Ce travail étudie l'apport de l'algèbre différentielle à deux problématiques principales de la robotique mobile à roues, la localisation et la navigation. La première problématique consiste à être capable de dire où le robot se situe dans son environnement. Nous supposons ici que nous possédons un certain nombre de points d'intérêt de l'espace dont les coordonnées dans cette espace sont connues. En fonction du nombre de points d'intérêt, il est possible ou non de localiser le robot. Cette notion de localisabilité est définie et étudiée dans le cadre algébrique. Nous montrons que ce cadre d'étude est plus intéressant que le cadre géométrique en ce sens que non seulement il permet l'étude de la localisabilité mais en plus il permet de construire des estimateurs d'états permettant de reconstruire la posture du robot. Cette étude est effectuée dans cinq cas d'études pour quatre des cinq classes de robots mobiles à roues. La deuxième problématique étudiée est celle de la navigation d'une flottille décentralisée de robots dans un environnement complexe. Ce travail présente une architecture pouvant être utilisée dans une large classe de problème et bénéficiant des avantages des approches discrètes et des approches continues. En effet, à haut niveau, un bloc stratégie spécifie l'objectif, les contraintes et leurs paramètres ainsi que la fonction coût utilisée, à bas niveau, une trajectoire est calculée afin de minimiser la fonction coût en respectant l'objectif et les contraintes du problème. Cette minimisation est faite sur un horizon glissant de manière à pouvoir prendre en compte des modifications de l'environnement ou de la mission en cours de navigation / This work investigates the contribution of differential algebra to two main issues of wheel mobile robotics, localization and navigation. The first issue is to be able to tell where the robot is in its environment. We assume that we have a number of landmarks in space whose coordinates are known in this area. Depending on the number of landmarks, it is possible or not to localize the robot. This notion of localizability is defined and studied in the algebraic framework. We show that this framework is more interesting than the geometric framework in the sense that it not only allows the study of localizability, but it also allows us to construct estimators states to reconstruct the posture of the robot. This study was conducted in five cases study for four of the five classes of wheeled mobile robots. The second problem studied is that of a robot decentralized swarm navigation in a complex environment. This work presents an architecture that can be used in a wide class of problems and enjoying the benefits of discrete approaches and continuous approaches. Indeed, high-level block strategy specifies the goal, constraints and parameters as well as the cost function, a low-level block is used to compute a trajectory that minimize the cost function in accordance with the objective and the problem constraints. This minimization is done on a sliding window so it is possible to take changes in the environment or mission during navigation into account

Ce travail s’inscrit dans le cadre de la commande d’un système multi agents/ multi véhicules. Cette thèse traite en particulier le cas de la commande d’un système multi-robots mobiles non-holonomes. L'objectif est de concevoir des lois de commandes appropriées pour chaque robot de sorte que l’ensemble des robots puisse exécuter des tâches spécifiques, de suivre des trajectoires désirées tout en maintenant des configurations géométriques souhaitées. L’approche leadeur-suiveur pour la commande d’un groupe de robots mobiles non-holonomes est étudiée en intégrant la technologie backstepping, avec une approche basée sur les neurodynamiques bioinspirées. Le problème de commande distribuée d’un système multi robots sur le consensus est également étudié. Des lois de commandes cinématiques distribuées sont développés afin de garantir au système multi-robots la convergence exponentielle vers une configuration géométrique souhaitée. Afin de tenir compte de la dynamique des paramètres inconnus, des commandes adaptatives de couple sont développés pour que le système multi-robots puisse converger asymptotiquement vers le modèle géométrique souhaité. Lorsque la dynamique est inconnue, des commandes à base de réseaux de neurones sont proposées / This work is based on the multi-agent system / multi-vehicles. This thesis especially focuses on formation control of multiple nonholonomic mobile robots. The objective is to design suitable controllers for each robot according to different control tasks and different constraint conditions, such that a group of mobile robots can form and maintain a desired geomantic pattern and follow a desired trajectory. The leader-follower formation control for multiple nonholonomic mobile robots is investigated under the backstepping technology, and we incorporate a bioinspired neurodynamics scheme in the robot controllers, which can solve the