Mathieu Porez

Model for a Sensor Inspired by Electric Fish

This paper reports the first results from a program of work aimed at developing a swimming robot equipped with electric sense. After having presented the principles of a bioinspired electric sensor that is 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, i.e., another parallel program of ours.

Fast Dynamics of an Eel-Like Robot—Comparisons With Navier–Stokes Simulations

This paper proposes a dynamic model of the swim of elongated fish suited to the online control of biomimetic eel-like robots. The approach can be considered as an extension of the original reactive ldquolarge elongated body theoryrdquo of Lighthill to the 3-D self-propulsion to which a resistive empirical model has been added. While all the mathematical fundamentals have been detailed by Boyer . (http://www.irccyn.ec-nantes.fr/hebergement/Publications/2007/3721.pdf, 2007), this paper 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 fish head and the field of internal control torque from the knowledge of the imposed internal strain fields. Based on the Newton-Euler formalism of robot dynamics, this algorithm works faster than real time. As far as precision is concerned, many tests obtained with several planar and 3-D gaits are reported and compared (in the planar case) with a Navier-Stokes solver, which, until today have been devoted to the planar swim. The comparisons obtained are very encouraging since in all the cases we tested, the differences between our simplified and reference simulations do not exceed 10%.

Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons

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.

Macrocontinuous Dynamics for Hyperredundant Robots: Application to Kinematic Locomotion Bioinspired by Elongated Body Animals

In this paper, we present 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 in the geometric mechanics of locomotion, the approach applies to any hyperredundant or continuous robot that is devoted to manipulation and/or locomotion. Furthermore, by the exploitation of the nature of the resulting model of being a continuous version of the Newton-Euler model of discrete robots, an algorithm is proposed that is capable of 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 that are related to terrestrial locomotion. Finally, in this case, which 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 biomimetic artifacts.

Poincaré–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 Poincaré equations of a Cosserat beam to an open system containing a fluid stratified around the slender beam.

Multi-physics model of an electric fish-like robot: Numerical aspects and application to obstacle avoidance

The paper deals with the modeling of a fish-like robot equipped with the electric sense, suited to study sensorimotor loops. The proposed multi-physics model merges a swimming dynamic model of a fish-like robot with an electric model of an embedded electrolocation sensor. Based on a TCP-IP and threaded framework, the resulting simulator works in real time. After presenting the modeling aspects of this work, this article focuses on two numerical studies. In the first, the interactions between body deformations and perception variables are studied and a current correction process is proposed. In the second study, an electric exteroceptive feedback loop based on a direct current measurement method is designed and tested for obstacle avoidance.

Multibody system dynamics for bio-inspired locomotion: from geometric structures to computational aspects

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.

Estimation of relative position and coordination of mobile underwater robotic platforms through electric sensing

In the context of underwater robotics, positioning and coordination of mobile agents can prove a challenging problem. To address this issue, we propose the use of electric sensing, with a technique inspired by weakly electric fishes. In particular, the approach relies on one or several of the agents applying an electric field to their environment. Using electric measures, others agents are able to reconstruct their relative position with respect to the emitter, over a range that is function of the geometry of the emitting agent and of the power applied to the environment. Efficacy of the technique is illustrated using a number of numerical examples. The approach is shown to allow coordination of unmanned underwater vehicles, including that of bio-inspired swimming robotic platforms.

Sensor model for the navigation of underwater vehicles by the electric sense

We present an analytical model of a sensor for the navigation of underwater vehicles by the electric sense. This model is inspired from the electroreception structure of the electric fish. In our model, that we call the poly-spherical model (PSM), the sensor is composed of n spherical electrodes. Some electrodes play the role of current-emitters whereas others play the role of current-receivers. By imposing values of the electrical potential on each electrode we create an electric field in the vicinity of the sensor. The region where the electric field is created is considered as the bubble of perception of the sensor. Each object that enters this bubble is electrically polarized and creates in return a perturbation. This perturbation induces a variation of the measured current by the sensor. The model is tested on objects for which the expression of the polarizability is known. A unique off-line calibration of the poly-spherical model permits to predict the measured current of a real immersed sensor in an aquarium. Comparisons in a basic scene between the predicted current given by the poly-spherical model and the measured current given by our test bed show a very good agreement, which confirms the interest of using such fast analytical models for the purpose of navigation.

Nonlinear motion control of CPG-based movement with applications to a class of swimming robots

In bio-inspired robotics, use of a Central Pattern Generator (CPG) to coordinate actuation is fairly common. The gait achieved depends on a number of CPG parameters, which can be adjusted to control the robots motion. This paper presents an output feedback motion control framework, addressing issues encountered when dealing with this type of control problem, including partial state measurements and system uncertainty. Efficacy of the presented approach is illustrated by results of numerical simulations in the case of a swimming robot.