng Liu and Zexiang Li, "A unified geometric approach to
modeling and control of constrained mechanical systems, " , IEEE
Trans. Robotics & Auto., Vol. 18, No. 4, 574-587, 2002.
[5] Haruhisa Kawasaki, Satoshi Ito, and Rizauddin Bin Ramli, "Adaptive
Decentralized coordinated control of multiple robot arms," 7th IFAC
Symposium on Robot Control, 461-466, Sept. 2003.
[6] Wayne J. Book, "Controlled motion in an elastic world," ASME J. of
Dyn. Sys., Measurement & Control, 252-261, Vol. 115, June 1993.
[7] O. alJarrah and Y. F. Zheng and K.-Y. Yi "Efficient trajectory planning
for two manipulators to deform flexible materials with experiments,"
IEEE International Conference on Robotics and Automation 1:312--317,
1995.
[8] Yuan F. Zheng and Ming Z Chen, "Trajectory planning for two
manipulators to deform flexible beams, "IEEE International Conference
on Robotics and Automation, 1019-1024, April 1993.
[9] Werner Kraus Jr. and Brenan J. McCarragher, "Hybrid position/force
coordination for dual arm manipulation of flexible materials," IEEE
International Conference on Robotics and Automation, 202ÔÇö207, 1997.
[10] Wai Nguyen and James K. Mills, "Multi-Robot control for flexible
fixtureless assembly of flexible sheet metal auto body parts," IEEE
International Conference on Robotics and Automation, 2340ÔÇö2345,
April 1996.
[11] David W. Meer, "Experiment in cooperative manipulation of flexible
objects, "PhD Thesis, Stanford University, 1995.
[12] David W. Meer and Stephen M. Rock, Lee, K.-F., "Experiments in
Object Impedance Control for Flexible Objects, "IEEE International
Conference on Robotics and Automation, 1222ÔÇö1227, May 1994.
[13] Stanely A. Schneider and Robert H. Cannon, Jr., " Object Impedance
Control for Cooperative Manipulation: Theory and Experimental
Results," IEEE Trans. on Robotics and Automation Vol. 8, No. 3 , June
1992.
[14] Amer S. alYahmadi, T.C. Hsia, "Internal force-based impedance control
of dual arm manipulation of flexible objects" Proceedings ICRA2000
Millennium Conference, IEEE International Conference on Robotics &
Automation, pages 3296-3301, 24-28 April 2000.
[15] Robert G. Bonitz and T. C. Hsia"Internal force based impedance control
for cooperating manipulators", IEEE Trans. On Robt. Aut., 12(1), Feb
1996.
[16] Dong Sun and Yunhui Liu, "Modeling and Impedance Control of a Two
Manipulator System Handling a flexible Beam," ASME J. Dynamic
System, measurement and Control, V. 119, 736ÔÇö742, December 1997.
[17] Dong Sun and Yunhui Liu, "Modeling and Impedance Control of a Two
Manipulator System Handling a flexible Beam, " IEEE International
Conference on Robotics and Automation, 1787ÔÇö1792, April 1997.
[18] D.M. Dawson et. al., "Robust control for the tracking of robot motion, "
International Journal of Control, Vol.52, No. 3, 581-595, 1990.
[19] J.J. Slotine and S.S Sastry, "Tracking control of nonlinear systems using
sliding surfaces, with application to robot manipulators, " International
Journal of Control, Vol. 38, No. 2, 465-492.
[20] Vadim Utkin, "Sliding modes in control and optimization," Springer-
Verlag, 1992.
[21] Kar-Keung D. Youn, " Controller design for a manipulator using theory
of variable structure, " Transactions on systems, man and cybernetics,
Vol. SMC-8, No. 2, 101-109, Feb. 1978.
[22] V. I. Utkin, "Variable sructures systems with sliding mode," IEEE
Trans. Autom. Contr., Vol. AC-22, No. 2, 212-222, 1977.
[23] Romeo Ortega et. al, "Passivity-based control of Euler-lagrange systems,
" Springer-Verlag, 1998.