L'objectif de cette thèse est de proposer des méthodes pour étalonner un robot parallèle à câbles de grande dimension. Afin d'améliorer le comportement global d'un robot, il est nécessaire d'identifier au mieux les paramètres de son modèle. Pour cela, il est important d'obtenir des informations redondantes en mesurant l'état du robot dans différentes configurations. Cependant, le modèle choisi est un compromis entre sa capacité à représenter le comportement réel du manipulateur et les informations disponibles pour le renseigner. Dans le cas particulier des robots à câbles de grande dimension, la masse et l'élasticité des câbles ont une influence non négligeable sur le comportement du robot mais sont difficiles à modéliser. En effet, le modèle physique des câbles est complexe et nécessite de connaître la tension à laquelle ils sont soumis. Les capteurs disponibles ne pouvant nous fournir cette information avec une précision suffisante pour renseigner un modèle de câble réaliste, nous proposons d'utiliser un modèle simplifié. Dans le but de proposer un étalonnage efficace, il est donc nécessaire de définir les conditions pour l'emploi de ce modèle simplifié. Ensuite, nous avons adapté et implanté d'une part plusieurs techniques classiques pour l'étalonnage des robots parallèles mais nous avons également élaboré des approches plus innovantes. Nous proposons en effet un modèle pour les robots à câbles reposant sur une représentation des incertitudes de modélisation, de mesures et de paramètres au moyen d'intervalles. / The main objective of this thesis is to propose new methods for the calibration of a large scale cable-driven robot. The principal method to improve the global behavior of a robot consists to identify the parameters of the model. For this, it is important to get redundant information by measuring the state of the robot in different configurations. However, the model used is a compromise between its ability to represent the actual behavior of the manipulator and the information available to fill in it. In the special case of the large scale cable-driven robots, mass and elasticity of the cables have a significant influence on the behavior of the robot but they are difficult to model. Indeed, the physical model of the cable is complex and requires knowledge of the tension inside it. Available sensors cannot provide this information with a sufficient accuracy to fill in a model of a realistic cable, we thus propose to use a simplified model. In order to provide an efficient calibration, it is necessary to fix the requirements to use this simplified model. Then, we have adapted and implemented some classical techniques for the calibration of parallel robots, but we also developed more innovative approaches. We propose a model for cable robots based on a representation of the uncertainties from modeling, measurements and parameters using intervals. By exploiting the interval analysis, we have developed various approaches to identify with certification the geometric parameters of the structure. We thus propose a new approach and associated algorithms to characterize and compute different kind of solutions for the calibration problem.

Cette thèse étudie le problème de la localisation et de la cartographie simultanée (SLAM), dans des environnements non structurés, c'est-à-dire, qui ne peuvent pas être décrits par des équations ou des formes géométriques. Ces types d'environnements sont souvent rencontrés dans le domaine sous-marin. Contrairement aux approches classiques, l'environnement n'est pas modélisé par une collection de descripteurs ou d'amers ponctuels, mais directement par des ensembles. Ces ensembles, appelés forme ou shape, sont associés à des caractéristiques physiques de l'environnement, comme par exemple, des textures, du relief ou, de manière plus symbolique, à l'espace libre autour du véhicule. D'un point de vue théorique, le problème du SLAM, basé sur des formes, est formalisé par un réseau de contraintes hybrides dont les variables sont des vecteurs de Rn et des sous-ensembles de Rn. De la même façon que l'incertitude sur une variable réelle est représentée par un intervalle de réels, l'incertitude sur les formes sera représentée par un intervalle de forme. La principale contribution de cette thèse est de proposer un formalisme, basé sur le calcul par intervalle, capable de calculer ces domaines. En application, les algorithmes développés ont été appliqués au problème du SLAM à partir de données bathymétriques recueillies par un véhicule sous-marin autonome (AUV). / This thesis deals with the simultaneous localization and mapping (SLAM) problem in unstructured environments, i.e. which cannot be described by geometrical features. This type of environment frequently occurs in an underwater context.Unlike classical approaches, the environment is not described by a collection of punctual features or landmarks, but directly by sets. These sets, called shapes, are associated with physical features such as the relief, some textures or, in a more symbolic way, the space free of obstacles that can be sensed around a robot. In a theoretical point of view, the SLAM problem is formalized as an hybrid constraint network where the variables are vectors and subsets of Rn. Whereas an uncertain real number is enclosed in an interval, an uncertain shape is enclosed in an interval of sets. The main contribution of this thesis is the introduction of a new formalism, based on interval analysis, able to deal with these domains. As an application, we illustrate our method on a SLAM problem based on bathymetric data acquired by an autonomous underwater vehicle (AUV).

