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International audience; This paper contributes to the design of a family of homogeneous controllers to deal with the trajectory tracking problem in unicycle mobile robots (UMRs). The control strategy is based on a cascade control paradigm, which includes the position and orientation tracking error subsystems. The proposed homogeneous controllers provide different types of convergence to zero for the tracking error dynamics, i.e., asymptotic, exponential and finite-time convergence. Simulation results illustrate the performance of the proposed family of homogeneous controllers.

International audience; The problem of prescribed-time cooperative state estimation is addressed in this paper. A network of strongly connected (linear homogenous) distributed observers are designed under the assumption that each observer can receive a time-varying scalar signal broadcasted by a supervisor. By a proper parameter tuning, the observer gains go infinity and estimation errors correspondingly reach zeros at the settling time prescribed by users.

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International audience; In this paper, we propose a physics-based model of suction phenomenon to achieve simulation of deformable objects like suction cups. Our model uses a constraint-based formulation to simulate the variations of pressure inside suction cups. The respective internal pressures are represented as pressure constraints which are coupled with anti-interpenetration and friction constraints. Furthermore, our method is able to detect multiple air cavities using information from collision detection. We solve the pressure constraints based on the ideal gas law while considering several cavity states. We test our model with a number of scenarios reflecting a variety of uses, for instance, a spring loaded jumping toy, a manipulator performing a pick and place task, and an octopus tentacle grasping a soda can. We also evaluate the ability of our model to reproduce the physics of suction cups of varying shapes, lifting objects of different masses, and sliding on a slippery surface. The results show promise for various applications such as the simulation in soft robotics and computer animation.

A generalized homogeneous control with integral action for a multiple-input plant operating under uncertainty conditions is designed. The stability analysis is essentially based on a special version of the non-smooth Lyapunov function theorem for differential equations with discontinuous right-hand sides. A Lyapunov function for analysis of the closed-loop system is presented. For negative homogeneity degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, the maximum control magnitude and the settling-time of the closed-loop system are estimated and a class of disturbances to be rejected by the control law is characterized. The control parameters are tuned by solving a system of Linear Matrix Inequalities (LMIs), whose feasibility is proved at least for small (close to zero) homogeneity degrees. The theoretical results are illustrated by numerical simulations.

International audience; Cochlear implants made of standard silicone electrode array (EA) are currently used to stimulate the auditory nerve of patients’ cochlea. The implants have a proximaldiameter of 0.5mm and 2~3cm long composed of 20 bulk platinum electrodes and connection wires (Ø 25µm). Due to their stiffness and passive nature, the most difficult task during implant surgery is inserting the EA properly into the tympanic ramp of the patient's cochlea, often leading to trauma or incomplete insertion. In this work, we developed an original smart EA for efficient insertion. This prototype has a lower stiffness and functionalized with an electronic conducting polymer based micro-actuators able to bend under low electrical voltage stimulation. This prototype is expected to reduce the friction forces during insertion, allow better control of the insertion process, facilitate the work of the surgeon and decrease the probability of trauma.

International audience; Highlights Solutions to Large Beam-deflection Problems by Taylor series and Padé approximant for Compliant Mechanisms Ke Wu,Gang Zheng • We solved large beam-deflection problems by Taylor series method. • We solved large beam-deflection problems by Padé approximant. • We provided convergence analysis on the 2 methods. • We proved the feasibility of modeling CMs using the 2 methods.

International audience; Tendon-driven continuum robots show promise for use in surgical applications as they can assume complex configurations to navigate along tortuous paths. However, to achieve these complex robot shapes, multiple segments are required as each robot segment can bend only with a single constant curvature. To actuate these additional robot segments, multiple tendons must typically be added on-board the robot, complicating their integration, robot control, and actuation. This work presents a method of achieving two curvatures in a single tendon-driven continuum robot segment through use of a novel magnetic locking mechanism. Thus, the need for additional robot segments and actuating tendons is eliminated. The resulting two curvatures in a single segment are demonstrated in two and three dimensions. Furthermore, the maximum magnetic field required to actuate the locking mechanism for different robot bending angles is experimentally measured to be 6.1 mT. Additionally, the locking mechanism resists unintentional unlocking unless the robot assumes a 0°bending angle and a magnetic field of 18.1 mT is applied, conditions which are not typically reached during routine use of the system. Finally, addressable actuation of two locking mechanisms is achieved, demonstrating the capability of producing multiple curvatures in a single robot segment.

International audience; Embodied intelligence, or intelligence that requires and leverages a physical body, is ubiquitous in biological systems, both in animals and plants. Through embodied intelligence, biological systems efficiently interact with and use their surrounding environment to let adaptive behaviour emerge. In soft robotics, this is a well-known paradigm, whose mathematical description and consequent computational modelling remain elusive. We argue that filling this gap will enable full uptake of embodied intelligence in soft robots. The resulting models can be used for design and control purposes. In this paper, we provide a concise guide to the main mathematical modelling approaches, and consequent computational modeling strategies, that can be used to describe soft robots and their physical interactions with the surrounding environment, including fluid and solid media. The goal of this perspective is to convey the challenges and opportunities within the context of modeling the physical interactions underpinning embodied intelligence. We emphasize that interdisciplinary work is required, especially in the context of fully coupled robot-environment interaction modeling. Promoting this dialogue across disciplines is a necessary step to further advance the field of soft robotics.

