Cette thèse contribue à l'analyse des raideurs statique et dynamique des robots parallèles à câbles dans un objectif d'amélioration de la précision de positionnement statique et de la précision de suivi de trajectoire. Les modélisations statique et dynamique proposées des câbles considèrent l'effet du poids du câble sur son profil et l'effet de masse du câble sur la dynamique de ce dernier. Sur la base du modèle statique de câble proposé, l'erreur de pose statique au niveau de l'organe terminal du robot est définie et sa variation en fonction de la charge externe appliquée est utilisée pour évaluer la raideur statique globale de la structure. Un nouveau modèle dynamique vibratoire de robots à câbles est proposé en considérant le couplage de la dynamique des câbles avec les vibrations de l'organe terminal. Des validations expérimentales sont réalisées sur des prototypes de robots à câbles. Une série d'expériences de statique, d'analyses modales, d'analyses en régime libre et de suivi de trajectoire sont réalisées. Les modèles statiques et dynamiques proposés sont confirmés. Les dynamiques des câbles et du robot ainsi que leur couplage sont discutées montrant la pertinence des modèles développés pour l’amélioration des performances des robots à câbles en termes de design et le contrôle. Outre l'analyse des raideurs statique et dynamique, les modèles proposés sont appliqués dans l'amélioration du calcul de la distribution des efforts dans les câbles des robots redondants. Une nouvelle méthode de calcul de la distribution des efforts dans les câbles basée sur la détermination de la limite inférieure des forces dans les câbles est présentée. La prise en compte de la dépendance à la position dans l'espace de travail permet de limiter les efforts dans les câbles et ainsi d'améliorer l'efficience des robots d'un point de vue énergétique. / This thesis contributes to the analysis of the static and dynamic stiffness of cable-driven parallel robots (CDPRs) aiming to improve the static positioning accuracy and the trajectory tracking accuracy. The proposed static and dynamic cable modeling considers the effect of cable weight on the cable profile and the effect of cable mass on the cable dynamics. Based on the static cable model, the static pose error of the end-effector is defined and the variation of the end-effector pose error with the external load is used to evaluate the static stiffness of CDPRs. A new dynamic model of CDPRs is proposed with considering the coupling of the cable dynamics and the end-effector vibrations. Experimental validations are carried out on CDPR prototypes. Static experiments, modal experiments, free vibration experiments and trajectory experiments are performed. The proposed static and dynamic models are verified. Cable dynamics, robot dynamics and their coupling are discussed. Results show the relevance of the proposed models on improving the performances of CDPRs in terms of design and control. Besides stiffness analysis, the proposed models are applied on the force distribution of redundant actuated CDPRs. A new method on the calculation of the cable forces is proposed, where the determination of the lower-boundary of the cable forces is presented. The consideration of the pose-dependence of the lower force boundary can minimize the cable forces and improve the energy efficiency of CDPRs.

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Robot Operating System (ROS) ist ein Framework für Robotersteuerung, das die Kommunikation zwischen verschiedenen Robotermodulen ermöglicht. Weiterhin bietet es fertige Lösungen für Vorwärts- und Rückwärtskinematik serieller Roboter. Für parallele Roboter muss die Berechnung der Kinematik in ROS allerdings individuell erfolgen. Diese ist durch lange, verschachtelte Formeln gekennzeichnet, was die Wahrscheinlichkeit für Fehler in der Programmierung erhöht. Hier kommt die geometrische Mathematiksoftware GeoGebra zum Einsatz. Durch die geometrische Modellierung des parallelen Roboters in GeoGebra kann jeder Schritt in der Kinematikberechnung nachverfolgt und mit den Ergebnissen aus der Programmierung in ROS kontrolliert werden. Dadurch können Fehler in den Formeln schneller erkannt und behoben werden. Danach erfolgt die Simulation des parallelen Roboters in der Visualisierungsumgebung von ROS RViz. / Robot Operating System (ROS) is a framework for controlling robots that enables communication between different robot modules. It also provides complete solution for forward and inverse kinematics of serial robots. However, for parallel robots, kinematics calculation must be done individually. These are characterized by long, nested formulas, which increases the likelihood of errors in programming. The geometric mathematics software GeoGebra can be implemented to overcome this problem. By geometrically modelling the parallel robot in GeoGebra, every step in kinematics calculation can be traced and checked against the result from the programming in ROS. This allows errors in the formulas to be detected and corrected more quickly. Then, the parallel robot is simulated in the visualization environment in ROS RViz.

