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International audience; Cosserat rod theory proved efficient modeling performances in robotics, especially in the context of continuum robots, in the past decade. The implementation of such theory is far from being unique and straightforward. We consider the illustrative example of multi-segment, general routing tendon actuated continuum robots in their nominal static operating regime. This paper details two main approaches based on Cosserat rod modeling, namely the Newtonian and Lagrangian approaches. We provide a walk-through guide regarding theoretical derivations and numerical implementation of both approaches, together with a proof of equivalence. This comparative study is supplemented with novel contributions and extensions of each approach and in-depth discussion of their performances and applicability, as well as highlighting their special features.

International audience; This paper explores the relationship between optimal control and Cosserat beam theory from the perspective of solving the forward and inverse dynamics (and statics as a subcase) of continuous manipulators and snake-like bio-inspired locomotors. By invoking the principle of minimum potential energy, and the Gauss principle of least constraint, it is shown that the quasi-static and dynamic evolution of these robots, are solutions of optimal control problems (OCPs) in the space variable, which can be solved at each step (of loading or time) of a simulation with the shooting method. In addition to offering an alternative viewpoint on several simulation approaches proposed in the recent past, the optimal control viewpoint \fred{allows us to improve some of them while providing a better understanding of their numerical properties}. The approach and its properties are illustrated through a set of numerical examples validated against a reference simulator.

International audience; In this article we propose a new solution to the forward dynamics of Cosserat beams with in perspective, its application to continuum and soft robotics manipulation and locomotion. In contrast to usual approaches, it is based on the non-linear parametrization of the beam shape by its strain fields and their discretization on a functional basis of strain modes. While remaining geometrically exact, the approach provides a minimal set of ordinary differential equations in the usual Lagrange matrix form that can be solved with standard explicit time-integrators. Inspired from rigid robotics, the calculation of the matrices of the Lagrange model is performed with a continuous inverse Newton-Euler algorithm. The approach is tested on several numerical benches of non-linear structural statics, as well as further examples illustrating its capabilities for dynamics.

In the 50s, biologists discovered that some electric fish is capable of discriminating the pose as well as the electric and geometric properties of surrounding objects by navigating and measuring the distortions of a self-generated electric field. In this article, we address the challenging issue of ellipsoidal objects pose and size estimation for underwater robots equipped with artificial electric sense. Unlike current methods, the approach can estimate both the position and size in parallel with a single straight trajectory. Neither multipolarization nor reactive self-alignment control are necessary to locate the object. The approach is a purely model-based heuristic that selects the best ellipsoid parameters among a set of potential candidates. It is based on a set of four electric measurements recorded at several positions along the robot trajectory along which the displacement is measured. The efficiency of the method is assessed over numerous experiments with different objects, several positions, and orientations, and two different kinds of water (fresh and salt water). Despite some model simplifications and experimental errors, location and size estimation errors are on average below $\text{1}\,$ cm and $\text{15}\%$ , respectively, while offering promising perspectives for real-time computation.

We propose a novel variable-strain parametrization for soft manipulators, which discretizes the continuous Cosserat rod model onto a finite set of strain basis functions. This approach generalizes the recently proposed piecewise-constant strain method to the case of non-constant strain sections. As for its predecessor, the discrete model is based on the relative pose between consecutive cross-sections and is provided in its minimal matrix form (Lagrangian-like). The novel variable-strain model is applied to the static equilibrium of tendon and/or fluidic actuated soft manipulators. It is shown that, for a specific choice of strain basis, exploiting the actuator geometry, the system is trivialized, providing useful tools for control and actuator routing design. Comparisons with the full continuous Cosserat model demonstrate the feasibility of the approach.