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 77-80).

The work in this thesis contains some contributions to constructive point-free topology and the theory of apartness spaces. The first two papers deal with constructive domain theory using formal topology. In Paper I we focus on the notion of a domain representation of a formal space as a way to introduce generalized points of the represented space, whereas we in Paper II give a constructive and point-free treatment of the domain theoretic approach to differential calculus. The last two papers are of a slightly different nature but still concern constructive topology. In paper III we consider a measure theoretic covering theorem from various constructive angles in both point-set and point-free topology. We prove a point-free version of the theorem. In Paper IV we deal with issues of impredicativity in the theory of apartness spaces. We introduce a notion of set-presented apartness relation which enables a predicative treatment of basic constructions of point-set apartness spaces.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2009. / Includes bibliographical references.

Made available in DSpace on 2014-12-02T11:16:49Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-04-04Bitstream added on 2014-12-02T11:21:26Z : No. of bitstreams: 1 000799100_20160501.pdf: 178170 bytes, checksum: ad33fa72380e16b463991462e4fe7838 (MD5) Bitstreams deleted on 2016-05-04T13:08:24Z: 000799100_20160501.pdf,. Added 1 bitstream(s) on 2016-05-04T13:09:29Z : No. of bitstreams: 1 000799100.pdf: 819920 bytes, checksum: 17cebb8c641b774f126d7d29db02f400 (MD5) / Nesta dissertação propomos estudar a aritmética intervalar restrita em níveis simples ou simplesmente SLCIA (Single Level Constraint Interval Arithmetic) e também a ordem total no espaço intervalar. Detalharemos uma estrutura algébrica adequada, falaremos sobre as propriedades do espaço métrico intervalar, assim como a caracterização das funções intervalares. Além disto faremos um estudo crítico destas funções que seja pela sua classificação em Simples, Extremais ou Totais ou por suas propriedades mais gerais. Estudaremos as sequências de números intervalares, os limites de funções intervalares. Mostraremos uma aplicação de todas estas utilizando o principio de extensão de Zadeh no contexto fuzzy / This work proposes to study the Single Level Constraint Interval Arithmetic or simply SLCIA, an appropriate algebraic structure and a metric of the interval space. Additionally, it will also make a critical study of interval functions and the characterization of these functions depending on their classification in Simple, Extremal or Totals or by its general properties. Furthermore, we will study the sequences of interval numbers and the limits of interval functions. Lastly, it will also show an application of all these using Zadeh´s extension principle on the Fuzzy context

Orientador: Geraldo Nunes Silva / Coorientador: Weldon Lodwick / Banca: Laécio Carvalho de Barros / Banca: Valeriano Antunes de Oliveira / Resumo: Nesta dissertação propomos estudar a aritmética intervalar restrita em níveis simples ou simplesmente SLCIA (Single Level Constraint Interval Arithmetic) e também a ordem total no espaço intervalar. Detalharemos uma estrutura algébrica adequada, falaremos sobre as propriedades do espaço métrico intervalar, assim como a caracterização das funções intervalares. Além disto faremos um estudo crítico destas funções que seja pela sua classificação em Simples, Extremais ou Totais ou por suas propriedades mais gerais. Estudaremos as sequências de números intervalares, os limites de funções intervalares. Mostraremos uma aplicação de todas estas utilizando o principio de extensão de Zadeh no contexto fuzzy / Abstract: This work proposes to study the Single Level Constraint Interval Arithmetic or simply SLCIA, an appropriate algebraic structure and a metric of the interval space. Additionally, it will also make a critical study of interval functions and the characterization of these functions depending on their classification in Simple, Extremal or Totals or by its general properties. Furthermore, we will study the sequences of interval numbers and the limits of interval functions. Lastly, it will also show an application of all these using Zadeh's extension principle on the Fuzzy context / Mestre

