La robotique mobile autonome est un axe de recherche qui vise à donner à une machine la capacité de se mouvoir dans un environnement sans assistance ni intervention humaine. Cette thèse s’intéresse à la partie décisionnelle de la navigation robotique à savoir la planification de mouvement pour un robot mobile non-holonome, pour lequel, la prise en compte des contraintes cinématiques et non-holonomes est primordiale. Aussi, la nécessité de considérer la géométrie propre du robot et la bonne maîtrise de l’environnement dans lequel il évolue constituent des contraintes à assurer. En effet la planification de mouvement consiste à calculer un mouvement réalisable que doit accomplir le robot entre une position initiale et une position finale données. Selon la nature de l’environnement, notamment les obstacles qui s’y présentent, deux instances du problème se distinguent : la planification de chemin et la planification de trajectoire. L’objectif de cette thèse est de proposer de nouveaux algorithmes pour contribuer aux deux instances du problème de planification de mouvement. La méthodologie suivie repose sur des solutions génériques qui s’appliquent à une classe de systèmes robotiques plutôt qu’à une architecture particulière. Les approches proposées intègrent les B-splines Rationnelles non uniformes (NURBS) dans le processus de modélisation des solutions générées tout en s’appuyant sur la propriété de contrôle local, et utilisent les algorithmes génétiques pour une meilleure exploration de l’espace de recherche. / The mobile robotics is an area of research that aims to give a machine the ability to move in an environment without assistance or human intervention. This thesis focuses on the decisional part of robotic navigation, namely motion planning for a non-holonomic mobile robot, for which, the consideration of kinematic and non-holonomic constraints is paramount. Also, the need to consider the specific geometry of the robot and the good control of the environment in which it operates are constraints to insure. Indeed, motion planning is to calculate a feasible movement to be performed by the robot between an initial and a final given position. Depending on the nature of the environment, two instances of the problem stand out: the path planning and the trajectory planning. The objective of this thesis is to propose new algorithms to contribute to the two instances of motion planning problem. The followed methodology is based on generic solutions that are applicable to a class of robotic systems rather than a particular architecture. The proposed approaches include the Non-Uniform Rational B-Spline (NURBS) in the modeling process of the generated solutions while relying on the local control property. Also, they use genetic algorithms for better exploration of the search space.

Ce travail de thèse vise à mettre en place un système d’extraction de réseau routier en milieu urbain à partir d’image satellite à très haute résolution. Dans ce contexte, nous avons proposé deux méthodes de localisation de routes. La première approche est fondée sur la procédure de conversion de l’image vers un format vectoriel. L’originalité de cette approche réside dans l’utilisation d’une méthode géométrique pour assurer le passage vers une représentation vectorielle de l’image d’origine et la mise en place d’un formalisme logique fondé sur un ensemble de critères perceptifs permettant le filtrage de l’information inutile et l’extraction des structures linéaires. Dans la deuxième approche, nous avons proposé un algorithme fondé sur la théorie des ondelettes, il met particulièrement en évidence les deux volets multi-résolution et multi-direction. Nous proposons donc une approche de localisation des routes mettant en jeux l'information fréquentielle multi directionnelle issue de la transformée en ondelette Log-Gabor. Dans l’étape de localisation, nous avons présenté deux détecteurs de routes qui exploitent l’information radiométrique, géométrique et fréquentielle. Cependant, ces informations ne permettent pas un résultat exact et précis. Pour remédier à ce problème, un algorithme de suivi s’avère nécessaire. Nous proposons la reconstruction de réseaux routiers par des courbes NURBS. Cette approche est basée sur un ensemble de points de repères identifiés dans la phase de localisation. Elle propose un nouveau concept, que nous avons désigné par NURBSC, basé sur les contraintes géométriques des formes à approximer. Nous connectons les segments de route identifiés afin d’obtenir des tracés continus propres aux routes. / The aim of this thesis is to establish a road network extraction system in urban areas from very high resolution satellite images. In this context, we proposed two approaches to locate roads. The first one is based on the process of converting the image into a vector form. The originality of this approach lies in the use of a geometric method to ensure the shift into a vector representation of the original image and the establishment of a logical formalism based on a set of perceptual criteria. It allows the filtering of unnecessary information and extracting linear structures. In the second approach, we proposed an algorithm based on the wavelet theory, it particularly highlights the two axis multi-resolution and multi-direction. Thus, we introduce a road localization approach, which manage the frequency multidirectional data resulting from the transform using the Log-Gabor wavelet. In the localization step, we presented two road detectors, which are capable of exploiting the radiometric, geometric and frequency data. However, this data cannot allow accurate and precise results. To overcome this drawback, a tracking algorithm is needed. We propose the reconstruction of road networks by NURBS curves. This approach is based on a landmark set of points identified in the localization phase and presents a new concept, noted by NURBSC. NURBSC is based on the geometrical constraints of shapes to be approximated. We connect road segments identified in order to obtain continuous road network.