International audience; This article exploits a bio-inspired sensor technology named artificial electric-sense to emulate underwater pre-touch. The sensor is considered as an electric finger remote-controlled by an operator to follow the boundaries of objects. Using electric measurements only, the approach feeds back pre-touch forces and torques to the operator through an haptic interface. These forces and torques are generated by a set of virtual electric charges and dipoles arranged on the probe and reacting in the electric field reflected by the objects. This model of emulated forces is passive and guarantees the stability of a position-position haptic feedback loop. The whole approach is assessed through a set of experiments carried out on a Cartesian slave robot coupled to an haptic interface. The obtained results show the feasibility of the concept and its robustness to different configuration of objects. Such an electro-haptic feedback opens new perspectives in both electric field sensing and underwater robotics.

We report an investigation aiming to understand the stability mechanisms of semi-aquatic snakes (like Cottonmouth viper or grass snakes) on a free water surface. To address this complex problem, we start by reviewing the specific morphological features of these snakes. Then, we analyse the poses of a semi-aquatic snake in its natural environment. We show that surface stability is achieved by complex combinations of all three rotational degrees of freedom of each vertebra. Based on a new theoretical model, a control law is developed to seek the finite body deformation from the strain (torsion and bending) to maintain an equilibrium stance (position and orientation). Our conclusions lead us to consider a new actuation mechanism based on a controlled rolling motion for each body segment in order to achieve static and dynamic positioning. During the conference, we will present our new swimming snake-like robot, named NATRIX, that can achieve static and dynamic positioning on a free water surface.

International audience; This article addresses the dynamic modelling of geometrically exact sliding Cosserat rods. Such systems need to consider nonmaterial time-varying domains to which the Lagrangian view point of solid mechanics is inappropriate. In the article here presented, we use the geometrically exact model of inextensible Kirchhoff rods along a non-material domain whose time variations are not necessarily imposed but are governed by the dynamics, i.e. depend on the configuration of the rod. To progress through derivation, we use the variational calculus on Lie group introduced by Poincaré, and apply it to an extension of Hamilton's principle holding for open rod systems, which is derived in the article. This extended variational principle uses a moving non-material tube across which the material rod slides. The resulting closed formulation of sliding rods dynamics takes the form of a set of non-material Cosserat-Poincaré's partial differential equations governing the time-evolution of the cross-section pause of the non-material tube, coupled with an ordinary Lagrange's differential equation for the sliding motion of the rod across the tube. While emphasize is on the dynamic formulations, the modelling approach is numerically illustrated on a few examples related to the so called sliding spaghetti problem.

This article presents different use of the electric sense perception in the context of underwater robot navigation. To illustrate the developed navigation behaviours we will introduce a recently launched european project named subCULTron and will show some simulation and experimentation results. The project subCULTron aims at achieving long-term collective robot exploration and monitoring of underwater environments. The demonstration will take place in the lagoon of Venice, a large shallow embayment composed of salt turbid water that represents a challenging environment for underwater robots as common sensors like vision or acoustic are difficult to handle. To overcome turbidity and confinement problems our robots will be equipped with artificial electric sensors that will be used as the main sensorial modality for navigation. Electric sense is a bio-inspired sense that has been developed by several species of fish living in turbid and confined underwater environment. In this paper, many different robotic behaviours based on the electric field perception will be presented, in particular we will address reactive navigation, object/robots detection, and object localization and estimation.

Underwater navigation in turbid water for exploration in catastrophic conditions or navigation in confined unstructured environments is still a challenge for robotics. In these conditions, neither vision nor sonar can be used. Pursuing a bio-inspired approach in robotics, one can seek solutions in nature to solve this difficult problem. Several hundred fish species in families Gymnotidae and Mormyridae have developed an original sense well adapted to this situation: the electric sense. Gnathonemus petersii first polarizes its body with respect to an electric organ discharge located at the base of its tail and generates a dipolar electric field in its near surroundings. Then, using many transcutaneous electro-receptors distributed along its body, the fish “measures” the distortion of the electric field and infers an image of its surroundings. Understanding and implementing this bio-inspired sense offers the opportunity to enhance the navigation abilities of our underwater robots in confined spaces bathed by turbid waters.