International audience; Due to the compliance of tendon-driven continuum robots, carrying a load or experiencing a tip force result in variations in backbone curvature. While the spatial robot configuration theoretically needs an infinite number of parameters for exact description, it can be well approximated using Euler Arc Splines which use only six of them. In this letter, we first show the accuracy of this representation by fitting the Euler Arc splines directly to experimentally measured robot shapes. Additionally, we propose a 3D static model that can account for gravity, friction and tip forces. We demonstrate the utility of using efficient parameterization by analyzing the computation time of the proposed model and then, using it to propose a hybrid model that combines physics-based model with observed data. The average tip error for the Euler arc spline representation is 0.43% and the proposed static model is 3.25% w.r.t. robot length. The average computation time is 0.56 ms for nonplanar deformations for a robot with ten disks. The hybrid model reduces the maximum error predicted by the static model from 8.6% to 5.1% w.r.t. robot length, while using 30 observations for training.

International audience; We formulated the large beam-deflection problem as a general nonlinear BVP. • We reviewed the commonly used methods for modeling beam deflection in CMs. • We introduced efficient numerical methods to solve beam deflection problems. • We provided comments and analysis about all the mentioned methods.

International audience; This paper investigates the exterior workspace boundary of a soft robot with a certain configuration controlled by equipped bounded actuators. To achieve this, we implement an optimization-based approach on the studied soft robot which has been modeled by the Finite Element Method (FEM). Finally, we provide numerical simulations of various configurations to demonstrate the validity of the suggested technique, which, in comparison to the conventional forward method, may considerably minimize the complexity of exterior workspace boundary estimation.

International audience; Recently soft robotics has rapidly become a novel and promising area of research with many designs and applications due to their flexible and compliant structure. However, it is more difficult to derive the nonlinear dynamic model of such soft robots. The differential kinematics and dynamics of the soft manipulator can be formulated as a set of highly nonlinear partial differential equations (PDEs) via the classic Cosserat rod theory. In this work, we propose a discrete modeling technique named piecewise linear strain (PLS) to solve the PDEs of Cosserat-based models, based on which the associated analytic models are deduced. To validate the accuracy of the proposed Cosserat model, the static model of the conical cantilever rod under gravity as a simple example is simulated by using different discretization methods. Results indicate that PLS Cosserat model is comparable to the mechanical deformation behavior of real-world soft manipulator. Finally, a parameters identification scheme for this model is established, and the simulation as well as experimental validation demonstrate that using this method can identify the model physical parameters with high accuracy.

Compliant mechanisms (CMs) have presented its inherently advantageous properties due to the fact that CMs utilize elastic deformation of the elementary flexible members to transfer motion, force, and energy. Previously, the classic Euler–Bernoulli beam theory is the most used theory in terms of modeling large beam deflections in CMs. However, it has some assumptions that may decrease the modeling accuracy, such as ignoring the shear strain and the axial strain of cross sections. In this article, to take into account the shear and axial strains, we adopt the Timoshenko beam theory along with some modifications to consider the axial elongation. To simplify the complexity of the proposed governing boundary value problem (BVP), we transform the BVP into an explicit formulation and use weighted residual methods to numerically approximate the solution. We first focus on the single-beam deflection of a straight beam and an initially curved beam (ICB) using Euler–Bernoulli beam theory, Timoshenko beam theory, and solid mechanics to analyze the contributions of the influences of shear and axial strains in beam deflections. Then, we prove the feasibility of the proposed modeling strategy via mechanism synthesis for a bi-stable mechanism and an ICB-based parallelogram mechanism. Finally, the deduction of the mathematical model and the numerical results are provided along with brief analysis on the mechanical performances of the studied CMs.

International audience; Considering a soft robot with installed bounded actuators, this paper studies the reachable workspace estimation problem for a pre-chosen point of interest. To this aim, the method of nite-element has been used to obtain the static model of the studied robot and two methods are proposed (forward one which is based on Newton iterative method and forward-backward one which is based on interval analysis techniques) to study this estimation problem. Various simulations with dierent conguration scenarios are provided to show the eectiveness of the forward-backward approach which can largely reduce the exploration time, compared to the forward method.

International audience; This paper presents a sliding mode observer (SMO) design method to estimate the states and unknown inputs (UIs) in a class of non-infinitely observable (NIO) descriptor systems that contain UIs in both the state and output equations. Existing works on SMO design for NIO systems did not consider UIs in the output equation. In order to overcome the difficulty caused by UIs in output channels and the NIO condition, we reformulated the original system and introduced new UIs to replace the original UIs to obtain an equivalent infinitely observable descriptor system whose output does not contain any UI. Based on the developed equivalent system, a new SMO method is proposed to estimate both the states and the UIs. Subsequently, the necessary and sufficient conditions for the existence of the SMO are derived in terms of the original system matrices, which thus makes the conditions easy to be examined. Finally, an example is used to verify the effectiveness of the proposed method.

International audience; The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the computation to make it real-time. In this paper, we propose a learning-based approach to obtain a compact but sufficiently rich mechanical representation. Our choice is based on nonlinear compliance data in the actuator/effector space provided by a condensation of the FEM model. We demonstrate that this compact model can be learned with a reasonable amount of data and, at the same time, be very efficient in terms of modeling, since we can deduce the direct and inverse kinematics of the robot. We also show how to couple some models learned individually in particular on an example of a gripper composed of two soft fingers. Other results are shown by comparing the inverse model derived from the full FEM model and the one from the compact learned version. This work opens new perspectives, namely for the embedded control of soft robots, but also for their design. These perspectives are also discussed in the paper.

