In this article, we propose a new algorithm for solving the forward dynamics of multibody systems consisting of rigid bodies connected in arbitrary topologies by localized joints and/or soft links, possibly actuated or not. The simulation is based on the implicit time integration of the Lagrangian model of these systems, where the soft links are modeled by Cosserat rods parameterized by assumed strain modes. This choice imposes a predictor–corrector structure on the approach, and requires computing both the residual vector and the Jacobian of the residual vector of the dynamics constrained by the time integrator. These additional calculations are handled here with a new Newton–Euler recursive inverse dynamics algorithm and its linearized tangent version. The approach is illustrated with numerical examples from the Cosserat rod literature and from recent robotic applications.

Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question:Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found?Not only we show that the answer to this question isyes, but we also provide necessary and sufficient conditions. More specifically, we look for a representation of the configuration space such that the right-hand side of the dynamics in Euler-Lagrange form becomes [IO]tu, being u the system input. We identify a class of systems, calledcollocated, for which this problem is solvable. Under mild conditions on the input matrix, a simple test is presented to verify whether a system is collocated or not. By exploiting power invariance, we provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, we use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, we consider several Lagrangian systems with a focus on continuum soft robots.

The robotics community has seen an exponential growth in the level of complexity of the theoretical tools presented for the modeling of soft robotics devices. Different solutions have been presented to overcome the difficulties related to the modeling of soft robots, often leveraging on other scientific disciplines, such as continuum mechanics, computational mechanics, and computer graphics. These theoretical and computational foundations are often taken for granted and this leads to an intricate literature that, consequently, has rarely been the subject of a complete review. For the first time, we present here a structured overview of all the approaches proposed so far to model soft robots. The chosen classification, which is based on their theoretical and numerical grounds, allows us to provide a critical analysis about their uses and applicability. This will enable robotics researchers to learn the basics of these modeling techniques and their associated numerical methods, but also to have a critical perspective on their uses.

This article 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 bioinspired 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 evolutions of these robots are the solutions of optimal control problems 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 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.

There is a growing interest on the study of continuum parallel robots (CPRs) due to their higher stiffness and better dynamics capacities than serial continuum robots (SCRs). Several works have focused on the computation of their geometrico- and kinemato-static models that can be sorted into two main categories. Models based on the continuous Cosserat equations are very accurate but assessing elastic stability with them is tricky, and discretized models allow easily checking the elastic stability, but they require a large number of elastic variables to be accurate. In this article, we extend an approach based on assumed strain modes developed for the dynamics of SCRs to the statics of CPRs. This method is able to predict the robot configuration with an excellent accuracy with a very limited number of elastic variables, contrary to other discretization methods. The method is also more than 100 times faster than finite differences for a better prediction accuracy. Finally, it is possible to assess the robot elastic stability by only checking the Hessian of the potential energy as for any discretization method, thus making the analysis of this property simpler than for the continuous Cosserat model. All results are validated through simulations on two case studies.

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 multisegment, general routing tendon actuated continuum robots in their nominal static operating regime. This article 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.

This paper reports methods to compute the equilibrium stances of a new snake-like robot designed to stabilize its head on a free water surface. To adjust rapidly the stability of the robot, this bio-inspired robot can rotate independently each body-shell, and modify the level of immersion of each module. To predict the stable stance accessible by this additional degree of freedom, a model is developed to compute the equilibrium configurations of the robot from a given parametrization of the body shape. Then, an algorithm is introduced to compute a sequence of controlled body deformations, such that the head configuration relatively to the water surface remains unchanged. Finally, we explore in simulation stances and quasi-static gaits, and investigate to what extent the buoyancy and the body deformations can be used to stabilize the head of the snake-like robot.

In this article, we propose a new dynamic model of Cosserat beams in view of its application to continuum and soft robotics manipulation and locomotion. In contrast to usual approaches, it is based on the nonlinear parameterization of the beam shape by its strain fields and their reduction on a functional basis of strain modes. While remaining geometrically exact, the approach provides us with a minimal set of ordinary differential equations in the usual Lagrange matrix form that can be exploited for analysis and control design. Inspired from rigid robotics, the calculation of the matrices of this Lagrangian model is performed with a new reduced inverse Newton-Euler algorithm. To assess the approach, this Lagrangian model is compared against a well-validated finite element method through several benches of nonlinear structural statics and dynamics.

In the 50s, biologists discovered that some electric hsh 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 held. In this article, we address the challenging issue of ellipsoidal objects pose and size estimation for underwater robots equipped with artihcial 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 efhciency 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 1 cm and 15%, respectively, while offering promising perspectives for real-time computation.

