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Tracking control of flexible robot manipulators with active 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 flexible structure of a robot multi-links manipulator can be either a side effect or, on the contrary, an essential feature. We present a fairly general model to derive the corresponding dynamic equations in quite a systematic and simple way. To this end, we use the Lagrange formulation with strain energy potential and Raleigh (dissipation) functions. The approach can incorporate torsional deformation and aerodynamic friction, and it applies easily to robots working in the sea. The trajectory control appears to be one in the presence of model imprecision, and a slightly modified version of the classical sliding control technique is utilized to design the tracking control of the manipulator. Then we introduce the time-varying inertia link device (carried out by means of sliding masses) which we suggested in earlier work, and we show how it can be used to improve the tracking control scheme above. This paper contributes new ideas concerning flexible multi-links arms and active inertia links.

Keywords

Manipulator flexibilityInertia linksMultilinks armsdynamic equations
Type
Article
Information
Robotica , Volume 8 , Issue 1 , January 1990 , pp. 73 - 80
Copyright
Copyright © Cambridge University Press 1990

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References

1.Hughes, P.C., ‘Space structure vibration modes: How many exist? Which ones are important?’ IEEE Contr. Syst. Mag. 7, No 1, 22–28 (1987).CrossRefGoogle Scholar
2.Gibson, J.S., ‘An analysis of optimal modal regulation: convergence and stability’ SIAM J., Control 19, 537–565 (1979).Google Scholar
3.Balas, M.J., ‘Modal control of certain flexible dynamic systems’ SIAM J. Control 16, 450–462 (1978).CrossRefGoogle Scholar
4.Sakawa, Y., Ito, R. and Fujii, M.J., ‘Optimal control of rotation of a flexible arm’ Lecture Notes in Control and information Sciences 54, 175–188 (1984).CrossRefGoogle Scholar
5.Davis, J.H. and Hirschorn, R.M., ‘Tracking control of a flexible robot link’ IEEE Trans. Autom. Control 33, No. 3238–248 (1988).CrossRefGoogle Scholar
6.Cannon, R.M. and Schmitz, E., ‘Initial experiments on the end-point control of a flexible one-link robot’ Int. Robotics Res. 3, No 3, 186–197 (1984).Google Scholar
7.Gevarter, W.B., ‘Basic relations for control of vehicles’ AIAA J. 8, No 4, 666–672 (1970).CrossRefGoogle Scholar
8.Zalucky, A. and Hart, D.E., ‘Active control of robot structure deflection’ J. Dyn. Syst. Measurement and Control 166, 63–69 (1984).CrossRefGoogle Scholar
9.Jumarie, G., ‘Trajectory control of manipulators with time-varying inertia links’ Robotica 6, No 3, 197–202 (1988).CrossRefGoogle Scholar
10.Jumarie, G., ‘Two-stages sliding controllers for manipulators with time-varying inertia links’ Robotica (In Press).Google Scholar
11.Antman, S. and Nachman, A., ‘Large buckled stales of rotating rods’ Nonlinear Analysis 4, 303–327 (1980).CrossRefGoogle Scholar
12.Paul, R.P., Robot Manipulators (MIT Press, Cambridge, Mass., 1982).Google Scholar
13.Asada, H. and Slotine, J.J.E., Robot Analysis and Control (John Wiley, New York, 1986).Google Scholar
14.Denavit, J. and Hartenberg, R.S., ‘A kinematic notation for lower pair mechanisms based on matrices’ ASME J. Applied Mechanics, Series E, 22, 215–221 (1955).CrossRefGoogle Scholar
15.Landau, L.D. and Lifschitz, E.M., Theory of Elasticity (Pergamon, London, 1959).Google Scholar
16.Pars, A., Treatise on Analytic Dynamics (Wiley, New York, 1965).Google Scholar
17.Slotine, J.J.E. and Sastry, S.S., ‘Tracking control of nonlinear systems using sliding surfaces with applications to robot manipulators’ Intern. J. Control 39, 2–17 (1983).Google Scholar