Abstract-This paper presents the dynamic modeling of a continuous three-dimensional swimming eel-like robot. The modeling approach is based on the "geometrically exact beam theory" and on that of Newton-Euler, as it is well known within the robotics community. The proposed algorithm allows us to compute the robot's Galilean movement and the control torques as a function of the expected internal deformation of the eel's body.

The best known analytical model of swimming was originally developed by Lighthill and is known as the large amplitude elongated body theory (LAEBT). Recently, this theory has been improved and adapted to robotics through a series of studies ranging from hydrodynamic modeling to mobile multibody system dynamics. This article marks a further step towards the Lighthill theory. The LAEBT is applied to one of the best bio-inspired swimming robots yet built: the AmphiBot III, a modular anguilliform swimming robot. To that end, we apply a Newton-Euler modeling approach and focus our attention on the model of hydrodynamic forces. This model is numerically integrated in real time by using an extension of the Newton-Euler recursive forward dynamics algorithm for manipulators to a robot without a fixed base. Simulations and experiments are compared on undulatory gaits and turning maneuvers for a wide range of parameters. The discrepancies between modeling and reality do not exceed 16% for the swimming speed, while requiring only the one-time calibration of a few hydrodynamic parameters. Since the model can be numerically integrated in real time, it has significantly superior accuracy compared with computational speed ratio, and is, to the best of our knowledge, one of the most accurate models that can be used in real-time. It should provide an interesting tool for the design and control of swimming robots. The approach is presented in a self contained manner, with the concern to help the reader not familiar with fluid dynamics to get insight both into the physics of swimming and the mathematical tools that can help its modeling.

This article reports the first results from a programme of work aimed at developing a swimming robot equipped with electric sense. After having presented the principles of a bioinspired electric sensor, now working, we will build the models for electrolocation of objects that are suited to this kind of sensor. The produced models are in a compact analytical form in order to be tractable on the onboard computers of the future robot. These models are tested by comparing them with numerical simulations based on the boundary elements method. The results demonstrate the feasibility of the approach and its compatibility with online objects electrolocation, another parallel programme of ours.

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 uid stratied around the slender beam.

Abstract-This article presents a unified dynamic modeling approach of (elongated body) continuum robots. The robot is modeled as a geometrically exact beam continuously actuated through an active strain law. Once included into the geometric mechanics of locomotion, the approach applies to any hyperredundant or continuous robot devoted to manipulation and/or locomotion. Furthermore, exploiting the nature of the resulting model as being a continuous version of the Newton-Euler model of discrete robots, an algorithm is proposed which is capableo f computing the internal control torques (and/or forces) as well as the rigid net motions of the robot. In general, this algorithm requires a model of the external forces (responsible for the self propulsion), but we will see how such a model can be replaced by a kinematic model of a combination of contacts related to terrestrial locomotion. Finally, in this case, that we name "kinematic locomotion", the algorithm is illustrated through many examples directly related to elongated body animals such as snakes, worms or caterpillars and their associated bio-mimetic artifacts.