Nowadays, the most adopted model for the design and control of soft robots is the piecewise constant curvature model, with its consolidated benefits and drawbacks. In this work, an alternative model for multisection soft manipulator dynamics is presented based on a discrete Cosserat approach, in which the continuous Cosserat model is discretized by assuming a piecewise constant strain along the soft arm. As a consequence, the soft manipulator state is described by a finite set of constant strains. This approach has several advantages with respect to the existing models. First, it takes into account shear and torsional deformations, which are both essential to cope with out-of-plane external loads. Furthermore, it inherits desirable geometrical and mechanical properties of the continuous Cosserat model, such as intrinsic parameterization and greater generality. Finally, this approach allows to extend to soft manipulators, the recursive composite-rigid-body and articulated-body algorithms, whose performances are compared through a cantilever beam simulation. The soundness of the model is demonstrated through extensive simulation and experimental results.

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.

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.

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 foreign objects 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 object.

This paper reports on the development and validation of the elastodynamics model of an innovative underwater soft-bodied robot inspired by cephalopods. The vehicle, for which the model is devised, is propelled by a discontinuous activation routine which entails the collapse of an elastic shell via cable transmission and its following passive re-inflation under the action of the elastic energy stored in the shell walls. Activation routine and thrust characterization have been determined to depend massively on the capability of the shell to elastically return to its unstrained state, hence an accurate description of the dynamics of the shell during all stages of actuation and at various degrees of deformation is essential. The model, based on a geometrically exact Cosserat theory, is validated against measurement achieved from an ad-hoc experimental apparatus, bringing evidence of its aptness at capturing the key parameters of the system. Eventually the model is employed for simulating a proper propulsion routine in water demonstrating that, upon suitable parametrization of the internal and external hydrodynamics, it can reliably be employed for the realistic quantitative characterization of the cephalopod-inspired robot.

In paper [“Reduced locomotion dynamics with passive internal DoFs: Application to nonholonomic and soft robotics,” IEEE Trans. Robot., vol. 30, no. 3, pp. 578–592, Jun. 2014; Boyer, F. and Belkhiri, A.], we proposed a general modeling framework to address locomotion systems containing internal passive degrees of freedom. Unfortunately, we committed an error in illustrating the approach on the 3-D model of the bicycle. In this erratum, we correct this error which concerns the kinematic model of the bicycle.

The paper deals with the dynamic modeling of bio-inspired robots with soft appendages such as flying insect-like or swimming fish-like robots. In order to model such soft systems, we propose to use the Mobile Multibody System framework introduced in [1], [2], [3]. In such a framework, the robot is considered as a tree-like structure of rigid bodies where the evolution of the position of the joints is governed by stress-strain laws or control torques. Based on the Newton-Euler formulation of these systems, we propose a new algorithm able to compute at each step of a time loop both the net and passive joint accelerations along with the control torques supplied by the motors. To illustrate, based on previous work [4], the proposed algorithm is applied to the simulation of the hovering flight of a soft flapping-wing insect-like robot (see the attached video).

Bio-inspired by moth or humming-birds, several micro air vehicles (MAV) have recently been developed. In these systems, the motion of the lifting surface is complex and modeled by flapping motion-controlled soft wings. The synchronization of the actuated periodic flapping motion of the wings and that of passive twisting degrees of freedom (dof) allows producing hovering flight. Depending on the feature of the MAV such as stiffness, and geometric characteristic, hovering flight can be naturally stable or not. In the first case hovering is obtained via an open loop control (or a local closed loop control) while in the second case a global control strategy is required to achieve the same objectives. Thus, it is crucial to take into account the influence of the design of the MAV on the control in order to choose an appropriate morphology that can reduce the burden of control. In this paper mathematical tools and methodologies are proposed to achieve this objective and reduce the computational cost of control.

This paper proposes a general modeling approach for locomotion dynamics of mobile multibody systems containing passive internal degrees of freedom concentrated into (ideal or not) joints and/or distributed along deformable bodies of the system. The approach embraces the case of nonholonomic mobile multibody systems with passive wheels, the pendular climbers, and the locomotion systems bioinspired by animals that exploit the advantages of soft appendages such as fish swimming with their caudal fin or moths that use the softness of their flapping wings to improve flight performance. The paper proposes a general structured modeling approach of MMS with tree-like structures along with efficient computational algorithms of the resulting equations. The approach is illustrated through nontrivial examples such as the 3-D bicycle and a compliant version of the snake-board.

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.

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.

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.

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.

