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Two–Stages Sliding Controller for Manipulators with Time–Varying Inertia Links*

Published online by Cambridge University Press:  09 March 2009

Guy Jumarie
Guy Jumarie
Affiliation:
Department of Mathematics and Computer Science, Université du Québec à Montréal, P.O. Box 8888, St A, Montréal, QUE, H3C 3P8 (Canada)
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Summary

The author introduced the use of time–varying inertia links to increase the flexibility (or versatility) of manipulators in the sense that they can so achieve more tracking capabilities. Clearly, we then have a pair of control vectors (link inertias and external forces) instead of one control vector only (applied forces). After a careful derivation of the dynamical equations of such manipulators, one shows that their control procedure can be decomposed into two stages, each of them involving sliding control schemes via prescribed dynamics on the error term, that is to say the difference between the desired position and the actual position. This approach provides a good technique to take account of possible constraints on the magnitude of the control, and in addition, it is possible to consider the sliding conditions as an ideal mechanical constraint, therefore the use of the principle of virtual displacements.

This paper is a continuation of the one entitled “Trajector control of manipulators with time–varying inertia links” (Robotica 6, No. 3, 197–202, 1988). It described new techniques to circumvent difficulties arising when the values of the mechanical parameters are not exactly known and when linearization does not apply because of the important deviation. In addition this paper shows that Appel's principle of virtual displacements is more efficient than the Lagrangian parameters for the derivation of the manipulator's dynamic parameters in the presence of mechanical constraints.

Keywords

ControllerManipulatorInertia linksTime-varyingTwo stagesAppel principle
Type
Article
Information
Robotica , Volume 7 , Issue 3 , July 1989 , pp. 255 - 261
Copyright
Copyright © Cambridge University Press 1989

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References

1.Gutowski, R. and Radziszewski, B., “On the Exact Control Problem of Motion of a Mechanical System With Program Constraints”, Zagadniena Drgan Nieliniowych 10, 38–49 (1969).Google Scholar
2.Gutowski, R., Mechanical Analityczna (Panstwowe Wydawnictwo Techniczne, Warsaw, 1971).Google Scholar
3.Kirghetov, V.I., “On The Motion of Controlled Mechanical Systems”, Prikl. Math. Mikh. 2, 13–19 (1964) (in Russian).Google Scholar
4.Koronev, G.V., Introduction to Mechanics of a Controlled Body (Izd. Nauka, 1965, Moscow) (in Russian).Google Scholar
5.Kirghetov, V.I., “On The Motion of a Controlled Mechanical System With Servo-constraints” Prikl. Math. Mekh. 3, 42–46 (1967) (in Russian).Google Scholar
6.Vukobratovic, M. and Stokic, D., Scientific Fundamental of Robotics 2. Control of Manipulators (Springer Verlag, Berlin, 1982).Google Scholar
7.Jumarie, G., “A Small Parameter Method to Improve Optimum Control Via Linearization Technique” Robotica 3, No. 2, 85–88 (1985).CrossRefGoogle Scholar
8.Paul, R.P., Robot Manipulators (MIT Press, Cambridge, Mass., 1982).Google Scholar
9.Asada, H. and Slotine, J.-J.E., Robot Analysis and Control (John Wiley, New York, 1986).Google Scholar
10.Lopez, P. and Foulc, J.-N., Introduction to Robotics I, II (Editests, Paris, 1984) (in French).Google Scholar
11.Emelyanov, S.V., Theory of Variable Structure Systems (Nauka, Moscow, 1967).Google Scholar
12.Utkin, V.I., “Equations of Sliding Mode in Discontinuous Systems” I, II, Automation and Remote Control 1897–1907 (1971).Google Scholar
13.Utkin, V.I., Sliding Modes and Their Application to Variable Structure Systems (MIR Publishers, Moscow, 1978).Google Scholar
14.Itkis, U., Control Systems of Variable Structure (John Wiley, New York, 1986).Google Scholar
15.Slotine, J.-J.E., “Sliding Controller Design for Nonlinear Systems” Int. J. Control 40, 2 (1984).CrossRefGoogle Scholar
16.Young, D. Kar-Keug, “Controller Design For a Manipulator Using Theory of Variable Structure Systems” In: Robot Motion (Edited by Brady, M. et al. ) (M.I.T., Cambridge, Mass., 1982) pp. 201–219.Google Scholar
17.Jumarie, G., “On The Use of Time Varying Inertia Links to Increase The Versatility of Manipulators” Robotica 4, No. 2, 101–105 (1986).CrossRefGoogle Scholar
18.Jumarie, G., “Trajectory Control of Manipulators With Time Varying Inertia Links” Robotica 6, No. 3, 197–202 (1988).CrossRefGoogle Scholar
19.Denavit, J. and Hartenberg, R.S., “A Kinematic Notation For Lower Pair Mechanisms Based on Matrices”, ASME J. Applied Mechanics 22, 215–221 (1955).CrossRefGoogle Scholar