Cette thèse s’inscrit dans la problématique générale de la caractérisation et de la classification des systèmes. Plus précisément, nos contributions s’orientent vers les applications robotiques et, plus particulièrement, vers la classification de manipulateurs. Les algorithmes et méthodologies proposés dans ce document s’appuient sur plusieurs théories mathématiques dont la théorie des singularités et l’Analyse par Intervalles, qui sont formalisés dans la première partie de cette Thèse.Classifier des systèmes induit deux objectifs que sont la formalisation des éléments communs aux systèmes dans la même classe ainsi que leur détection formelle et pratique. Ainsi, ce mémoire compile, pour chacun dans un chapitre dédié, nos contributions vis-à-vis de ces deux objectifs associés à la classification. Une méthodologie générale est proposée, afin de distinguer plusieurs sous ensembles singuliers caractéristiques et génériquement non vides. Cette méthodologie est illustrée pour des fonctions entre espaces de même dimension, allant de 1à 3. Chaque application met en lumière des propriétés différentes de la méthodologie générale proposée.Complémentairement, chacune de ces applications mène à la conception d’algorithmes, basé sur l’Analyse par Intervalles, mettant en œuvre cette méthodologie.Complémentairement à la détection de points d’intérêt,nous présentons une méthodologie générale pour définir un objet combinatoire codant le comportement d’une fonction. Cette méthodologie s’appuie sur la détection préalable d’ensembles d’intérêt dont les topologies sont invariantes pour l’équivalence choisie. Ces développements ouvrent vers de nombreuses perspectives futures qui concluent ce mémoire. / This thesis is within the scope of the general problematic of characterizing and classifying systems. More precisely, our contributions are aimed toward robotic applications and, more particularly, at the classification of manipulators. The algorithms and methodologies proposed in this document are based upon several mathematical theories including Singularity Theory and Interval Analysis, which are formalized in the first part of this Phd Thesis report. Classifying systems induces two objectives that are the formalization of the elements commons to systems in the same class as well as their formal and practical detection. Then, this report compiles, for each one in a dedicated chapter, our contributions regarding these two objectives associated with the classification. A general methodology is proposed, with the objective to distinguish several characteristic singular subsets that prove to be generically not empty. This methodology is illustrated for functions between spaces of the same dimension, ranging from 1 to 3. Each application highlights different properties that are admitted by the proposed general methodology. Furthermore, each of these applications leads to the conception of severalalgorithms, based on Interval Analysis, that enforce the proposed methodology. Complementarily to the detection of interest points, we introduce a general methodology to define a combinatorial object encoding the behavior of a function. This methodology is based on the preliminary detection of interest sets whose topologies are invariant for the chosen equivalence. These developments open up to numerous future perspectives that conclude this report.