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.

Compliant mechanisms (CMs), as a novel type of mechanical systems, utilize the elastic deformation of the builtin elementary flexible members to transfer motion, force and energy. Due to their inherent advantages, CMs have been widely used in various mechanical applications. However, in the current literature, researchers still suffer from the lack of efficient tools and a comprehensive analysis framework for designing CMs. To more systematically and efficiently analyze CMs for application-oriented purposes, this thesis aims to propose a comprehensive methodology of designing, modeling, optimizing and controlling CMs. Detailed derivations have been presented on the aforementioned perspectives, followed by both numerical and experimental validation.; Les mécanismes compliants (CM), en tant que nouveau type de systèmes mécaniques, utilisent la déformation élastique des éléments flexibles intégrés pour transférer le mouvement, la force et l'énergie. En raison de leurs avantages inhérents, les CM sont largement utilisés dans diverses applications mécaniques. Cependant, dans la littérature actuelle, les chercheurs souffrent toujours du manque d'outils efficaces et d'un cadre d'analyse complet pour la conception des CM. Afin d'analyser de manière plus systématique et efficace les CM, cette thèse vise à proposer une méthodologie complète de conception, de modélisation, d'optimisation et de contrôle des CM. Des dérivations détaillées ont été présentées sur les perspectives mentionnées ci-dessus, suivies de validations numériques et expérimentales.

International audience; In this paper, a novel concept for a phantom of the prostate is introduced. To study and improve automated, robotized medical interventions, reliable phantoms are essential. During brachytherapy and biopsy, the prostate will undergo displacements and changes in orientation due to the needle insertion. Therefore, there is a shift in the target regions for radioactive seed deposition or biopsy acquisition. These shifts need to be taken into account for precise dosimetry. Furthermore, the organ can undergo deformations due to edemas with the same shifting result. Therefore, in this paper we propose a bioinspired phantom (BIP) for the prostate that is equipped with sensors and coupled with a numerical simulation for estimating deformations due to external forces. We have also put in place a cavity inside the phantom where pressure can be applied to enable the emulation of prostate growth due to inflammation. The phantom is conceived in such a way that it will be MRIsafe. It can thus be deployed for the in-bore study of automated brachytherapy and biopsy. In our evaluation, we verify that the changes in pose of the phantom can be correctly estimated and that these motions are plausible from a clinical point of view.

The research works briefly reviewed in this dissertation deal with questions related to the use of data in interactive simulations for applications in medicine and soft robotics. Geometrical modeling, (bio-)mechanical modeling as well as optimization techniques to reduce the computational footprint are presented. Using patient- specific or environment data with optimization techniques and simulation enables more realistic and predictive models and opens the way for new applications. Several examples are presented in the manuscript where our simulations were fed with data from medical images, videos streams or pre-operative data in order to provide more accurate medical simulations to provide better diagnoses or in the context of soft-robotics where visual servoing provides a more robust and stable control of soft-robots.; Les travaux de recherche examinés dans ce manuscrit traitent des questions liées à l’utilisation des données dans les simulations interactives pour des applications en médecine et en robotique déformable. La modélisation géométrique, la modélisation (bio-)mécanique ainsi que les techniques d’optimisation pour réduire l’empreinte de calcul sont présentées. L’utilisation de données spécifiques au patient ou à l’environnement avec des techniques d’optimisation et de simulation permet des modèles plus réalistes et prédictifs et ouvre la voie à de nouvelles applications. Plusieurs exemples sont présentés dans le manuscrit où nos simulations ont été alimentées avec des données provenant d’images médicales, de flux vidéo ou de données préopératoires afin de fournir des simulations médicales plus précises pour fournir de meilleurs diagnostics ou dans le contexte de la robotique déformable où l’asservissement visuel fournit un contrôle plus robuste et stable des robots souples.

International audience; Conducting polymer (CP) actuator has nonlinear dynamic characteristics during its charge process. In this study, we proposed an electromechanic model and an optimal controller for a type of ionic electroactive polymer (IEPA) actuator with submillimeter scale, which can produce large deformation under low actuation voltage. The electronic model is to describe the evolution of charge state in time domain. The mechanic model is to calculate the deformation of CP actuator under the actuation force and external force. Based on the electromechanic coupling model, a parameter identification method is proposed to estimate the nonlinear parameter of CP actuator. The experiments show that our electromechanic model successfully predicts the deformation of actuator under different input voltages with the identified parameters. In the last step, an optimal controller is designed to control the orientation of IEAP actuator, which achieves at a high control performance in our experiments. The success of the modeling and control lays the foundation work for the subsequent biomedical applications.

International audience; OpenAI Gym is one of the standard interfaces used to train Reinforcement Learning (RL) Algorithms. The Simulation Open Framework Architecture (SOFA) is a physics based engine that is used for soft robotics simulation and control based on real-time models of deformation. The aim of this paper is to present SofaGym, an open source software to create OpenAI Gym interfaces, called environments, out of soft robot digital twins.The link between soft robotics and RL offers new challenges for both fields: representation of the soft robot in a RL context, complex interactions with the environment, use of specific mechanical tools to control soft robots, transfer of policies learned in simulation to the real world, etc. The article presents the large possible uses of SofaGym to tackle these challenges by using RL and planning algorithms. This publication contains neither new algorithms nor new models but proposes a new platform, open to the community, that offers non existing possibilities of coupling RL to physics based simulation of soft robots. We present 11 environments, representing a wide variety of soft robots and applications, we highlight the challenges showcased by each environment. We propose methods of solving the task using traditional control, RL and planning and point out research perspectives using the platform.