This article proposes a solution to the problem of the navigation of underwater robots in confined unstructured environments wetted by turbid waters. The solution is based on a new sensor bio-inspired from electric fish. Exploiting the morphology of the sensor as well as taking inspiration from passive electro-location in real fish, the solution turns out to be a sensory-motor loop encoding a simple behavior relevant to exploration missions. This behavior consists in seeking conductive objects while avoiding insulating ones. The solution is illustrated on experiments. It is robust and works even in very unstructured scenes. It does not require any model and is quite cheap to implement.

Electric fish feel 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 bio-inspired from this active sense to address the problem of small objects reconstruction and electrolocation. Based on a Kalman filter, any small object in the surrounding of the motion controlled sensor can be encapsulated into an equivalent sphere whose location is well estimated by the filter. Experimental results illustrate the feasibility of the approach.

Morphology, perception and locomotion are three key features highly inter-dependent in robotics. This paper gives an overview of an underwater modular robotic platform equipped with a bio-inspired electric sense. The platform is reconfigurable in the sense that it can split into independent rigid modules and vice-versa. Composed of 9 modules, the longer entity can swim like an eel over long distances, while once detached, each of its modules is efficient for small displacements with a high accuracy. Challenges are to mechanically ensure the morphology changes and to do it automatically. Electric sense is used to guide the modules during docking phases and to navigate in unknown scenes. Several aspects of the design of the robot are described and a particular attention is paid to the inter-module docking system. The feasibility of the design is assessed through experiments.

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.

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.

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.

BACKGROUND: The automatic identification of syntenies across multiple species is a key step in comparative genomics that helps biologists shed light both on evolutionary and functional problems. RESULTS: In this paper, we present a versatile tool to extract all syntenies from multiple bacterial species based on a clear-cut and very flexible definition of the synteny blocks that allows for gene quorum, partial gene correspondence, gaps, and a partial or total conservation of the gene order. CONCLUSIONS: We apply this tool to two different kinds of studies. The first one is a search for functional gene associations. In this context, we compare our tool to a widely used heuristic--I-ADHORE--and show that at least up to ten genomes, the problem remains tractable with our exact definition and algorithm. The second application is linked to evolutionary studies: we verify in a multiple alignment setting that pairs of orthologs in synteny are more conserved than pairs outside, thus extending a previous pairwise study. We then show that this observation is in fact a function of the size of the synteny: the larger the block of synteny is, the more conserved the genes are.

This paper is related to the inverse-dynamic modeling of mobile multibody systems articulated with joints and wheels. An easily-implementable algorithm, which is based on Newton-Euler (NE) recursive dynamics, is proposed. From imposed joint and/or actuated-wheel motions, the algorithm performs fast calculations of the control torques, as well as the overall rigid motions involved in locomotion tasks. The engineering applications include tree-like mobile manipulators, satellite-reorientation systems, and modular robots, such as snake-like robots, eel-like robots, and a snakeboard.

The aim of this paper is to perform the navigation of an underwater robot equipped with a sensor using the electric sense. The robot navigates in an unbounded environment in presence of spheres. This sensor is inspired of some species of electric fish. A model of this sensor composed of n spherical electrodes is established. The variations of the current due to the presence of the sphere is related to the model of Rasnow. Unscented Kalman Filter is used to localize the robot with respect to the sphere and to estimate the size of the sphere. We show that bio-inspired motions improve the detection of the spheres. We illustrate the efficiency of the method in two cases: a two electrodes sensor and a four electrodes sensor.

MOTIVATION: Fluorescent and luminescent reporter gene systems in combination with automated microplate readers allow real-time monitoring of gene expression on the population level at high precision and sampling density. This generates large amounts of data for the analysis of which computer tools are missing to date. RESULTS: We have developed WellReader, a MATLAB program for the analysis of fluorescent and luminescent reporter gene data. WellReader allows the user to load the output files of microplate readers, remove outliers, correct for background effects and smooth and fit the data. Moreover, it computes biologically relevant quantities from the measured signals, notably promoter activities and protein concentrations, and compares the resulting expression profiles of different genes under different conditions. AVAILABILITY: WellReader is available under a LGPL licence at http://prabi1.inrialpes.fr/trac/wellreader.

In this paper, a multi-variable feedback design for the 3D movement of an eel-like robot is presented. Such a robot is under construction in the context of a national French robotic project. The proposed feedback enables the tracking of a desired 3D position of the eelpsilas head as well as the stabilization of the rolling angle. The control design is based on a recently developed reduced model that have been validated using a 3D complete continuous model described in [3]. Several scenarios are proposed to assess the efficiency of the proposed feedback law.

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%.