Orientador: Paulo Augusto Valente Ferreira / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-06T11:17:31Z (GMT). No. of bitstreams: 1 Benjovengo_FabioPereira_M.pdf: 2854202 bytes, checksum: b1bccce6d2ea6efa1b55778d0fba1399 (MD5) Previous issue date: 2006 / Resumo: Esta Dissertação tem como objetivos o projeto de sistemas de controle e a análise de estabilidade de plantas lineares e invariantes no tempo imprecisamente conhecidas (com incertezas do tipo intervalar). O problema de projeto de controladores é tratado através da técnica de alocação de pólos. A técnica de alocação robusta de pólos proposta nesta Dissertação é uma extensão da técnica de projeto clássica e utiliza resultados de Análise Intervalar. A extensão proposta resulta numa equação Diofantina intervalar. Busca-se, então, a redução do raio de sua solução através do tratamento de multiincidências de elementos intervalares. Outro tema tratado é o projeto de controladores que visem o rastreamento de sinais de referência e a rejeição de distúrbios, assintoticamente. Estuda-se ainda o problema da estabilidade de sistemas intervalares formulado como o problema de encontrar uma matriz intervalar simétrica definida positiva como solução de uma equação de Lyapunov intervalar / Abstract: This Dissertation is focused on control system design and stability analysis of linear timeinvariant uncertain plants, with uncertainties of interval nature. The control system design problem is treated in the context of the pole placement technique. An extension of the classical technique to robust pole placement based on Interval Analysis is proposed. The main objective of the work is to handle multiple incidences of plant parameters in order to reduce the radii of the solutions of the resulting interval Diophantine equations. Another subject treated is the design of robust controllers for interval plants which guarantee reference tracking and disturbance rejection asymptotically. The stability of linear interval systems as the problem of finding a symmetric positive definite interval solution of an interval Lyapunov equation is also considered. / Mestrado / Engenharia Eletrica / Mestre em Engenharia Elétrica

Les robots à câbles (CDPRs) se présentent comme une nouvelle classe de robots parallèles. Ces robots, décrits par l'architecture RRPS des hexapodes, utilisent des câbles enroulés pour leurs jambes plutôt que les chaînes d'éléments rigides des robots parallèles classiques. Cette technologie est dépendante des câbles, donc sujette à l'unilatéralité des efforts exercés par les câbles sur la plate-forme, l'élasticité, ou bien l'affaissement dû à la flexibilité et à la masse. Dans un premier temps nous revisitons la modélisation de ce type de robot, en particulier pour le comportement de type chaînette élastique, approprié pour les robots de grandes dimensions. Dans un second temps nous traitons de la détection de collision, et ce aussi bien entre les câbles, qu'avec et entre les objets que sont la plate-forme et d'éventuels obstacles. S'agissant d'une problématique de sûreté, la détection se doit d'être garantie face aux incertitudes et face à la forme complexe des câbles. Elle est déclinée pour le modèle RRPS et le modèle chaînette élastique. L'analyse par intervalles est utilisée pour traiter les incertitudes, et les objets sont munis de définitions hiérarchiques. Enfin, nous aborderons un processus de conception, qui a pour objectif de répondre au besoin exprimé par une application. À cette fin, il cherche l'ensemble des valeurs des paramètres d'un modèle générique de CDPR, permettant de satisfaire un ensemble de contraintes. Ces paramètres sont toutefois soumis à leurs propres incertitudes. Aussi, on assure la faisabilité de la conception en garantissant et la validité de tous les robots possibles donnés par les intervalles de solutions, et la largeur minimale. / Cable-Driven Parallel Robots form a new class of parallel robots. Those robots, described by the RRPS architecture of hexapods, use coiled cables for their legs instead of rigid element chains of classical parallel robots. This technology is subject to the specifics of cables, particularly the unilateral aspect of the forces exerted by the cables on the platform, the elasticity, the sagging caused by the flexibility and the mass of the cables. We start by revisiting the model of those robots. We do so by considering the elastic catenary behavior of the cables, suitable for large dimension robots. Then we handle interference detection of such a robot, which concern just as much interference between cables, than with and between objects. Said objects are the platform and arbitrary obstacles. Being a safety matter, interference detection must be guaranteed in front of uncertainties and of the complex shapes of the cables. The detection scheme is issued for the RRPS model and the elastic catenary one. Interval analysis methods are used to deal with uncertainties; hierarchic definitions are used for objects. Lastly, we deal with a design process for those robots. This process aims at fitting a robot that satisfy the expressed needs of a given application. To this end, the process looks for the set of values of parameters of a CDPR generic model. Those values allow the resulting robot to satisfy a set of constraints. Those parameters are subject to their own uncertainties. We guarantee the practical usability of the design both by guaranteeing the suitability of all possible robots given by the intervals of the solutions for the parameters, and with minimal widths.