In this article, we investigate the position-access workspace estimation of slender soft manipulators controlled via arranged bounded actuators. For this, we implement a so-called forward-backward approach on the mathematical model of the investigated soft robot deduced via the adopted Discrete Cosserat method. The proposed methodology is validated on several planar and spatial slender soft manipulators’ configurations, where we show its advantage of reducing computation complexity for estimating the workspace, compared to traditional forward approach.

International audience; An attitude tracking problem for a full-actuated rigid body in 3-D is studied using a model of rotation dynamics on the Lie group SO(3). A generalized homogeneous control is adopted to achieve tracking of a smooth attitude trajectory in a finite-time. The attitude dynamics on the Lie algebra so(3) is utilized to design the homogeneous control, since SO(3) is not a vector space. A switch control is proposed for achieving global finite-time tracking by combining a global asymptotic control with local homogeneous control. The simulations illustrate the performance of the proposed control algorithm.

Soft robotics is a recent field of robotics. It differs from classical rigid robotics by exploiting the compliance of the robot to create motion by deformation, rather than relying on articulations. Thanks to their inherent compliant composition, soft robots are particularly adapted for motion for deploying through unknown environment, grasping fragile objects or notably for human interactions. Soft systems are essentially fabricated with a homogeneous compliant material, like silicone. However, other, more relevant material choices could be made to design theserobots. Recent works started to investigate the use of multimaterials, metamaterials or even smart materials inside soft structures to build systems with programmed compliance. In this work, we make the choice of using a stochastic foam to program soft robots structures with anisotropy using fiber direction on a given geometry. Using this foam, we show that we can create new controllable kinematics without changing the geometry of soft robots. The anisotropic soft robots are modeled using a Finite Element Method (FEM) with homogenised mechanical properties. We present a complete workflow: from model simulation and design to fabrication and interactive control with inverse simulation. Finally, we present a new generic mechanical calibration method and use it to reduce the sim2real discrepancy.; Soft robotics is a recent field of robotics. It differs from classical rigid robotics by exploiting the compliance of the robot to create motion by deformation, rather than relying on articulations. Thanks to their inherent compliant composition, soft robots are particularly adapted for motion for deploying through unknown environment, grasping fragile objects or notably for human interactions. Soft systems are essentially fabricated with a homogeneous compliant material, like silicone. However, other, more relevant material choices could be made to design theserobots. Recent works started to investigate the use of multimaterials, metamaterials or even smart materials inside soft structures to build systems with programmed compliance. In this work, we make the choice of using a stochastic foam to program soft robots structures with anisotropy using fiber direction on a given geometry. Using this foam, we show that we can create new controllable kinematics without changing the geometry of soft robots. The anisotropic soft robots are modeled using a Finite Element Method (FEM) with homogenised mechanical properties. We present a complete workflow: from model simulation and design to fabrication and interactive control with inverse simulation. Finally, we present a new generic mechanical calibration method and use it to reduce the sim2real discrepancy.

International audience; Soft continuum robots, and comparable instruments allow to perform some surgical procedures noninvasively. While safer, less morbid and more cost-effective, these medical interventions increase the complexity for the practitioners: the manipulation of anatomical structures is indirect through telescopic and flexible devices and the visual feedback is indirect through monitors. Interventional cardiology is an example of complex procedures where catheters and guidewires are manipulated to reach and treat remote areas of the vascular network. Such interventions may be assisted with a robot that will operate the tools but the planning (choice of tools and trajectories) remains a complex task. In this paper we use a simulation framework for flexible devices inside the vasculature and we propose a method to automatically control these devices to reach specific locations. Experiments performed on 15 patient geometries exhibit good performance. Automatic manipulation reaches the goal in more than 90% of the cases.

International audience; This paper aims at contributing to the sim2real challenge in soft robotics. We present a method for automatic finite element model calibration based on real data using quadratic programming optimisation. The method is generic and evaluated in this study to fit mechanical parameters from anisotropic materials. We show that we are able to optimise the mechanical properties of a given structure along its shape to achieve a given configuration goal. We show the methods interest for calibration by taking reference points from a real world robot and use them in our optimisation process as goals the simulation has to match. Our process will minimise the errors introduced by manufacturing, imperfect models or even mechanical fatigue/plasticity.

International audience; In this paper, we investigate the observation and stabilisation problems for a class of linear time-invariant systems, subject to unknown states, and network constraints, including time-delays and event-triggered sampling. A new type of event-triggered mechanism is proposed based on an appropriate storage function, which is chosen larger than the derivative of Lyapunov function. Thus, the convergence of the observer system is guaranteed by the negativity of this storage function. With the utilisation of LMI techniques and the designed novel event-triggered mechanism, as well as the utilisation of a Wirtinger-based inequality, only a slight over-estimation exists in the process of obtaining stability conditions, leading to reduced conservatism. With simulations of a mobile cart system, the effectiveness of this novel event-triggered mechanism is proven through a comparison with a classical event-triggered and also periodic time-triggered mechanisms.