impractical velocity jumps problem. The distributed formation control problem using consensus-based approach is also investigated. Distributed kinematic controllers are developed, which guarantee that the multi-robots can at least exponentially converge to the desired geometric pattern under the assumption of "perfect velocity tracking". However, in practice, "perfect velocity tracking" doesn’t hold and the dynamics of robots should not be ignored. Next, in consideration of the dynamics of robot with unknown parameters, adaptive torque controllers are developed such that the multi-robots can asymptotically converge to the desired geometric pattern under the proposed distributed kinematic controllers. Furthermore, When the partial knowledge of dynamics is available, an asymptotically stable torque controller has been proposed by using robust adaptive control techniques. When the dynamics of robot is unknown, the neural network controllers with the robust adaptive term are proposed to guarantee robust velocity tracking

La complexité associée à la coordination d’un groupe de robots mobiles est traitée dans cette thèse en investiguant plus avant les potentialités des architectures de commande multi-contrôleurs dont le but est de briser la complexité des tâches à exécuter. En effet, les robots mobiles peuvent évoluer dans des environnements très complexes et nécessitent de surcroît une coopération précise et sécurisée pouvant rapidement devenir inextricable. Ainsi, pour maîtriser cette complexité, le contrôleur dédié à la réalisation d’une tâche est décomposé en un ensemble de comportements/contrôleurs élémentaires (évitement d’obstacles et de collision entre les robots, attraction vers une cible, planification, etc.) qui lient les informations capteurs (provenant des capteurs locaux du robot, etc.) aux actionneurs des différentes entités robotiques. La tâche considérée dans cette thèse correspond à la navigation d’un groupe de robots mobiles dans des environnements peu ou pas connus en présence d’obstacles (statiques et dynamiques). La spécificité de l’approche théorique consiste à allier les avantages des architectures multi-contrôleurs à ceux des systèmes multi-agents et spécialement les modèles organisationnels afin d’apporter un haut niveau de coordination entre les agents/robots mobiles. Le groupe de robots mobiles est alors coordonné suivant les différentes normes et spécifications du modèle organisationnel. Ainsi, l’activation d’un comportement élémentaire en faveur d’un autre se fait en respectant les contraintes structurelles des robots en vue d’assurer le maximum de précision et de sécurité des mouvements coordonnés entre les différentes entités mobiles. La coopération se fait à travers un agent superviseur (centralisé) de façon à atteindre plus rapidement la destination désirée, les événements inattendus sont gérés quant à eux individuellement par les agents/robots mobiles de façon distribuée. L’élaboration du simulateur ROBOTOPIA nous a permis d’illustrer chacune des contributions de la thèse par un nombre important de simulations. / The difficulty of coordinating a group of mobile robots is adressed in this thesis by investigating control architectures which aim to break task complexity. In fact, multi-robot navigation may become rapidly inextricable, specifically if it is made in hazardous and dynamical environment requiring precise and secure cooperation. The considered task is the navigation of a group of mobile robots in unknown environments in presence of (static and dynamic) obstacles. To overcome its complexity, it is proposed to divide the overall task into a set of basic behaviors/controllers (obstacle avoidance, attraction to a dynamical target, planning, etc.). Applied control is chosen among these controllers according to sensors information (camera, local sensors, etc.). The specificity of the theoretical approach is to combine the benefits of multi-controller control architectures to those of multi-agent organizational models to provide a high level of coordination between mobile agents-robots systems. The group of mobile robots is then coordinated according to different norms and specifications of the organizational model. Thus, activating a basic behavior in favor of another is done in accordance with the structural constraints of the robots in order to ensure maximum safety and precision of the coordinated movements between robots. Cooperation takes place through a supervisor agent (centralized) to reach the desired destination faster ; unexpected events are individually managed by the mobile agents/robots in a distributed way. To guarantee performance criteria of the control architecture, hybrid systems tolerating the control of continuous systems in presence of discrete events are explored. In fact, this control allows coordinating (by discrete part) the different behaviors (continuous part) of the architecture. The development of ROBOTOPIA simulator allowed us to illustrate each contribution by many results of simulations.

