Poincar,-Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics
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 Poincar, equations of a Cosserat beam to an open system containing a fluid stratified around the slender beam.
Keywords: Swimming dynamics ; Eel-like robots ; Hyper-redundant locomotion ; Lie groups ; Lagrangian reduction ; Poincare-Cosserat equations ; Geometrically Exact Approach ; Eel-Like Robot ; Articulated-Body ; Rod Model ; Locomotion ; Fluid ; Dynamics ; Simulations ; Propulsion ; Element
Record created on 2011-12-16, modified on 2016-08-09