This paper relates recent advances in the design of feedback laws for the 3D movement of an Eel-like robot. Such a robot is under construction in the context of a national French robotic project. The proposed feedback enables the tracking of a desired 3D position of the Eel head as well as the stabilization of the rolling angle. A velocity controller is also proposed. The controller is tested on a recently developed complete 3D model in order to assess its efficiency in tackling 3D manoeuvres.

UNLABELLED: Chromosomes or other long DNA sequences contain many highly similar repeated sub-sequences. While there are efficient methods for detecting strict repeats or detecting already characterized repeats, there is no software available for detecting approximate repeats in large DNA sequences allowing for weighted substitutions and indels in a coherent statistical framework. Here, we present an implementation of a two-steps method (seed detection followed by their extension) that detects those approximate repeats. Our method is computationally efficient enough to handle large sequences and is flexible enough to account for influencing factors, such as sequence-composition biases both at the seed detection and alignment levels. AVAILABILITY: http://wwwabi.snv.jussieu.fr/public/RepSeek/

This paper presents the dynamic modeling of a 3-D-serial underwater eel-like robot using recursive algorithms based on the Newton--Euler equations. Both direct and inverse models are treated in the paper. The inverse dynamic model algorithm gives the head acceleration and the joint torques as a function of the joint positions, velocities, and accelerations. The direct dynamic model gives the head and joint accelerations as a function of the joint positions, velocities, and input torques. The proposed algorithms can be considered as a generalization of the recursive Newton--Euler dynamic algorithms of serial manipulators with fixed base. The algorithms are easy to implement and to simulate whatever the number of degrees of freedom of the robot. An example with 12 spherical joints is presented. The fluid forces have been taken into account using a simple model based on Morison's model.

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

In this paper, we present the dynamic modeling of a 3D-serial underwater eel-like robot using recursive algorithm based on the Newton-Euler equations. The algorithm gives the head accelerations and the joint torques as a function of the joint positions, velocities and accelerations. The proposed algorithm can be considered as a generalization of the recursive Newton-Euler inverse dynamic algorithm of serial manipulators with fixed base. The proposed algorithm is easy to implement and to simulate whatever the number of degrees of freedom of the robot. Simulation results with a 12-spherical joint structure are presented.

MOTIVATION: Modern comparative genomics does not restrict to sequence but involves the comparison of metabolic pathways or protein-protein interactions as well. Central in this approach is the concept of neighbourhood between entities (genes, proteins, chemical compounds). Therefore there is a growing need for new methods aiming at merging the connectivity information from different biological sources in order to infer functional coupling. RESULTS: We present a generic approach to merge the information from two or more graphs representing biological data. The method is based on two concepts. The first one, the correspondence multigraph, precisely defines how correspondence is performed between the primary data-graphs. The second one, the common connected components, defines which property of the multigraph is searched for. Although this problem has already been informally stated in the past few years, we give here a formal and general statement together with an exact algorithm to solve it. AVAILABILITY: The algorithm presented in this paper has been implemented in C. Source code is freely available for download at: http://www.inrialpes.fr/helix/people/viari/cccpart.

This article presents two simulators of the dynamics of flexible manipulators composed of slender elastic beams. Contrary to the standard dynamic modelling approaches the dynamic models proposed can model moderate deformations or some second order effects, which appear in some limit cases as high velocities, accelerations or tip forces and torques. The models are premised on an exact nonlinear Euler Bernouilli field and the expansion in perturbations is only achieved at the end of the dynamic modelling. This procedure allows one to obtain consistent linear and quadratic models. The two simulation algorithms are based on the Newton-Euler model of the dynamics: a global projective algorithm and a recursive one. Simulation results are reported for a long and thin 4-DOF manipulator.

This article presents a new approach of modeling the dynamics of flexible manipulators composed of slender elastic beams. Contrary to the standard dynamic modeling approaches the model proposed here does not require any assumption on the smallness of the elastic displacement and rotation fields. Thus the given model is completely nonlinear with respect to the elastic kinematics and leads by using Taylor series expansions to the exact first and second order dynamic models.

This paper presents an efficient algorithm for the calculation of the direct dynamic model of flexible manipulators. The algorithm is based on the inverse Newton-Euler model of flexible manipulators as developed previously by the authors (1995). The given algorithm can be considered as a generalization of the rigid manipulators algorithm given by Walker-Orin (1982). The algorithm is programmed using Mathematica to obtain automatically customized symbolic models with reduced number of operations.

In this paper, we propose an efficient recursive computation of the nonlinear computed torque law of flexible manipulators. The algorithm is based on the generalized Newton-Euler model of flexible manipulators and can be considered as a generalization of the computed torque control algorithm of rigid robots proposed by Luh-Walker-Paul (1980). It is programmed using Mathematica to get automatically an efficient customized symbolic model with reduced number of operations.