La problématique étudiée dans cette thèse concerne le guidage en formation d’une flotte de robots mobiles en environnement naturel. L’objectif poursuivi par les robots est de suivre une trajectoire connue (totalement ou partiellement) en se coordonnant avec les autres robots pour maintenir une formation décrite comme un ensemble de distances désirées entre les véhicules. Le contexte d’évolution en environnement naturel doit être pris en compte par les effets qu’il induit sur le déplacement des robots. En effet, les conditions d’adhérence sont variables et créent des glissements significatifs des roues sur le sol. Ces glissements n’étant pas directement mesurables, un observateur est mis en place, permettant d’obtenir une estimation de leur valeur. Les glissements sont alors intégrés au modèle d’évolution, décrivant ainsi un modèle cinématique étendu. En s’appuyant sur ce modèle, des lois de commande adaptatives sur l’angle de braquage et la vitesse d’avance d’un robot sont alors conçues indépendamment, asservissant respectivement son écart latéral à la trajectoire et l’interdistance curviligne de ce robot à une cible. Dans un second temps, ces lois de commande sont enrichies par un algorithme prédictif, permettant de prendre en compte le comportement de réponse des actionneurs et ainsi d’éviter les erreurs conséquentes aux retards de la réponse du système aux commandes. À partir de la loi de commande élémentaire en vitesse permettant d’assurer un asservissement précis d’un robot par rapport à une cible, une stratégie de commande globale au niveau de la flotte est établie. Celle-ci décline l’objectif de maintien de la formation en consigne d’asservissement désiré pour chaque robot. La stratégie de commande bidirectionnelle conçue stipule que chaque robot définit deux cibles que sont le robot immédiatement précédent et le robot immédiatement suivant dans la formation. La commande de vitesse de chaque robot de la formation est obtenue par une combinaison linéaire des vitesses calculées par la commande élémentaire par rapport à chacune des cibles. L’utilisation de coefficients de combinaison constants au sein de la flotte permet de prouver la stabilité de la commande en formation, puis la définition de coefficients variables est envisagée pour adapter en temps réel le comportement de la flotte. La formation peut en effet être amenée à évoluer, notamment en fonction des impératifs de sécurisation des véhicules. Pour répondre à ce besoin, chaque robot estime en temps réel une distance d’arrêt minimale en cas d’urgence et des trajectoires d’urgence pour l’évitement du robot précédent. D’après la configuration de la formation et les comportements d’urgence calculés, les distances désirées au sein de la flotte peuvent alors être modifiées en ligne afin de décrire une configuration sûre de la formation. / This thesis focuses on the issue of the control of a formation of wheeled mobile robots travelling in off-road conditions. The goal of the application is to follow a reference trajectory (entirely or partially) known beforehand. Each robot of the fleet has to track this trajectory while coordinating its motion with the other robots in order to maintain a formation described as a set of desired distances between vehicles. The off-road context has to be considered thoroughly as it creates perturbations in the motion of the robots. The contact of the tire on an irregular and slippery ground induces significant slipping and skidding. These phenomena are hardly measurable with direct sensors, therefore an observer is set up in order to get an estimation of their value. The skidding effect is included in the evolution of each robot as a side-slip angle, thus creating an extended kinematic model of evolution. From this model, adaptive control laws on steering angle and velocity for each robot are designed independently. These permit to control respectively the lateral distance to the trajectory and the curvilinear interdistance of the robot to a target. Predictive control techniques lead then to extend these control laws in order to account for the actuators behavior so that positioning errors due to the delay of the robot response to the commands are cancelled. The elementary control law on the velocity control ensures an accurate longitudinal positioning of a robot with respect to a target. It serves as a base for a global fleet control strategy which declines the overall formation maintaining goal in local positioning objective for each robot. A bidirectionnal control strategy is designed, in which each robot defines 2 targets, the immediate preceding and following robot in the fleet. The velocity control of a robot is finally defined as a linear combination of the two velocity commands obtained by the elementary control law for each target. The linear combination parameters are investigated, first defining constant parameters for which the stability of the formation is proved through Lyapunov techniques, then considering the effect of variable coefficients in order to adapt in real time the overall behavior of the formation. The formation configuration can indeed be prone to evolve, for application purposes and to guarantee the security of the robots. To fulfill this latter requirement, each robot of the fleet estimates in real time a minimal stopping distance in case of emergency and two avoidance trajectories to get around the preceding vehicle if this one suddenly stops. Given the initial configuration of the formation and the emergency behaviors calculated, the desired distances between the robots can be adapted so that the new configuration thus described ensures the security of each and every robot of the formation against potential collisions.

