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Analysis and Control of Underactuated Mechanical Systems pp 15–33Cite as

Underactuated Mechanical Systems from the Lagrangian Formalism

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Abstract

When one is interested in controlling systems for which their nonlinear dynamics cannot be neglected, it is well-known, since the time of Poincaré, that these nonlinear systems have extremely complex behaviors so that the application of a particular design method in control theory might not be suitable. It is therefore necessary to clarify, somehow or other, the class of systems we are interested in.

In this chapter, we are interested in the class of UMSs that are derived from the Lagrangian formalism. As a result, the first part of this chapter is dedicated to an introduction on Lagrangian systems. After that, the notion of underactuation is explained. Then, we give the definition of non-holonomic constraints as well as highlighting the differences and subtleties that exist between underactuation and non-holonomy. We demonstrate why the control of UMSs leads to challenging theoretical problems, some of which are still open till now. Finally, the end of this chapter is dedicated to the presentation of the models of some UMSs.

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Notes

  1. 1.

    Holonomic: Greek word that signifies whole, integer.

  2. 2.

    Translational Oscillator Rotational Actuator.

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Authors and Affiliations

  1. University of Aboubekr Belkaid, Chetouane, Tlemcen, Algeria

    Amal Choukchou-Braham & Brahim Cherki

  2. LAMIH ASHM, University of Valenciennes and Hainaut-Cambrésis, Valenciennes, France

    Mohamed Djemaï

  3. Faculty of Engineering and Environment, Northumbria University, Newcastle-upon-Tyne, UK

    Krishna Busawon

Authors
  1. Amal Choukchou-Braham
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  2. Brahim Cherki
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  3. Mohamed Djemaï
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  4. Krishna Busawon
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Choukchou-Braham, A., Cherki, B., Djemaï, M., Busawon, K. (2014). Underactuated Mechanical Systems from the Lagrangian Formalism. In: Analysis and Control of Underactuated Mechanical Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-02636-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-02636-7_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02635-0

  • Online ISBN: 978-3-319-02636-7

  • eBook Packages: EngineeringEngineering (R0)

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