International audience; It is of importance to design observers for multi-variable nonlinear systems with unknown parameters and partially driven by unknown inputs. Such a problem arises in systems subject to disturbances or with inaccessible inputs and in many applications such as parameter identification, fault detection and isolation or cryptography. In this paper, the problem of fixed-time observation for nonlinear dynamical systems with unknown parameter and inputs is studied. Conditions on full/partial state and parameters identification are provided by the the way of an observation algorithm based on differential geometry theory. Then, an uniform differentiator for estimating simultaneously the states and unknown parameters in fixed-time while avoiding observability singularities is designed. An example on topology identification of network systems is described to show the effectiveness of the proposed method.

International audience; In this article, an observer‐based adaptive boundary iterative learning control law is developed for a class of two‐link rigid‐flexible manipulator with input backlash, the unknown external disturbance, and the endpoint constraint. To tackle the backlash nonlinearities and ensure the vibration suppression, the disturbance observers based upon the iterative learning conception are considered in the adaptive boundary control design. A barrier Lyapunov function is incorporated with boundary control law to restrict the endpoint state. Based on the defined barrier composite energy function, the tracking angle error convergence of the rigid part is guaranteed, and the vibrations of the flexible part are suppressed through the rigorous analysis. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed control.

International audience; In this paper, we propose to use new 3D-printed meso-structured materials to build soft robots and we present a modeling pipeline for design assistance and control. These meta-materials can be programmed before printing to target specific mechanical properties, in particular heterogeneous stiffness and anisotropic behaviour. Without changing the external shape, we show that using such meta-material can lead to a dramatic change in the kinematics of the robot. This highlights the importance of modeling. Therefore, to help the design and to control soft robots made of these meso-structured materials, we present a modeling method based on numerical homogenization and Finite Element Method (FEM) that captures the anisotropic deformations. The method is tested on a 3 axis parallel soft robot initially made of silicone. We demonstrate the change in kinematics when the robot is built with meso-structured materials and compare its behavior with modeling results.

Soft robots are an emergent instrument that has gradually been investigated by researchers in recent years to overcome the limitations of traditional rigid robots as well as to propose novel robotic applications. Rigid robots are challenged when operating in restricted and dynamic environments. Being made from a soft and flexible material, soft robots provide many benefits such as high dexterity, safe interactions, and increased adaptability, which are very useful for various applications, especially the manipulation of fragile objects, environment exploration, and medical operations. However, owing to their natural conformity and compliance, soft robots consist of a large number of degrees of freedom, their deformation is highly nonlinear, and they are characterized by different mechanical laws compared to that of rigid robots. All these aspects make theirmodeling more complex. Consequently, scientific challenges such as workspace evaluation and design optimization of soft robots arise and with them the opportunities of new contributions in the field of soft robotics. The workspace evaluation provides many benefits for different soft robotic applications mainly related to their design and control.Accordingly, the present thesis investigates the workspace evaluation and design optimization of soft robots. For this, two different methods are adopted for the mathematical modeling of soft robots. The first is the Piece-wise Constant Strain (PCS), which focuses on slender-shaped soft robots and the second is the Finite Element Method (FEM), which concerns soft robots with a general shape. Based on the adopted mathematical models, this thesis proposes different methodologies to estimate the workspace of soft robots. In fact, two strategies can be followed for the workspace estimation of soft robots: the first consists of discretizing the inputs (actuators)space, and the second consists of discretizing the outputs (end-effector) space. However, the first strategy is not efficient as it depends on the dimension of the actuators which are used to control the investigated soft robot and varies corresponding to the particular studied configuration.Conversely, the second strategy presents a stable and efficient way for the workspace estimation since the end-effector’s space is always constant (smaller or equal to 3, if we focus on the position-access) regardless of the studied soft robot’s configuration and the dimension of actuators. Each proposed workspace estimation approach was then applied to both the PCS and the FEM models and validated via a variety of soft robots’ configurations. Finally, this thesis proposes a model-based optimization approach in order to optimize the design of soft robots for the purpose of achieving specific performance objectives; Les robots rigides présentent de nombreux inconvénients lorsqu’ils fonctionnent dans des environnements dynamiques et fragiles et par conséquent, les robots déformables ont été un engin émergent qui a été graduellement étudié par les chercheurs afin de surmonter ces limitations et de faire face à de nouvelles applications robotiques. Les robots déformables sont fabriqués à partir de matériaux souples et flexibles, ce qui leur permet d’avoir plusieurs caractéristiques telles qu’une grande dextérité, des collisions prudentes et sans danger ainsi qu’une flexibilité importante. Toutes ces fonctionnalités offrent de nombreux avantages pour différentes applications, notamment l’exploration de l’environnement et les opérations médicales.Cependant, en raison de leur conformité naturelle, la modélisation des robots souples est plus complexe que celle des robots rigides, car les robots déformables comportent un nombre élevé de degrés de liberté, leur déformation est non linéaire et ils sont caractérisés par des lois mécaniques différentes de celles des robots rigides. Par conséquent, des problèmes scientifiques tels que la détermination de l’espace de travail et l’optimisation de la conception des robots déformables émergent et avec eux les possibilités de nouvelles contributions dans le domaine de la robotique souple. L’évaluation de l’espace de travail offre de nombreux avantages pour différentes applications de la robotique souple principalement liées à leur conception et à leur contrôle. En conséquence, cette thèse étudie l’estimation de l’espace de travail et l’optimisation de la conception des robots souples. Afin d’accomplir cette tâche, on propose deux méthodes différentes pour la modélisation des robots déformables, la première est la méthode de déformation constante par morceaux (PCS), qui est utilisée pour la modélisation des robots déformables avec une géométrie continue et la deuxième est la méthode des éléments finis (FEM), qui est utilisé pour la modélisation des robots déformables avec une géométrie générale. Ensuite, basée sur ces modèles mathématiques, cette thèse propose différentes méthodologies pour estimer l’espace de travail des robots souples. Deux stratégies ont été proposées pour l’estimation de l’espace de travail, la première consiste à discrétiser l’espace des entrées (actionneurs), et la deuxième consiste à discrétiser l’espace des sorties (l’effecteur du robot). Cependant, la première stratégie est inefficace, car elle dépend de la dimension des actionneurs et celle-ci varie en fonction de la configuration du robot déformable étudiée. En revanche, la seconde stratégie présente une méthodologie stable et efficace pour l’estimation de l’espace de travail puisque l’espace de l’effecteur est toujours constant (inférieur ou égal à 3, si nous nous concentrons sur l’aspect position de l’espace de travail), quelles que soient la configuration du robot souple étudié et la dimension des actionneurs. Les approches proposées pour l’estimation de l’espace de travail ont ensuite été appliquées aux deux modèles mathématiques adoptés et validées à l’aide de différentes configurations de robots déformables. Enfin, cette thèse propose une approche d’optimisation basée sur les modèles mathématiques adoptés pour optimiser la conception des robots souples afin d’atteindre certains objectifs spécifiques