The navigation tasks in advanced home robotic applications incorporating reliable revisiting strategies are dependent on very low cost but nevertheless rather accurate localization systems. In this paper a localization system based on the principle of trilateration is described. The proposed system uses only a single small base station, but achieves accuracies comparable to systems using spread beacons and it performs sufficiently for map building. Thus it is a standalone system and needs no odometry or other auxiliary sensors. Furthermore a new approach for the problem of the reliably detection of areas without direct line of sight is presented. The described system is very low cost and it is designed for use in indoor service robotics. The paper gives an overview on the system concept and special design solutions and proves the possible performances with experimental results.

Real-time spatial awareness is essential in areas such as robotics and autonomous navigation. However, as environments expand and become increasingly complex, maintaining both a low computational load and high mapping accuracy remains a significant challenge. This thesis addresses these challenges by proposing a novel method for real-time construction of continuous Euclidean distance fields (EDF) using Gaussian process (GP) regression, hereafter referred to as GP-EDF, tailored specifically for large indoor environments. The proposed approach focuses on leveraging the inherent structural information of indoor spaces by partitioning them into rooms and constructing a local GP-EDF model for each, reducing the computational cost tied to large matrix operations in GPs. By also exploiting the geometric regularities commonly found in indoor spaces it detects walls and represents them as line segments. This information is integrated into the models’ priors to both improve accuracy and further reduce the computational expense. Comparison with two baselines demonstrated the proposed approach’s effectiveness. It maintained low computation times despite increasing amounts of sensor data, signifying a significant improvement in scalability. Results also confirmed that the EDF quality remains high and isn’t affected by partitioning the GP-EDF into local models. The method also reduced the influence of sensor noise on the EDF’s accuracy when incorporating the line segments into the model. Additionally, the proposed room segmentation method proved to be efficient and generated accurately partitioned rooms, with a high degree of independence between them. In conclusion, the proposed approach offers a scalable, accurate and efficient solution for real-time construction of EDFs, demonstrating significant potential in aiding autonomous navigation within large indoor spaces. / Realtidsrumslig medvetenhet är avgörande inom områden som robotik och autonom navigering. Emellertid, när miljöer expanderar och blir alltmer komplexa, kvarstår det en betydande utmaning att bibehålla både en låg beräkningsbelastning och hög kartläggningsnoggrannhet. Denna avhandling bemöter dessa utmaningar genom att föreslå en ny metod för realtidskonstruktion av kontinuerliga euklidiska avståndsfält (EDF) med hjälp av regression via gaussiska processer (GP), hädanefter benämnd GP-EDF, specifikt anpassad för stora inomhusmiljöer. Den föreslagna metoden fokuserar på att utnyttja den inneboende strukturella informationen i inomhusmiljöer genom att dela upp dem i rum och konstruera en lokal GP-EDF-modell för varje rum, vilket minskar den beräkningsbelastning som är kopplad till stora matrisoperationer i GP:er. Genom att även utnyttja de geometriska regelbundenheter som vanligtvis finns i inomhusutrymmen, detekterar den väggar och representerar dem som linjesegment. Denna information integreras sedan i modellernas a priori-fördelningar, både för att förbättra noggrannheten och ytterligare minska den beräkningsmässiga kostnaden. Jämförelse med två baslinjemodeller demonstrerade den föreslagna metodens effektivitet. Den bibehöll låga beräkningstider trots ökande mängder sensordata, vilket indikerar en betydande förbättring av skalbarheten. Resultaten bekräftade även att kvaliteten på EDF:en förblir hög och påverkas inte av uppdelningen av GP-EDF:en i lokala modeller. Metoden minskade även sensorbrusets inverkan på EDF:ens noggrannhet vid integrering av linjesegment i modellen. Dessutom visade sig den föreslagna rumsegmenteringsmetoden vara effektiv och genererade korrekt uppdelade rum, med en hög grad av oberoende mellan dem. Sammanfattningsvis erbjuder den föreslagna metoden en skalbar och effektiv lösning för realtidskonstruktion av EDF:er, och visar på betydande potential att underlätta autonom navigering inom stora inomhusutrymmen.