This paper presents the research done in the field of robotic cultural evolution in challenging real world environments. We hereby present these efforts, as part of project subCULTron, where we will create an artificial society of three cooperating sub-cultures of robotic agents operating in a challenging real-world habitat. We introduce the novel concept of “cultural learning”, which will allow a swarm of agents to locally adapt to a complex environment and exchange the information about this adaptation with other subgroups of agents. Main task of the presented robotic system is autonomous environmental monitoring including self organised task allocation and organisation of swarm movement processes. One main focus of the project is on the development and implementation of bio-inspired controllers, as well as novel bio-inspired sensor systems, communication principles, energy harvesting and morphological designs. The main scientific objective is to enable and study the emergence of a collective long-term autonomous cognitive system in which information survives the operational lifetime of individuals, allowing cross-generation learning of the society by self-optimising.

International audience; In underwater robotics, several homing and docking techniques are currently being investigated. They aim to facilitate the recovery of underwater vehicles, as well as their connection to underwater stations for battery charging and data exchange. Developing reliable underwater docking strategies is a critical issue especially in murky water and/or in confined and cluttered environments. Commonly used underwater sensors such as sonar and camera can fail under these conditions. We show how a bio-inspired sensor could be used to help guide an underwater robot during a docking phase. The sensor is inspired by the passive electro-location ability of electric fish. Exploiting the electric interactions and the morphology of the vehicle, a sensor-based reactive control law is proposed. It allows the guidance of the robot toward the docking station by following an exogenous electric field generated by a set of electrodes fixed to the environment. This is achieved while avoiding insulating perturbative objects. This control strategy is theoretically analysed and validated with experiments carried out on a setup dedicated to the study of electric sense. Though promising, these results are but a first step towards the implementation of an approach to docking in more realistic conditions, such as in turbid salt water or in the presence of conductive perturbative objects.

International audience; Recently, biologists have shown that the weakly electric fish are able to estimate the electric nature, the localization and the 3D geometric properties of an object using active electric sense. Incredibly, the Gnathonemus petersii performs this task in the dark only by moving towards and around the object, its vision is not required. In this paper, we proposed to address the challenging issue of object localization and shape estimation using a real underwater robot equipped with artificial electric sense. To that end, we used a corrected version of the dipolar tensor dedicated to small objects [Ammari et al., 2014] able to capture the electric response of big objects (typically objects whose size is about the one half of the robot length < 10cm). The principal contribution consists in the development of a multi-scale exhaustive search algorithm based on this tensor that allows to estimate in a same step the localization, orientation and shape of an object from electric currents measured along a given trajectory close to the object. Over 108 experiments, our method shows good results as on average we obtained 18% of shape error, 25 • of orientation error and 1cm of localization error within a range of [5, 11]cm distance with the robot. These results are promising since the problem solved is known to be complex localization and shape being intricately linked in the electrical measurements [Rasnow, 1996].

International audience; In this article we address the issue of shape estimation using electric sense inspired by the active electric fish. These fish can perceive their environment by measuring the perturbations in a self-generated electric field caused by nearby objects. The approach proceeded in three stages. Firstly the object was detected and its electric properties (insulator or conductor) identified. Secondly, the object was localized using the MUSIC (MUltiple SIgnal Classification) algorithm, which was originally developed to localize a radio wave emitter using a network of antennas. Thirdly, the shape estimation relied on the concept of generalized polarization tensor (GPT), which enabled modeling the electric response of an object polarized by an ambient electric field. We describe the implementation of the approach through numerous experiments. The system was able to estimate shape with an average error of 16%, and opened the way toward further improvements. In particular, self aligning the sensor with the ellipsoid through a reactive feedback makes the shape estimation errors drop to 10%.

International audience; This paper shows how a sensor inspired by an electric fish could be used to help navigate in confined environments. Exploiting the morphology of the sensor, the physics of electric interactions, as well as taking inspiration from passive electrolocation in real fish, a set of reactive control laws encoding simple behaviors, such as avoiding any electrically contrasted object, or seeking a set of objects while avoiding others according to their electric properties, is proposed. These reflex behaviors are illustrated on simulations and experiments carried out on a setup dedicated to the study of electric sense. The approach does not require a model of the environment and is quite cheap to implement.