O presente trabalho consiste no desenvolvimento de uma ferramenta computacional para análises de fratura e fadiga de componentes tridimensionais a partir de modelos geométricos de Desenho Assistido por Computador (CAD, acrônimo do inglês). Modelos de propagação de fissuras associados a leis empíricas de fadiga permitem a determinação da vida útil de peças mecânico-estruturais. Tais análises são de vital importância para garantir a segurança estrutural em diversos projetos de engenharia tais como os de pontes, plataformas off-shore e aeronaves. No entanto, a criação de modelos de análise a partir de modelos geométricos de CAD envolve diversas etapas intermediárias que visam a obtenção de malhas volumétricas adequadas. A grande maioria dos modelos de CAD trabalha com a representação de sólidos a partir de seu contorno utilizando superfícies paramétricas, dentre as quais se destacam as superfícies B-Splines Racionais Não Uniformes (NURBS, acrônimo do inglês). Para gerar malhas volumétricas é necessário que o conjunto de superfícies NURBS que descrevem o objeto seja \"estanque\", ou seja, sem lacunas e/ou superposições nas conexões das superfícies, o que não é possível garantir na grande maioria dos modelos constituídos por NURBS. As contribuições propostas no presente trabalho são aplicáveis a modelos baseados no Método dos Elementos de Contorno dual (MEC dual), os quais exigem apenas a discretização das superfícies do problema, ou seja, contorno mais fissuras. No intuito de criar os modelos de análise de maneira eficiente a partir dos modelos geométricos de CAD, desenvolveu-se uma estratégia de colocação que permite discretizar de maneira independente cada uma das superfícies NURBS que compõem os modelos geométricos sólidos. Com a estratégia proposta evitam-se as dificuldades no tratamento das conexões entre as superfícies sendo possível analisar modelos geométricos \"não estanques\". A implementação abrange superfícies NURBS, aparadas ou não, de ordens polinomiais quaisquer e elementos de contorno triangulares e quadrilaterais de aproximação linear. As equações integrais de deslocamentos e de forças de superfície são regularizadas e as integrais singulares e hipersingulares são tratadas pelo Método de Guiggiani. Fissuras de borda são inseridas nos modelos de análise a partir de um algoritmo de remalhamento simples baseado em tolerâncias dimensionais. O mesmo algoritmo é utilizado para as análises incrementais de propagação. Três técnicas de extração dos Fatores de Intensidade de Tensão (FIT) foram implementadas para os modelos baseados na Mecânica da Fratura Elástica Linear (MFEL), a saber, as técnicas de correlação, de extrapolação e de ajuste de deslocamentos. A extensão dessa última técnica para problemas tridimensionais é outra contribuição do presente trabalho. Os critérios da máxima taxa de liberação de energia e de Schöllmann foram utilizados para determinar o FIT equivalente e o caminho de propagação das fissuras. O ângulo de deflexão é determinado por um algoritmo de otimização e o ângulo de torção, definido para o critério de Schöllmann, é imposto no vetor de propagação a partir de uma formulação variacional unidimensional, definida sobre a linha de frente da fissura. Nos modelos de fadiga adota-se a MFEL e a equação de Paris-Erdogan para determinar a vida útil à propagação de defeitos preexistentes. Um procedimento iterativo foi desenvolvido para evitar a interpenetração da matéria após o contato das faces da fissura, permitindo análises de fadiga com carregamentos alternados. Como proposta para a continuidade da pesquisa propõe-se desenvolver formulações isogeométricas de elementos de contorno para analisar problemas de fratura e fadiga diretamente dos modelos geométricos de CAD, sem a necessidade de gerar as malhas de superfície. Um estudo numérico preliminar envolvendo uma versão isogeométrica do MEC dual baseada em NURBS e a versão convencional utilizando polinômios de Lagrange lineares e