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Forces of reaction and neighbouring Hamilton's principle in the tracking control of manipulators via a sliding scheme

Published online by Cambridge University Press:  09 March 2009

Guy Jumarie
Guy Jumarie
Affiliation:
Department of Mathematics and Computer ScienceUniversité du Québec à MontréalP.O. Box 8888StA, Montreal, QUE, H3C 3P8 (Canada)
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Summary

It is shown that if one comes back to the formulation of the Hamilton's variational principle, it is then possible to obtain new viewpoints on the tracking control of robot manipulators. First, the Lagrange multiplier associated to the sliding surface can be interpretated in terms of control effort and/or forces of reaction of the mechanical system. Secondly, one can use the Taylor expansion of the mechanical Lagrangian, combined with a neighbour- ing Hamilton's principle, to obtain control schemes via sliding surfaces. Thirdly, a perturbation approach combined with the neighbouring Hamilton's principle provides results on the robustness of the control.

Keywords

Robot controlHamilton's principleNeighbouring controlSliding surfaceControl effortReaction forcePerturbation method.
Type
Research Article
Information
Robotica , Volume 11 , Issue 3 , May 1993 , pp. 227 - 232
Copyright
Copyright © Cambridge University Press 1993

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