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On robots with flexible links: dynamics, control and stability

Über Roboter mit flexiblen Gliedern: Dynamik, Regelung und Stabilität

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Summary

It is shown that a possibly redundant robot with rigid links which is driven at the nodes can be stabilized for any feasible, given path of the nodes. This result is generalized to robots with stiff yet flexible links.

The Lagrangean equations of motion are used as a description of the robot. The controls are the polygenic generalized forces corresponding to the Lagrangean coordinates. The stabilizing controls are exhibited. Examples precede the general theory.

Übersicht

Es wird gezeigt, daß ein möglicherweise redundanter Roboter mit steifen Gliedern, welche in den Drehgelenken angetrieben werden, für jeden denkbaren gegebenen Weg der Drehpunkte stabilisiert werden kann. Dieses Resultat gilt ganz allgemein für Roboter mit steifen, jedoch flexiblen Gliedern.

Die Lagrangeschen Bewegungsgleichungen werden zur Beschreibung des Roboters benutzt. Die Regelungen sind die polygenen generalisierten Kräfte, die den Lagrangeschen Koordinaten entsprechen. Die stabilisierenden Regelungen werden hergeleitet. Beispiele sind der Behandlung der allgemeinen Theorie vorangestellt.

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References

  1. Lanczos, C.: The variational principles of mechanics, 1st ed. Toronto: University of Toronto Press 1949

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  2. Brady, M. et al. (eds.): Robot motion, planning and control. Cambridge: MIT Press 1984

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  3. Slotine, J. J. E.: Sliding controller design for nonlinear systems. Int. J. Control 40 (1984) 421–434

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Delft University of Technology, Julianalaan 132, NL-2628, BL Delft, The Netherlands

    J. J. Kalker &  G. J. Olsder

Authors
  1. J. J. Kalker
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  2. G. J. Olsder
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Kalker, J.J., Olsder, G.J. On robots with flexible links: dynamics, control and stability. Ing. arch 57, 16–24 (1987). https://doi.org/10.1007/BF00536808

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  • DOI: https://doi.org/10.1007/BF00536808

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