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

Frédéric Boyer (1, 2, 3, 4) , Mathieu Porez (2) , Alban Leroyer (5)

1 Mines Nantes - Mines Nantes
2 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
3 IMT Atlantique - DAPI - Département Automatique, Productique et Informatique
4 LS2N - équipe ReV - Robotique Et Vivant
5 LMF - Laboratoire de mécanique des fluides

In this article, we propose a dynamic model of the three-dimensional eel swim. This model is analytical and suited to the on-line control of eel-like robots. The proposed solution is based on the Large Amplitude Elongated Body Theory of Lighthill and a working frame recently proposed in [1] for the dynamic modeling of hyper-redundant robots. This working frame 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 proposes new results in two directions. Firstly, it achieves an extension of 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 is also derived in this article. These equations generalize the Poincaré equations of a Cosserat beam to the case of an open system containing a fluid stratified around the slender beam.

Domaines: Automatique / Robotique

Frédéric Boyer, Mathieu Porez, Alban Leroyer. Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics. Journal of Nonlinear Science, 2010, 20 (1), pp.47-79. ⟨10.1007/s00332-009-9050-5⟩. ⟨hal-00630754⟩