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

Journal of Nonlinear Science (Impact Factor: 1.57). 01/2010; 20:47-79. DOI: 10.1007/s00332-009-9050-5
Source: DBLP

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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