[pt] Nos últimos anos, os robôs móveis com pernas têm despertado o interesse da comunidade robótica, pois tais mecanismos apresentam maior versatilidade em relação aos robôs móveis de rodas e aéreos. Neste trabalho, o autor considera o problema de modelagem e projeto de controle robusto para uma classe de robôs móveis com pernas usando a abordagem de controle por modos deslizantes. Um estudo comparativo entre um algoritmo de planejamento baseado em técnicas de Fourier e controladores via modo deslizante é apresentado para o problema de estabilização de um robô móvel saltitante na fase de vôo. O autor também propõe a estabilização da postura de robôs móveis multipernas, como hexapod e robô bípede, utilizando duas abordagens de controle diferentes, o controle de regulação Cartesiana e o controle via modos deslizantes. A teoria de estabilidade de Lyapunov é usada para demonstrar as propriedades de estabilidade dos sistemas de controle em malha-fechada. Simulações numéricas em ambiente de simulação MATLAB e simulações computacionais em Gazebo, um simulador robótico 3D de código aberto, são incluídas para ilustrar o desempenho e a viabilidade da metodologia proposta. / [en] In the last years, legged mobile robots have increased the interest of the robotics community because such mechanisms have higher versatility compared to wheeled and aerial mobile robots. These characteristics make robot with legs a viable solution for rescue and monitoring operations in irregular terrains and difficult to access locations. Although singlelegged or multi-legged mechanisms can transverse any terrain, some of their disadvantages are higher complexity in modelling and control design and higher power consumption. In this work, the author considers the problem of modelling and robust control design for a class of legged mobile robots using the sliding mode control approach. A comparative study between a planning algorithm based on Fourier techniques and sliding mode controllers is presented for the stabilization problem of a hopping robot in flight phase. The author also proposes the stabilization of the posture of multilegged mobile robots such as, hexapod and biped robot, using two different control approaches, the Cartesian regulation control and the sliding mode control. The Lyapunov stability theory is used to demonstrate the stability properties of the closed-loop control systems. Numerical simulations in MATLAB simulation software and computer simulations in Gazebo, an open-source 3D robotic simulator, are included to illustrate the performance and feasibility of the propose methodology.

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[pt] Nos últimos anos, os avanços mais recentes em robótica e suas aplicações têm sido usados para reduzir a carga de trabalho e os requisitos de mão-de-obra, melhorando o ambiente, a saúde e a segurança, particularmente nos sistemas de produção agrícola. Robôs autônomos fazem parte de tal inovação tecnológica e os robôs móveis com esteiras, em particular, têm sido amplamente utilizados em campos agrícolas em todo o mundo, já que suas esteiras proporcionam uma grande área de contato em solos úmidos e terrenos irregulares, evitando que o robô fique preso e melhorando a sua mobilidade. Neste trabalho, aborda-se a modelagem e o controle de robôs móveis com esteiras (Tracked Mobiler Robots, TMRs) para executar tarefas de vigilância em campos agrícolas. A metodologia proposta considera que o modelo cinemático do TMR são incertos devido ao escorregamento inerente entre as esteiras e o terreno. Para lidar com as incertezas de modelagem e perturbações externas, utiliza-se uma estratégia de controle robusto baseada na abordagem de modos deslizantes. Uma interface de usuário móvel (Mobile User Interface, MUI) baseada no sistema operacional Android é desenvolvida para controlar o robô movél com esteiras de forma manual ou autônoma. A partir da MUI, o operador humano pode visualizar as informações capturadas de sensores externos e internos. Simulações numéricas em MATLAB são realizadas para verificar o desempenho do controladores, bem como validar o modelo cinemático do robô, em diferentes configurações iniciais. / [en] In recent years, the latest advances in robotics and its applications have been used to reduce the workload and manpower requirements, improving the environment, health and safety (EHS) conditions, particularly in agricultural production and farming systems. Autonomous robots are part of such technological innovation and Tracked Mobile Robots (TMRs), in particular, have being widely used on agricultural fields around the world, since their tracks provide a large contact area on the wet soils and irregular terrains avoiding the robot to get stuck. In this work, we address the modeling and control design of tracked mobile robots (TMRs) able to perform surveillance tasks in agricultural fields. The proposed methodology considers that the kinematic models of the TMRs are both uncertain due to the inherent slippage between the tracks and the terrain. To deal with the modeling uncertainties and external disturbances, we use the sliding mode control (SMC) approach. A Mobile User Interface (MUI) based on Android operating system. is developed to control the TMR manually or autonomously. By using the MUI the human operator can visualize the information captured from external and internal sensors. Numerical simulations in MATLAB are carried out to verify the performance of the controller as well as validate the robot kinematic model under different configurations.