In the research area of virtual reality, the term haptic rendering is defined as the process of computing and generating the interaction force between the virtual object and the operator. One of the major challenges of haptic rendering is the stably rendering contact with a stiff object. Traditional haptic rendering algorithms performs well when rendering contact with soft objects. But when it is used to simulate contact with objects with high stiffness, the algorithm may cause unstable response of haptic devices. Such unstable behavior (e.g., oscillation of the device) can destroy the fidelity of the virtual environment and even hurt the user.  To address the above stability issues, a new design approach has been proposed in this paper. The proposed approach consists of three main process steps: modeling and linearization in ADAMS, LQR position controller design, verification with co-simulation. In the first step, a simulation model of the system is firstly created in ADAMS/View. Then this nonlinear ADAMS multi-body dynamics model is linearized and exported as a set of linear state space matrices with the help of ADAMS/Linear. In the second step, different from the traditional force-control algorithms, LQR position controller is developed in Matlab Simulink based on the exported matrices to emulate interactions with stiff objects. At last, the verification of control performance is carried out by setting up co-simulation between ADAMS and Simulink.  A case study implementation of this proposed method was performed on the TAU device which was previously developed by Machine Design department at KTH. TAU is an asymmetrical parallel robot with six degrees of freedom for the simulation of surgical procedures like drilling and milling of hard tissues of bones and teeth. The results show that the linear model exported from ADAMS is sufficiently accurate and the proposed controller can render a virtual wall with stiffness at the level of 105 N/m. / Inom forskningsområdet virtuell verklighet definieras termen hatisk återgivning (haptic rendering) som processen för beräkning och generering av interaktiva krafter mellan det virtuella objektet och användaren. En av de största utmaningarna med haptisk återgivning är att stabilt simulera känslan av beröring av styv material för användare. Traditionella algoritmer fungerar när det gäller att simulera känslan av beröring av mjuk material, men när algoritmerna används för att simulera kontakt med materialer med stor styvhet kan det orsaka instabilitet hos haptiska enheter. Sådana instabilitet, bland annat svängning hos enheten, kan förstöra den virtuella miljöns exakthet och till och med skada användare.  Denna uppsats försöker ta itu med det ovanstående problemet genom att föreslå en ny designmetod. Metoden består av tre huvudsteg: modellering och linearisering med hjälp av ADAMS, design av LQR-positionskontroll, och verifiering med samsimulering (co-simulation). I det första steget skapas systemets simuleringsmodell med hjälp av ADAMS/View. Sedan linjäriseras denna icke-linjära ADAMS-multikroppsdynamikmodell. Modellen exporteras som linjära tillståndsmatriser med hjälp av ADAMS/Linear. I det andra steget designas en LQR-positionskontroll med hjälp av Matlab Simulink baserat på de exporterade matriserna tidigare för att simulera interaktioner med styv material, vilket skiljer sig från de traditionella kraftkontrollalgoritmer (force-control algorithms). I det sista steget utförs verifieringen av positionskontrollens prestanda genom att ställa in samsimulering (co-simulation) mellan ADAMS och Simulink.  En testkörning av denna föreslagna metod har utförs på TAU-enheten som tidigare utvecklades av KTH institutionen för maskinkonstruktion. TAU är en asymmetrisk parallellsrobot med sex frihetsgrader för att simulera kirurgiska ingrepp som borrning av hårda vävnader i ben och tänder. Resultaten visar att den linjära modellen som exporteras från ADAMS är tillräckligt korrekt, för den föreslagna positionskontrollen kan framställa en virtuell vägg med styvhet vid 105 N/m.