quadráticos foi realizado. A partir do estudo foi possível apontar as vantagens e desvantagens de cada formulação e sugerir melhorias para ambas. / The present work consists in the development of a computational tool for fracture and fatigue analysis of three-dimensional components obtained from geometrical models of Computer-Aided Design (CAD). Crack propagation models associated with empirical fatigue laws allow the determination of residual life for structural-mechanical pieces. These analyses are vital to ensure the structural safety in several engineering projects such as in bridges, offshore platforms and aircraft. However, the creation of the analysis models from geometrical CAD models requires several intermediary steps in order to obtain suitable volumetric meshes of the problems. The majority of CAD models represent solids with parametric surfaces to describe its boundaries, which is known as the Boundary representation (B-representation). The most common parametric surfaces are Non-Uniform Rational B-Splines (NURBS). To generate a volumetric mesh it is required that the set of surfaces that describe the object must be watertight, i.e., without gaps or superposition at the surfaces connections, which is not possible to unsure using NURBS. The contributions proposed at the present thesis are applicable to models based on the Dual Boundary Element Method (DBEM), which require only the discretization of the surfaces of the problems, i.e., boundary and cracks. A special collocation strategy was developed in order to create the analysis models efficiently from the geometrical CAD models. The collocation strategy allows discretizing independently each one of the NURBS surfaces that compose the geometrical solid models. Therefore, the difficulties in the treatment of the surface connections are avoided and it becomes possible to create analysis models from non-watertight geometrical models. The implementation covers trimmed and non-trimmed NURBS surfaces of any polynomial orders and also triangular and quadrilateral boundary elements of linear order. The displacement and traction boundary integral equations are regularized and the strong and hypersingular integrals are treated with the Guiggiani\'s method. Edge cracks are inserted in the models by a simple remeshing procedure based on dimensional tolerances. The same remeshing approach is adopted for the incremental crack propagation analysis. Three techniques were adopted to extract the Stress Intensity Factors (SIF) in the context of Linear Elastic Fracture Mechanics (LEFM), i.e., the displacement correlation, extrapolation and fitting techniques. The extension of this last technique to three-dimensional problems is another contribution of the present work. Both the general maximum energy realise rate and the Schöllmann\'s criteria were adopted to determine the equivalent SIF and the crack propagation path. The deflection angle is obtained by an optimization algorithm and the torsion angle, defined for the Schöllmann\'s criterion, is imposed in the propagation vector through a one-dimensional variational formulation defined over the crack front line. The concepts of LEFM are adopted together with the Paris-Erdogan equation in order to determine the fatigue life of pre-existing defects. An iterative procedure was developed to avoid the self-intersection of the crack surfaces allowing fatigue analysis with alternate loadings. Finally, as suggestion for future researches, it was started the study of isogeometric boundary element formulations in order to perform fracture and fatigue analysis directly from CAD geometries, without surface mesh generation. A preliminary numerical study involving an isogeometric version of the DBEM using NURBS and the conventional DBEM using linear and quadratic Lagrange elements was presented. From the study it was possible to point out the advantages and disadvantages of each approach and suggest improvements for both.

