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Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics

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Abstract

In this article, we describe a dynamic model of the three-dimensional eel swimming. This model is analytical and suited to the online control of eel-like robots. The proposed solution is based on the Large Amplitude Elongated Body Theory of Lighthill and a framework recently presented in Boyer et al. (IEEE Trans. Robot. 22:763–775, 2006) for the dynamic modeling of hyper-redundant robots. This framework was named “macro-continuous” since, at this macroscopic scale, the robot (or the animal) is considered as a Cosserat beam internally (and continuously) actuated. This article introduces new results in two directions. Firstly, it extends the Lighthill theory to the case of a self-propelled body swimming in three dimensions, while including a model of the internal control torque. Secondly, this generalization of the Lighthill model is achieved due to a new set of equations, which are also derived in this article. These equations generalize the Poincaré equations of a Cosserat beam to an open system containing a fluid stratified around the slender beam.

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Authors and Affiliations

  1. EMN, IRCCyN, La Chantrerie 4, rue Alfred Kastler, BP 20722, 44307, Nantes Cedex 3, France

    Frederic Boyer

  2. EPFL-BIRG, INN 241, Station 14, 1015, Lausanne, Switzerland

    Mathieu Porez

  3. ECN, LMF, 1 rue de la Noë, BP 92101, 44321, Nantes Cedex 3, France

    Alban Leroyer

Authors
  1. Frederic Boyer
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  2. Mathieu Porez
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  3. Alban Leroyer
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Correspondence to Frederic Boyer.

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Communicated by Shelley.

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Boyer, F., Porez, M. & Leroyer, A. Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics. J Nonlinear Sci 20, 47–79 (2010). https://doi.org/10.1007/s00332-009-9050-5

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  • DOI: https://doi.org/10.1007/s00332-009-9050-5

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