Fast Dynamics of a three dimensional eel-like robot : comparisons with Navier-Stokes simulations

This article proposes a dynamic model of the swim of elongated shes suited to the on-line control of bio-mimetic eel-like robots. The approach is analytic and can be considered as an extension of the original reactive "Large-Elongated-Body-Theory" of Lighthill to the three dimensional self propulsion augmented of a resistive empirical model. While all the mathematical fundamentals are detailed in [1], this article essentially focuses on the numerical validation and calibration of the model and the study of swimming gaits. The proposed model is coupled to an algorithm allowing us to compute the motion of the sh head and the eld of internal control torque from the knowledge of the imposed internal strain elds. Based on the Newton-Euler formalism of robots dynamics, this algorithm works faster than real time. As far as precision is concerned, many tests obtained with several planar and three dimensional gaits are reported and compared (in the planar case) with a Navier-Stokes solver, devoted until today to the planar swim. The comparisons obtained are very encouraging since in all the cases we tested, the di erences between our simpli ed and reference simulations do not exceed ten per cent.