International audience; — This paper deals with the geometrical properties of an ellipsoidal object (aspect ratio, volume, orientation) estimation with an underwater sensor inspired by the uncommon sense of the electric fish. The proposed method first locates the object independently of its geometrical properties thanks to the MUSIC (MUltiple SIgnal Classification) algorithm and then, estimates the geometrical properties using an optimization method and the object's electrical response model. The simulation results show the relevance of the method.

International audience; — By manipulation of electric fields, it is possible to detect the presence of foreign objects underwater. The presented work builds upon a previous result, in which was developed a neural network-based methodology allowing to address this detection problem for spherical objects. Hereafter, we show that the approach generalizes to the case of continuous walls. The technique relies on a neural model of the forward map (from scene configuration to electric measures). Exploiting this model, together with collected electric measures, it becomes possible to detect and infer the relative distance and orientation of a planar wall. In addition, we show that relying on a single forward model, only descriptive of the presence of a single wall, it is possible to address the same problem in presence of a combination of walls forming a corner or a corridor. Closing the motion control loop with information obtained using the proposed approach, it becomes possible to regulate position of a system at a fixed distance and orientation from a wall, with applications to the exploration and monitoring of flooded pipelines, or to surface quality monitoring of ships' hulls (in relation to biofouling). Data collected experimentally are used together with analytical models and numerical simulations to illustrate efficacy of the approach.

International audience; The weakly electric fish can perform complex cognitive tasks based on extracting information from blurry electric images projected from their immediate environment onto their electro-sensitive skin. In particular they can be trained to recognize the intrinsic properties of objects such as their shape, size and electric nature. They do this by means of original perceptual strategies that exploit the relations between the physics of a self generated electric field, their body morphology and the ability to perform specific movement termed Probing Motor Acts (PMA). In this article we artificially reproduce and combine these PMA to build an autonomous control strategy that allows an artificial electric sensor to find electrically contrasted objects and to orbit around them based on a minimum set of measurements and simple reactive feedback control laws of the probe's motion. The approach does not require any simulation model and could be implemented on an Autonomous Underwater Vehicle (AUV) equipped with artificial electric sense. The AUV has only to satisfy certain simple geometric properties, such as bilaterally (left/right) symmetrical electrodes and possess a reasonably high aspect (length/width) ratio.

International audience; — Navigation of cluttered underwater environments remains to this day a challenging task in mobile robotics. Applying an electric field to a mobile robot's direct environment and measuring perturbations of this field, one is able to detect the presence of obstacles in close proximity of the system. In addition, one is also able to infer a range of information relative to the detected objects, such as their position or electrical characteristics. Extracting such information from available measures typically requires a model (analytical, numerical or heuristic) descriptive of the relationship from geometry of the scene to measures performed (typically referred to as forward model), or of the inverse relationship (inverse model). In the following, we directly extract one such model from experimental data, and capture a forward model using a neural formalism. Then, using an iterative procedure, we are able to estimate the position of a detected object and assess the degree of confidence one can place on this estimate. Merit of the approach is illustrated using experimental data for a spherical obstacle.

Two observers based on high order sliding mode approach are proposed to determine the absolute orientation of a walking biped robot without feet. Contrary to velocities observers which have been often designed for robot control, very few works have been proposed for the orientation estimation: in this paper, the estimation of all state variables are derived from only the actuated joint variables. Then the technology problem of the absolute measurement is avoided. This latter point is an original contribution of this paper. The observers and the control law converge in finite-time and are well adapted for analysis of the cyclic walking gait. Then, a second original contribution consists in adapting an existing “simplified” Poincaré's sections-based analysis of the stability of the walking to nonlinear systems with not fully available state variables.