Thesis deals with solving the problems of continuum mechanics by method of Isogeometric analysis. This relatively young method combines the advantages of precise NURBS geometry and robustness of the classical finite element method. The method is described on procedure of solving a plane Poissons boundary value problem. Solver is implemented in MatLab and algorithms are attached to the text.

[pt] A Análise Isogeométrica (IGA) é um método de análise numérica de estruturas que surge com a proposta de unificação entre projeto e simulação, permitindo a criação de modelos computacionais que preservam a geometria exata do problema. Essa abordagem é possível por meio de uma classe de funções matemáticas denominadas NURBS (Non-Uniform Rational B-Splines), amplamente utilizadas em sistemas CAD (Computer-Aided Design) para modelagem de curvas e superfícies. Na análise isogeométrica, as mesmas funções que representam a geometria aproximam as variáveis de campo. Neste contexto, foi desenvolvido este trabalho que tem como objetivo fornecer uma ferramenta no âmbito da mecânica computacional para análise isogeométrica bidimensional de problemas de elasticidade linear, incluindo as etapas de modelagem, análise e visualização de resultados. O sistema é composto por dois softwares: FEMEP (Finite Element Method Educational Computer Program), desenvolvido em Python e responsável pela etapa de modelagem geométrica, e FEMOOLab (Finite Element Method Object-Oriented Laboratory), software MATLAB para análise e exibição de resultados. A ferramenta proposta apresenta uma interface gráfica de usuário (GUI) que permite a visualização e manipulação intuitiva de curvas NURBS com recursos avançados de modelagem, como interseção de curvas e recursos de reconhecimento de região que agilizam e simplificam o processo. Uma contribuição significativa deste trabalho reside na capacidade de gerar malhas isogeométricas não estruturadas, utilizando T-Splines baseadas em um algoritmo de decomposição de domínio. O sistema de código aberto permite a colaboração e o desenvolvimento contínuo pela comunidade de usuários e desenvolvedores. / [en] Isogeometric Analysis (IGA) is a numerical analysis method for structures that arises with the proposal of unification between design and simulation, allowing the creation of computational models that preserve the exact geometry of the problem. This approach is possible by a class of mathematical functions called NURBS (Non-Uniform Rational B-Splines), widely used in CAD (Computer-Aided Design) systems for modeling curves and surfaces. In isogeometric analysis, the same functions representing the geometry approximate the field variables. In this context, this work was developed to provide a tool within the scope of computational mechanics for two-dimensional isogeometric analysis of linear elasticity problems, including the steps of modeling, analysis, and visualization of results. The system consists of two software programs: FEMEP (Finite Element Method Educational Computer Program), developed in Python and responsible for the geometric modeling stage, and FEMOOLab (Finite Element Method Object-Oriented Laboratory), a MATLAB software for analysis and display of results. The proposed tool features a graphical user interface (GUI) that allows intuitive visualization and manipulation of NURBS curves with advanced modeling features such as curve intersection and region recognition features that streamline and simplify the process. A significant contribution of this work lies in the ability to generate non-structured isogeometric meshes, using T-Splines based on a domain decomposition algorithm. The open-source system allows collaboration and continuous development by the community of users and developers.

La production de dessins animés 2D, qui suit actuellement un schéma mis en place dans les années 1920, fait intervenir un très nombre de compétences humaines et de métiers différents. Par opposition à ce mode de travail traditionnel, la production de films de synthèse 3D, en exploitant les technologies et outils les plus récents de modélisation et d'animation 3D, s'affranchit pour une bonne part de cette composante artisanale et vient concurrencer l'industrie du dessin animé tradtionnel en termes de délais et de coûts de fabrication.<br /><br />Les défis à relever par l'industrie du dessin animé 2D se formulent donc en termes de:<br /><br /> 1. Réutilisation des contenus selon le paradigme Create once, render many,<br /> 2. Facilité d'échange et de transmission des contenus, ce qui nécessite de disposer d'un unique format de représentation,<br /> 3. Production efficace et économique des contenus, requérant une animation automatisée par ordinateur. <br /><br />Dans ce contexte compétitif, ce travail de thèse, réalisé dans le cadre du projet industriel TOON financé par la société Quadraxis avec le support de l' Agence Nationale de Valorisation de la Recherche (Oséo-ANVAR), a pour objectif de contribuer au développement d'une plate-forme de reconstruction, déformation et animation de modèles 3D pour les dessins animés 2D.<br /><br />Un état de l'art des méthodes et outils contribuant à la reconstruction de modèles 3D et à leur animation est présenté et discuté au regard des contraintes spécifiques des règles de création des dessins animés 2D et de la chaîne de fabrication traditionnelle. Ayant identifié les verrous technologiques à lever, nos contributions ont porté sur :<br /><br /> * l'élaboration d'une méthode de reconstruction de personnages virtuels 3D à partir de dessins 2D,<br /> * la mise au point d'une procédure de reconstruction surfacique par NURBS dotée d'une capacité de déformation interactive 2D/3D,<br /> * la conception d'un module de modélisation 3D pour surfaces maillées, compatible avec le standard d'animation MPEG-4/AFX. <br /><br />Les développements réalisés, intégrés dans un prototype de la plate-forme TOON, montrent un gain en temps de 20% sur l'ensemble de la chaîne de production tout en garantissant une complète interopérabilité des applications via le standard MPEG-4.