Les robots rigides présentent de nombreux inconvénients lorsqu'ils fonctionnent dans des environnements dynamiques et fragiles et par conséquent, les robots déformables ont été un engin émergent qui a été graduellement étudié par les chercheurs afin de surmonter ces limitations et de faire face à de nouvelles applications robotiques.Les robots déformables sont fabriqués à partir de matériaux souples et flexibles, ce qui leur permet d'avoir plusieurs caractéristiques telles qu'une grande dextérité, des collisions prudentes et sans danger ainsi qu'une flexibilité importante. Toutes ces fonctionnalités offrent de nombreux avantages pour différentes applications, notamment l'exploration de l'environnement et les opérations médicales. Cependant, en raison de leur conformité naturelle, la modélisation desrobots souples est plus complexe que celle des robots rigides, car les robots déformables comportent un nombre élevé de degrés de liberté, leur déformation est non linéaire et ils sont caractérisés par des lois mécaniques différentes de celles des robots rigides.Par conséquent, des problèmes scientifiques tels que la détermination de l'espace de travail et l'optimisation de la conception des robots déformables émergent et avec eux les possibilités de nouvelles contributions dans le domaine de la robotique souple. L'évaluation de l'espace de travail offre de nombreux avantages pour différentes applications de la robotique souple principalement liées à leur conception et à leur contrôle. En conséquence, cette thèse étudie l'estimation de l'espace de travail et l'optimisation de la conception des robots souples.Afin d'accomplir cette tâche, on propose deux méthodes différentes pour la modélisation des robots déformables, la première est la méthode de déformation constante par morceaux (PCS), qui est utilisée pour la modélisation des robots déformables avec une géométrie continue et la deuxième est la méthode des éléments finis (FEM), qui est utilisé pour la modélisation des robots déformables avec une géométrie générale.Ensuite, basée sur ces modèles mathématiques, cette thèse propose différentes méthodologies pour estimer l'espace de travail des robots souples. Deux stratégies ont été proposées pour l'estimation de l'espace de travail, la première consiste à discrétiser l'espace des entrées (actionneurs), et la deuxième consiste à discrétiser l'espace des sorties (l'effecteur du robot).Cependant, la première stratégie est inefficace, car elle dépend de la dimension des actionneurs et celle-ci varie en fonction de la configuration du robot déformable étudiée.En revanche, la seconde stratégie présente une méthodologie stable et efficace pour l'estimation de l'espace de travail puisque l'espace de l'effecteur est toujours constant (inférieur ou égal à 3, si nous nous concentrons sur l'aspect position de l'espace de travail), quelles que soient la configuration du robot souple étudié et la dimension des actionneurs. Les approches proposées pour l'estimation de l'espace de travail ont ensuite été appliquées aux deux modèles mathématiques adoptés et validées à l'aide de différentes configurations de robots déformables. Soft robots are an emergent instrument that has gradually been investigated by researchers in the recent years to overcome limitations of traditional rigid robots as well as to propose novel robotic applications. Rigid robots are challenged when operating in restricted and dynamic environments. Being made from a soft and flexible material, soft robots provide many benefits such as high dexterity, safe interactions, and increased adaptability, which are very useful for various applications, especially the manipulation of fragile objects, environment exploration, and medical operations.However, owing to their natural conformity and compliance, soft robots consist of a large number of degrees of freedom, their deformation is highly nonlinear, and they are characterized by different mechanical laws compared to that of rigid robots. All these aspects make their modeling more complex.Consequently, scientific challenges such as workspace evaluation and design optimization of soft robots arise and with them the opportunities of new contributions in the field of soft robotics. The workspace evaluation provides many benefits for different soft robotic applications mainly related to their design and control. Accordingly, the present thesis investigates the workspace evaluation and design optimization of soft robots.For this, two different methods are adopted for the mathematical modeling of soft robots. The first is the Piece-wise Constant Strain (PCS), which focuses on slender-shaped soft robots, and the second is the Finite Element Method (FEM), which concerns soft robots with a general shape. Based on the adopted mathematical models, this thesis proposes different methodologies to estimate the workspace of soft robots. In fact, two strategies can be followed for the workspace estimation of soft robots: the first consists of discretizing the inputs (actuators) space, and the second consists of discretizing theoutputs (end-effector) space. However, the first strategy is not efficient as it depends on the dimension of the actuators whichare used to control the investigated soft robot, and varies corresponding to the particular studied configuration. Conversely, the second strategy presents a stable and efficient way for the workspace estimation since the end-effector's space is always constant (smaller or equal to 3, if we focus on the position access) regardless of the studied soft robot's configuration and the dimension of actuators. Each proposed workspace estimation approach was then applied to both the PCS and the FEM models and validated via a variety of soft robots' configurations. Finally, this thesis proposes a model-based optimization approach in order to optimize the design of soft robots for the purpose of achieving specific performance objectives.

