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Modelling and Control of a Flexible Spherical Wrist

Published online by Cambridge University Press:  09 March 2009

Véronique Perdereau ,
S. Ng  and
D. Wang
Véronique Perdereau
Affiliation:
Construct Group, Department of Electrical and Computer EngineeringUniversity of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
S. Ng
Affiliation:
Construct Group, Department of Electrical and Computer EngineeringUniversity of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
D. Wang
Affiliation:
Construct Group, Department of Electrical and Computer EngineeringUniversity of Waterloo, Waterloo, Ontario N2L 3G1 (Canada)
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Summary

In this paper, a very inexpensive, lightweight and simple wrist mechanism is introduced. This wrist displays nonlinear torsional vibrations. This differs from conventional wrists in that structural flexibility in the mechanism is allowed to occur by design. In this paper, the dynamic equations of this wrist are derived. System identification techniques are then employed to obtain a linearized model. Various control strategies are studied. It is shown that the input-output feedback linearization technique is not feasible for these nonlinear dynamic equations. It is also shown that the use of conventional rigid body PID controllers on this proto-type is inadequate. A tracking controller which compensates for the flexible dynamics of the wrist is implemented with encouraging results. This controller allows the end-effector to be placed at an arbitrary orientation with little vibration. The effect of the controller is to make the wrist appear to have a much higher structural stiffness. The compliant nature of this wrist allows simple force control strategies to be implemented. It is the combination of the wrist with the control algorithm which makes this design viable.

Keywords

Spherical wristModellingControl: Modelling
Type
Article
Information
Robotica , Volume 14 , Issue 2 , March 1996 , pp. 155 - 163
Copyright
Copyright © Cambridge University Press 1996

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References

1.Book, W.J., “Modelling, Design and Control of Flexible Manipulator Arms: A Tutorial Review” Proceedings of the 29th Conference on Decision and Control,Honolulu, Hawaii(Dec, 1990) pp. 500–506.CrossRefGoogle Scholar
2.Cannon, R.H. and Schmitz, E., “Initial Experiments on the End-Point Control of a Flexible One-Link Robot” Int. J.Robotic Research 3, No. 3, 62–75 (Fall, 1984).CrossRefGoogle Scholar
3.Rosheim, M.E., Robot Wrist Actuators (John Wiley & Sons, New York, 1989).Google Scholar
4.Paul, R.P. and Stevenson, C.N., “Kinematics of Robot Wrists” Int. J.Robotics Research 2, 31–38 (Spring, 1983).CrossRefGoogle Scholar
5.Milenkovic, V., “Effect of Robot Wrist Singularity on Path Control”, 14th International Symposiun on Industrial Robots 10, 1984, Gothenburg, Sweden, IFS Publications (1984) pp. 279–286.Google Scholar
6.Oh, S.R., Hollis, R.L. and Salcudean, S.E., “Precision Assembly with a Magnetically Levitated Wrist”, Proceedings of the 1993 IEEE International Conference on Robotics and Automation,May, 1993,Atlanta, Georgia (1983) pp. 127–134.Google Scholar
7.Lee, K.M., Vachtsevanos, G. and Kwang, C., “Development of a spherical stepper wrist motor” J.Intelligent and Robotic Systems: Theory and Applications 1, No. 3, 225–42 (1988).CrossRefGoogle Scholar
8.Long, G., Paul, R.P. and Fisher, W.D., “The Hamilton Wrist: A 4-Revolute-Joint Spherical Wrist without Singularities”, Proceedings of the 1989 IEEE International Conference on Robotics and Automation(May, 1989) pp. 902–907.Google Scholar
9.Trevelyan, J.P., “A Wrist Mechanism without Singular Positions“ Int. J.Robotics Research 5, 71–85 (Winter, 1986).CrossRefGoogle Scholar
10.Nevins, J.L. & Whitney, D.E., “Computer Controlled Assembly” Scientific American Magazine (02, 1978) p. 67.Google Scholar
11.Cutkosky, M.R. and Wright, P.K., “Active Control of a Complaint Wrist in Manufacturing Tasks” J.Engineering for Industry 108, No. 1, 36–4302., 1986.CrossRefGoogle Scholar
12.Xu, Y. and Paul, R.P., “A Robot Compliant Wrist System for Automated Assembly” Proceedings of the 1990 IEEE International Conference on Robotics and Automation,Cincinnati, OH (1990) pp. 1750–1755.Google Scholar
13.Ng, S., “Modelling and Control of a Flexible Spherical Wrist” M.A.Sc. Thesis (Electrical Engineering, University of Waterloo, Canada, Winter, 1992).Google Scholar
14.Spong, M. and Vidyasagar, M., Robot Dynamics and Control (John Wiley & Sons.New York, 1989) ch. 6, pp. 129–163.Google Scholar
15.Ljung, L., System Identification: Theory for the User (Prentice-Hall, Englewood Cliffs, NJ., 1987).Google Scholar
16.Slotine, J.J.E. and Li, W., Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, N.J., 1991) ch. 6, pp. 207–271.Google Scholar
17.Wang, D. and Vidyasagar, M., “Control of a Class of Manipulators with a Single Flexible Link-Part I: Feedback Linearization” J.Dynamic Systems, Measurement, and Control 113, 655–661 (12, 1991).CrossRefGoogle Scholar
18.Chen, C.T., Linear System Theory and Design (Holt, Rinehart and Winston, New York, 1984) ch. 7, pp. 324–378.Google Scholar
19.D'Azzo, J.J. and Houpis, C.H., Linear Control System Analysis and Design: Conventional and Modern (McGraw Hill, New York, 1988) ch. 20, pp. 660–684.Google Scholar
20.Kuo, B.C., Automatic Control Systems (Prentice-Hall, Englewood Cliffs, N.J.., 1987).Google Scholar