The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.

Computer Numerical Control (CNC) is widely used in many industries that needs high speed machining of the parts with high precision, accuracy and good surface finish. In order to avail this the generation of the CNC part program size will be immensely big and leads to an inefficient process, which increases the delivery time and cost of products. This work presents the automation of high-accuracy CNC tool trajectory planning from CAD to G-code generation through optimal NURBs surface approximation. The proposed optimization method finds the minimum number of NURBS control points for a given admissible theoretical cord error between the desired and manufactured surfaces. The result is a compact part program that is less sensitive to data starvation than circular and spline interpolations with potential better surface finish. The proposed approach is demonstrated with the tool path generation of an involute gear profile and a topologically optimized structure is developed using this approach and then finally it is 3D printed.

ABSTRACT Beach and nearshore surveys are conducted in a variety of ways, the most commonly used being the level-and-transit method; because it is inexpensive, time conducive and highly accurate. Specifically, beach surveys are conducted to better understand cross-shore, long-shore sediment transport processes, as well as to quantify volume changes, which are used to evaluate beach performance. In this study, a section of the beach on Sand Key, FL was surveyed using rod-and-transit. In addition to the commonly used linear data analysis, a non-linear analysis was conducted using NURBS (Non-Uniform Rational B-Splines). Survey data was collected within a short time window to ensure minimal environmental changes associated with waves and anthropological factors. Beach profiles were surveyed using two spatial resolutions, including 1) a typical variable resolution determined by the rodman based on observed morphology changes, and 2) a uniform, high resolution of 25 centimeters per point. The results indicate that variable resolution survey with careful observation by the rodman provided adequate accuracy as compared to the very high-resolution survey. The goal of this study is to create a realistic surface between the beach profiles that are spaced relatively far apart. The commonly used contouring method (a linear method) may create mismatch among major morphology units, .e.g., bar crest, if they have different elevations alongshore. Here a non-linear method is developed by 1) identifying major morphological units, in this case dune top, berm crest, trough bottom, and bar crest 2) linking the units using a cubic spline, and 3) generating a surface using a NURBS sweep2 function. Bisector profiles are sliced from the surface generated using linear and non-linear methods, and compared with surveyed profiles at the same location. The profiles generated using the non-linear method matched more closely to the measured profile than that from the linear method. The non-linear NURBS surface resulted in a consistently greater beach volume between the surveyed profiles than the linear method of volume calculation.

The thesis focuses on special space--time computational techniquesintroduced recently for computational aerodynamics modeling of flapping wings of an actual locust. These techniques complement the Deforming-Spatial-Domain/Stabilized Space--Time (DSD/SST) formulation, which is the core computational technique. The DSD/SST formulation was developed for flows with moving interfaces, and the version used in the computations is "DST/SST-VMST," which is the space--time version of the residual-based variational multiscale (VMS) method. The special space--time techniques are based on using NURBS basis functions for the temporal representation of the motion of the locust wings. The motion data is extracted from the high-speed video recordings of a locust in a wind tunnel. In addition, temporal NURBS basis functions are used in representation of the motion of the volume meshes computed and also in remeshing. These ingredients provide an accurate and e fficient way of dealing with the wind tunnel data and the mesh. The thesis includes a detailed study on how the spatial and temporal resolutions influence the quality of the numerical solution.