International audience; In this study, a rigid robot is hybridized with a soft part to improve its properties of relative positioning and safe interaction. While the design of the device is quite simple, the kinematics, on the other hand, becomes complex. Pre-operative planning of such a robot is a challenge that is faced in this paper. The clinical context is the automation of transrectal prostate biopsy: a robot is connected to a thin ultrasound (US) probe instrumented with a needle through a flexible silicone part. The procedure consists of: moving the probe near the prostate through the rectum, aligning the probe with identified lesions in the prostate, and shooting the needle to collect tissue samples. In this paper we demonstrate in simulation the feasibility of our methods to solve the planning of the entire procedure. The approach we propose is based on numerical models of both robot and soft tissues, using the Finite Element Method (FEM) to model the soft parts, and a mapping mechanism to propagate the forces and displacements between the soft and rigid models. Finally, we extend the optimization algorithm proposed in previous work for the relative positioning of the hybrid robot on targets in the prostate, as it interacts with the soft tissues. With this formulation we can also set an upper limit to the force the robot is applying on its surroundings, which is particularly critical for the application we study in this paper.

International audience; In this paper, the quadrotor stabilization under time and state constraints is studied. The objective is to design a nonlinear controller under time and state constraint for quadrotor. The nonlinear quadrotor model is built by the Euler-Lagrange approach while ignoring the Coriolis terms, hub moment and force. Based on quadrotor's dynamic model, a nonlinear feedback controller is designed for the quadrotor stabilization under time and state constraints. This feedback is an implicit PID controller where the feedback gains are obtained from LMIs (Linear matrix inequalities). LMI system characterizing the system stability and convergence properties is built based on convex embedding approach and implicit Lyapunov function method. To demonstrate the application prospects of implicit PID controller, robustness analysis is provided to show the property of implicit PID controller under external disturbance. The key novelty of this paper is that the implicit PID controller is proven feasible for applying to the quadrotor under time and state constraints, which is also the main outcome.

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International audience; Sparse recovery (SR) based on spiking neural networks has been shown to be computationally efficient with ultra-low power consumption. However, existing spiking-based sparse recovery (SSR) algorithms are designed for the convex 1-norm regularized SR problem, which often underestimates the true solution. This paper proposes an adaptive version of SSR, i.e., A-SSR, to optimize a class of non-convex regularized SR problems and analyze its global asymptotic convergence. The superiority of A-SSR is validated with synthetic simulations and real applications, including image reconstruction and face recognition. Furthermore, it is shown that the proposed A-SSR essentially improves the recovery accuracy by avoiding systematic underestimation and obtains over 4 dB PSNR improvement in image reconstruction quality and around 5% improvement in recognition confidence. At the same time, the proposed A-SSR maintains energy efficiency in hardware implementation. When implemented on the neuromorphic Loihi chip, our method consumes only about 1% of the power of the iterative solver FISTA, enabling applications under energy-constrained scenarios.

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Current surgical robotic systems are teleoperated and do not have force feedback. Considerable practice is required to learn how to use visual input such as tissue deformation upon contact as a substitute for tactile sense. Thus, unnecessarily high forces are observed in novices, prior to specific robotic training, and visual force feedback studies demonstrated reduction of applied forces. Simulation exercises with realistic suturing tasks can provide training outside the operating room. This paper presents contributions to realistic interactive suture simulation for training of suturing and knot-tying tasks commonly used in robotically-assisted surgery. To improve the realism of the simulation, we developed a global coordinate wire model with a new constraint development for the elongation. We demonstrated that a continuous modeling of the contacts avoids instabilities during knot tightening. Visual cues are additionally provided, based on the computation of mechanical forces or constraints, to support learning how to dose the forces. The results are integrated into a powerful system-agnostic simulator, and the comparison with equivalent tasks performed with the da Vinci Xi system confirms its realism.

International audience; Compliant Mechanisms (CMs) present several desired properties for mechanical applications only depending on elastic deformation of the involved compliant beams/flexures. As reported in the current literature, most CM designs utilize straight beams and initially curved beams (ICBs) as the fundamental flexible members. In CM research community, many great contributions regarding modeling these elementary flexible members have been achieved. In this paper, a comprehensive modeling methodology, based on beam theory, has been established to characterize the static planar deflection of slender beam. Then such a methodology has been applied to solve 8 loading scenarios of large beam-deflection problems that exist in the design of CMs. Essentially speaking, all these beam-deflection problems are treated as a type of boundary value problems (BVPs) of an ordinary differential equation (ODE) and solved by a modified collocation method. After that, this methodology has been used to model some representative CMs with large-deflection strokes, such as compliant parallelograms.

