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

Journal of Nonlinear Science (Impact Factor: 2.14). 02/2010; 20(1):47-79. DOI: 10.1007/s00332-009-9050-5
Source: DBLP


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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    • "Following these projects, many swimming robots were then developed. Inspired by elongated anguilliform fishes such as the eel and the lamprey, some of them used undulation of the entire body with a high number of internal degrees of freedom instead of merely oscillating the rear part of their body (as did RoboTuna) to propel themselves in water [19]. Examples of such robots include the amphibious snake-like robots Amphibot [30], ACM-R5 [83], and the eel-like robot from the French project RAAMO [1]. "
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    ABSTRACT: This article presents a set of generic tools for multibody system dynamics devoted to the study of bio-inspired locomotion in robotics. First, archetypal examples from the field of bio-inspired robot locomotion are presented to prepare the ground for further discussion. The general problem of locomotion is then stated. In considering this problem, we progressively draw a unified geometric picture of locomotion dynamics. For that purpose, we start from the model of discrete mobile multibody systems (MMSs) that we progressively extend to the case of continuous and finally soft systems. Beyond these theoretical aspects, we address the practical problem of the efficient computation of these models by proposing a Newton–Euler-based approach to efficient locomotion dynamics with a few illustrations of creeping, swimming, and flying.
    Bioinspiration &amp Biomimetics 04/2015; 10(2). DOI:10.1088/1748-3190/10/2/025007 · 2.35 Impact Factor
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    • "In contrast to our earlier model [Boyer et al., 2010] which was based on abstract variational calculus, the model in this article uses the balance of the fluid kinetic momenta contained in a control volume enclosing each of the segments. Once derived, this model is introduced into the N- E model of the AmphiBot III. "
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    ABSTRACT: 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.
    The International Journal of Robotics Research 09/2014; 33(10):1322-1341. DOI:10.1177/0278364914525811 · 2.54 Impact Factor
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    • "In the first case, the directors remain perpendicular to the mid-surface while in the second case they can rotate freely with respect to the mid-surface with two additional degrees of freedom which, in turn, induce two further strain fields named "transverse shearing". The first kinematics correspond to the so called Kirchhoff model of shells while the second correspond to the Reissner model [23]. Geometrically exact beam theories have been recently applied to continuous (hyper-redundant) and soft robotics in the context of underwater and terrrestrial locomotion of fish [24] and snakes [25] and for manipulation of octopus like arms [26]. "
    Bioinspired Robotics, Frascati, Italy; 06/2014
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