Dans cette thèse, nous nous sommes intéressés à l 'étude d'un micro-robot destiné à la mise en oeuvre d'une technique de chirurgie mini-invasive pour le traitement des anévrismes de l'artère aorte abdominale. Ce micro-robot placé à l'extrémité d'un cathéter, rendant ce dernier actif, permettra la navigation à l'intérieur de l'artère en évitant les contacts avec les parois de celle-ci. Le système sera destiné à l'apprentissage du geste chirurgical et à l'assistance du chirurgienpendant l'opération. De par sa structure et ses propriétés physiques, le micro-robot, pouvantêtre composé de plusieurs modules élémentaires, entre dans la catégorie des robots continuum. Dans notre étude, un module élémentaire est considéré comme étant un robot parallèle. Lesmodèles géométriques et cinématiques inverses ont alors été établis en utilisant les techniques dela robotique parallèle. L'approche de modélisation proposée permet de faire ressortir explicitement du modèle les paramètres géométriques du micro-robot. Une étude sur l'identificationde ces paramètres a été effectuée par le calibrage du modèle géométrique inverse. Des résultatsde simulation sont présentés validant d'une part les modèles développés et d'autre part la méthode de calibrage proposée. Afin de mettre nos modèles en situation, nous avons développé unsimulateur tridimensionnel intégrant le modèle d'un segment de l'artère, le modèle du micro-robotet un syntaxeur à retour de force. La mise en place d'une navigation active, planifiée etguidée dans ce simulateur permet de contraindre les gestes du chirurgien lors de la navigation du micro-robot à l'intérieur de l'artère / In this thesis, we are interested in a micro-robot study for the implementation of a mini-invasivesurgery technique. The medical application concerns the treatment of the artery abdominal aorta aneurysms. This micro-robot located at the extremity of the catheter permits thecatheter movements into the artery avoiding minimizing contacts with the artery walls. The system can be used for the surgical gesture learning and for the surgeon assistance during the medical operation. Because of its structure and its physical properties the micro-robot is considered as a continuum robot. It is composed of one or several elementary modules. In our study we consider each elementary module as a parallel robot. Then the inverse kinematics model has been established by using techniques of parallel robotics. The proposed modelling approach allows the expression of the model according to the micro-robot geometric parameters. A study on the identification of these parameters has been developed by an inverse geometric modelcalibration. The given simulation results validate the developed models on the one hand, the proposed calibration method on the other hand. We have developed a three-dimensional simulator integrating the model of an artery segment, the micro-robot model, and a joystick with force feedback. The implementation of active, planned and guided navigation on this simulator allows to constrain the surgeon gestures during the movements of the micro-robot inside the artery

Cette thèse vise à améliorer le positionnement statique et la précision de suivi de trajectoire des Robots Parallèles à Câbles (RPC) tout en prenant en compte leur élasticité globale. A cet effet, deux stratégies de commandes complémentaires valables pour toute configuration de RPC sont proposées.Tout d'abord, une analyse de robustesse est réalisée pour aboutir à une commande robuste des RPC référencée modèle. Un modèle de RPC approprié est défini en fonction de l'application visée et les principales sources d'erreurs de pose de la plate-forme mobile sont identifiées.Une première méthode de commande est proposée sur la base des résultats de l'analyse de robustesse. Cette première méthode réside dans le couplage d'une commande référencée modèle d’un contrôleur PID.Dans le cadre de cette thèse, un modèle élasto-dynamique de RPC est exprimé afin de compenser le comportement oscillatoire de sa plate-forme mobile dû à l'élongation des câbles et de son comportement dynamique.La deuxième méthode de commande utilise des filtres "input-shaping" dans la commande référencée modèle proposée afin d'annuler les mouvements oscillatoires de la plate-forme mobile. Ainsi, le signal d'entrée est modifié pour que le RPC annule automatiquement les vibrations résiduelles. Les résultats théoriques obtenus sont validés expérimentalement à l'aide d'un prototype de RPC non redondant en actionnement et en configuration suspendue. Les résultats expérimentaux montrent la pertinence des stratégies de commande proposées en termes d'amélioration de la précision de suivi de trajectoire et de réduction des vibrations. / This thesis aims at improving the static positioning and trajectory tracking accuracy of Cable- Driven Parallel Robots (CDPRs) while considering their overall elasticity. Accordingly, two complementary control strategies that are valid for any CDPR configuration are proposed.First, a robustness analysis is performed to lead to a robust model-based control of CDPRs. As a result, an appropriate CDPR model is defined as a function of the targeted application and the main sources of CDPR moving-platforms pose errors are identified.A first control method is determined based on the results of the robustness analysis. This first method lies in the coupling of a model-based feed-forward control scheme for CDPR with a PID feedback controller.Here, an elasto-dynamic model of the CDPR is expressed to compensate the oscillatory motions of its moving-platform due to cable elongations and its dynamic behavior.The second control method uses input-shaping filters into the proposed model-based feed-forward control in order to cancel the oscillatory motions the movingplatform. Thus, the input signal is modified for the CDPR to self-cancel residual vibrations.Experimental validations are performed while using suspended and non-redundant CDPR prototype. The proposed feed-forward model-based control schemes are implemented, and their effectiveness is discussed.Results show the relevance of the proposed control strategies in terms of trajectory tracking accuracy improvement and vibration reduction.

The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators.