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International audience; This paper investigates a generalized homogeneous PI (Proportional-Integral) control for a linear plant. A Lyapunov function for analysis of the closed-loop system is designed. For negative homogeneity degree, the obtained Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, a class of the disturbances to be rejected by the control law is characterized, a maximum control magnitude and the settling-time of the closedloop system are estimated.

Compliant mechanisms (CMs) are used to transfer motion, force, and energy, taking advantages of the elastic deformation of the involved compliant members. A branch of special type of elastic phenomenon called (post) buckling has been widely considered in CMs: avoiding buckling for better payload-bearing capacity and utilizing post-buckling to produce multi-stable states. This paper digs into the essence of beam’s buckling and post-buckling behaviors where we start from the famous Euler–Bernoulli beam theory and then extend the mentioned linear theory into geometrically nonlinear one to handle multi-mode buckling problems via introducing the concept of bifurcation theory. Five representative beam buckling cases are studied in this paper, followed by detailed theoretical investigations of their post-buckling behaviors where the multi-state property has been proved. We finally propose a novel type of bi-stable mechanisms termed as pre-buckled bi-stable mechanisms (PBMs) that integrate the features of both rigid and compliant mechanisms. The theoretical insights of PBMs are presented in detail. To the best of our knowledge, this paper is the first study on the theoretical derivation of the kinematic models of PBMs, which could be an important contribution to this field.

This paper investigates event-triggered (ET) observers for output-sampled nonlinear state affine systems ( x = A ( u ) x + b ( u ) ). In particular, the sampling of the system’s output is aperiodic and decided by a designed system performance based event-triggered mechanism (ETM). Under this novel ETM, the global exponential stability of the observer system is guaranteed. The continuous state estimation is derived by using aperiodic sampled system output. The effectiveness of the proposed observer has been illustrated on a numerical example. For the special constant case of the considered system ( A ( u ) = A ), an LMI based ET observer is also proposed, and finally compared to the system performance based ET observer in a mobile cart system example.

International audience; A procedure of upgrading a linear observer to homogeneous (nonlinear) one is proposed and validated by experiment. The nonlinear observer design is based on the the concept of a linear geometric homogeneity. The simple procedure developed to apply the homogeneous nonlinear observer is based on the parameters provided by the linear observer, which is potential for many applications to improve their performance. A saturation function is introduced to guaranteed the improvement of estimation quality. Finally the theoretical results are confirmed by the QDrone platform of Quanser T M .

International audience; In this paper, the adaptive control design is investigated for the chaos synchronization of two identical hyperchaotic Liu systems. First, an adaptive control law with two inputs is proposed based on Lyapunov stability theory. Secondly, two other control schemes are obtained based on a further analysis of the proposed adaptive control law. Finally, numerical simulations are presented to validate the effectiveness and correctness of these results.

Mass Spectrometry Imaging (MSI) has shown to bring invaluable information for biological and clinical applications. However, conventional MSI is generally performed ex vivo from tissue sections. Here, we develop a novel MS-based method for in vivo mass spectrometry imaging. By coupling the SpiderMass technology - that provides in vivo minimally invasive analysis – to a robotic arm of high accuracy, we demonstrate that images can be acquired from any surface by moving the laser probe above the surface. By equipping the robotic arm with a sensor, we are also able to both get the topography image of the sample surface and the molecular distribution, and then and plot back the molecular data, directly to the 3D topographical image without the need for image fusion. This is shown for the first time with the 3D topographic MS-Based whole-body imaging of a mouse. Enabling fast in vivo MSI bridged to topography pave the way for surgical applications to excision margins.

Considering a soft manipulator configuration, controlled via installed bounded actuators, this paper addresses the end-effector workspace estimation problem for such a soft robot. For this, the Discrete Cosserat method is adopted to deduce the mathematical model of soft manipulators, based on which a continuation method that accounts for simple and multiple bifurcation points to solution curves is developed to map its workspace boundaries. Difficulties encountered in calculating tangents at simple and multiple bifurcation points are studied, and an efficient solution is provided. Numerical simulations applied to planar and spatial soft manipulator configurations are presented to emphasize the validity of the proposed methodology.

International audience; Parallel Continuum Robots (PCR) have received a lot of attention in recent years. This paper presents a new 6-degrees-of-freedom PCR derived from the conventional 3-PPSR parallel manipulator. This robot is driven by three limbs consisting of two flexible rods each and replacing the spherical and revolute joints of the original version. Each limb is mounted onto two linear axes arranged in series. To allow a direct comparison between the articulated and the continuum version, the parallel mechanism of an industrial manipulator has been replaced by an elastic structure of the same size. The simulations and the experiments show that the flexible counterpart of the manipulator is able to achieve a larger workspace, increasing the range of motion by 150% for rotations and by 157% in elevation. Moreover, the position repeatability is improved by 47% (reaching 3.4 µm) and the orientation repeatability by 57% (reaching 14.3 µrad). This can be explained by the removal of the spherical and revolute joints but also by the constant stress in the structure that acts as an anti backlash system on leadscrew actuators.