An observer-based controller is proposed for the walking of a biped without feet, i.e. an underactuated system in single support phase. The originality is both: first, the observer is based on second-order sliding mode approach and is original in biped robot context. Secondly, an existing “simplified” Poincare's sections-based analysis of the stability of the walking is adapted to nonlinear system with not fully available state variables.

International audience; Some fish species use electric sense to navigate efficiently in the turbid waters of confined spaces. This paper presents a first attempt to use this sense to control a group of nonholonomic rigid underwater vehicles navigating in a cooperative way. A leader whose motion is unknown to the others serves as an active agent for its passive neighbor, which perceives the leader's electric field via current measurements and moves in order to follow a trajectory relative to it. Then, this passive agent, becomes in its turn the leader for the next agent and so on. Sufficient conditions of convergence of the control law are derived for electric current servoing. This is achieved without the explicit knowledge of the location of the agents. Some limits on the possible motion of the leader along with the importance of the choice of controlled outputs are demonstrated. Switching between different group configurations by following a virtual agent is also described. Simulation and experimental results illustrate the theoretical study.

International audience; Thanks to an electro-sensible skin, some species of fish can feel the surrounding electric field generated by them-self or other fish. Known under the name of "electric-sense", this ability allows these fish to navigate in confined surroundings. Based on a bio-inspired electric sensor, this article presents how this electric sense can be used for the navigation in formation of several underwater vehicles. The formation considered is a file, each vehicle is assumed to follow its predecessor at a given distance. In confined environment, the file formation is interesting since fish can follow the same safe path. Being based on the servoing of the electric measurements, these laws do not require the knowledge of the location of the agents. The underwater vehicle studied have non holonomic properties, their forward velocity has no lateral component. Depending on the choice of the controlled outputs (combination of electric measures) we will see that path followed by the follower agents can be different and a methodology to choose the output will be defined in order that all the agents follow the leader path in presence of curved motion of the leader. The influence of the number of electrodes is discussed. Simulation results illustrate the proposed approach.

Electric fish sense the perturbations of a self-generated electric field through their electro-receptive skin. This sense allows them to navigate and reconstruct their environment in conditions where vision and sonar cannot work. In this article, we use a sensor inspired by this sense to address both problems of locating and estimating the size of small objects (electrolocation) and navigating in a tank. Based on a Kalman filter, any small object in the surroundings of the motion-controlled sensor can be modeled as an equivalent sphere whose location is well estimated by the filter. As a first application to the problem of navigation, the filter is included into a closed feedback loop in order to achieve wall following in a tank. Our experimental results demonstrate the feasibility of this approach.

International audience; This article presents the first research into designing an active sensor inspired by electric fish. It is notable for its potential for robotics underwater navigation and exploration tasks in conditions where vision and sonar would meet difficulty. It could also be used as a complementary omnidirectional, short range sense to vision and sonar. Combined with a well defined engine geometry, this sensor can be modeled analytically. In this article, we focus on a particular measurement mode where one electrode of the sensor acts as a current emitter and the others as current receivers. In spite of the high sensitivity required by electric sense, the first results show that we can obtain a detection range of the order of the sensor length, which suggests that this sensor principle can be used for robotics obstacle avoidance as it is illustrated at the end of the article.

International audience; Thanks to an electro-sensible skin, some species of fish can feel the perturbations of a self generated electric field caused by their surroundings variations. Known under the name of "electric-sense", this ability allows these fish to communicate and navigate in confined surroundings wetted by turbid waters where vision and sonar cannot work. Based on a bio-inspired electric sensor recently proposed in [1], this article presents a first attempt to use electric sense for the navigation in formation of a set of rigid underwater vehicles. The navigation strategy combines some behaviours observed in electric fish as well as a follower-leader strategy well known from multi-robot navigation. Being based one the servoing of the electric measurements, these laws do not require the knowledge of the location of the agents. Sufficient convergence conditions of the resulting control laws are given. Moreover, some limits on the possible motion of the leader are exhibited and the importance of the choice of controlled outputs is discussed too. Finally, simulation results illustrate the feasibility of the approach.