The objective of this thesis is to analyze the kinematics of a mobile parallel robot with contribution that pertain to the singularity analysis, the optimization of geometric parameters and the optimal control to avoid singularities when navigating across singular geometric configurations. The analysis of the workspace and singularities is performed in a prescribed reference workspace regions using discretization method. Serial and parallel singularities are analytically analyzed and all possible singular configurations are presented. Kinematic conditioning index is used to determine the robot’s proximity to a singular configuration. A method for the determination of a continuous and singularity-free workspace is detailed. The geometric parameters of the system are optimized in various types of pipe-like structures with respect to a suitable singularity index, in order to avoid singularities during the navigation across elbows. The optimization problem is formulated with an objective to maximize the reachable workspace and minimize the singularities. The objective function is also subjected to constraints such as collision avoidance, singularity avoidance, workspace continuity and contact constraints imposed between the boundaries and the wheels of the robot. A parametric variation method is used as a technique to optimize the design parameters. The optimal design parameters found are normalized with respect to the width of the pipe-like structures and therefore the results are generalized to be used in the development phase of the robot. An optimal control to generate singularity-free trajectories when the robotic device has to cross a geometric singularity in a sharp 90◦ elbow is proposed. Such geometric singularity inherently leads to singularities in the Jacobian of the system, and therefore a modified device with augmented number of degrees of freedom is introduced to be able to generate non-singular trajectories.

The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators.

L’amélioration des performances des robots est un enjeu important dans le domaine industriel. Les objectifs visés sont l’augmentation de l’espace de travail, de la capacité de charge transportable, de la vitesse de travail et de la précision du robot. Pour atteindre ces objectifs, il faut en général augmenter la rigidité, diminuer la masse et augmenter la capacité d’amortissement du robot. Les robots actuels sont généralement fabriqués en métaux : aluminium ou acier, ce qui limite leurs performances en raison des faibles capacités d’amortissement des vibrations de ces matériaux. Les matériaux composites présentent l’avantage de combiner des matériaux différents, ce qui conduit à une variété de leurs performances. Parmi les types de renforts, les fibres de carbone présentent un module d’élasticité élevé permettant la conception de pièces de grandes rigidités statiques mais elles possèdent une faible capacité d’amortissement. Les fibres végétales, par contre, possèdent une faible densité, de bonnes propriétés spécifiques et des capacités d’amortissement élevées. Cette thèse porte sur l’amélioration des performances d’un robot parallèle 3CRS en utilisant des matériaux composites pour reconcevoir des pièces initialement fabriquées en aluminium. La thèse commence d’abord par une caractérisation des comportements statiques et dynamiques du robot initial constitué de bras en aluminium. Ensuite, la forme des segments des bras robotiques est optimisée par rapport aux sollicitations mécaniques sur le robot. Un nouveau composite stratifié hybride renforcé par des fibres de carbone et des fibres de lin est alors proposé. Cette combinaison permet d’allier les avantages des deux types de fibres dans un composite pour le dimensionnement des composants sous sollicitation élevée. La structure de ce nouveau composite a été optimisée puis un segment est fabriqué pour valider la conception. Finalement, l’étude du nouveau robot avec des bras en matériaux composites a été réalisée, les résultats montrent que la rigidité du robot augmente, sa masse diminue légèrement et sa capacité d’amortissement augmente considérablement par rapport au robot initial. Donc, l’application du composite stratifié hybride peut améliorer les performances statiques et dynamiques et augmenter significativement la précision en fonctionnement du robot 3CRS. / Improvement of the robot’s performances is a major challenge in the industrial field. In general, improvement objectives are increasing workspace, transportable capacity, speed and precision of the robot. To achieve these objectives, it must increase rigidity, reduce weight and increase damping capacity of the robot. Currently, the robots are generally made of metals: aluminum or steel, which limits their performances due to low damping capacity of these materials.Composite materials present an advantage to combine different materials, which leads to a variety of composite material properties. Among the types of reinforcements, carbon fibers show high modulus that enables robotic parts with high static rigidities to be designed. However, carbon fibers have generally a low damping capacity. Natural fibers have low density, good specific properties and high damping capacity.This thesis focuses on the improvement of the performances of the 3CRS parallel robot by using the composite material to redesign robot parts initially made of aluminum. The thesis begins with static and dynamic characterizations of the original robot. Then, the shape of segments of the robotic arms is optimized with respect to applying force on the robot. A hybrid laminated composite reinforced with carbon fibers and flax fibers is proposed for the use. This combination enables to combine the advantages of two fiber types in a composite for using in high loaded components. The structure of the new hybrid laminated composite is optimized and a composite segment is then fabricated in order to validate the design. Finally, the analysis of the new robot with composite arms is executed. The result shows that the new robot has a slightly higher rigidity, lighter mass and considerably greater damping capacity in comparison with the original robot. Therefore, the application of the hybrid composite could improve the static and dynamic performances and increases considerably the accuracy in operation of the robot 3CRS.