For robotic deployments in planetary worksite environments, map construction and navigation are essential for tasks such as base construction, scientific investigation, and in-situ resource utilization. However, operation in a planetary environment imposes sensing restrictions, as well as challenges due to the terrain. In this thesis, we develop enabling technologies for autonomous mapping and navigation by employing a panning laser rangefinder as our primary sensor on a rover platform. The mapping task is addressed as a three-dimensional Simultaneous Localization and Mapping (3D SLAM) problem. During operation, long-range 360 degree scans are obtained at infrequent stops. These scans are aligned using a combination of sparse features and odometry measurements in a batch alignment framework, resulting in accurate maps of planetary worksite terrain. For navigation, the panning laser rangefinder is configured to perform short, continuous sweeps while the rover is in motion. An appearance-based approach is taken, where laser intensity images are used to compute Visual Odometry (VO) estimates. We overcome the motion distortion issues by formulating the estimation problem in continuous time. This is facilitated by the introduction of Gaussian Process Gauss-Newton (GPGN), a novel algorithm for nonparametric, continuous-time, nonlinear, batch state estimation. Extensive experimental validation is provided for both mapping and navigation components using data gathered at multiple planetary analogue test sites.

For robotic deployments in planetary worksite environments, map construction and navigation are essential for tasks such as base construction, scientific investigation, and in-situ resource utilization. However, operation in a planetary environment imposes sensing restrictions, as well as challenges due to the terrain. In this thesis, we develop enabling technologies for autonomous mapping and navigation by employing a panning laser rangefinder as our primary sensor on a rover platform. The mapping task is addressed as a three-dimensional Simultaneous Localization and Mapping (3D SLAM) problem. During operation, long-range 360 degree scans are obtained at infrequent stops. These scans are aligned using a combination of sparse features and odometry measurements in a batch alignment framework, resulting in accurate maps of planetary worksite terrain. For navigation, the panning laser rangefinder is configured to perform short, continuous sweeps while the rover is in motion. An appearance-based approach is taken, where laser intensity images are used to compute Visual Odometry (VO) estimates. We overcome the motion distortion issues by formulating the estimation problem in continuous time. This is facilitated by the introduction of Gaussian Process Gauss-Newton (GPGN), a novel algorithm for nonparametric, continuous-time, nonlinear, batch state estimation. Extensive experimental validation is provided for both mapping and navigation components using data gathered at multiple planetary analogue test sites.

Nous présentons une nouvelle méthode pour la restauration d'images sismiques. Quand on l'observe, une image sismique est le résultat d'un système de dépôt initial qui a été transformé par un ensemble de déformations géologiques successives (flexions, glissement de la faille, etc) qui se sont produites sur une grande période de temps. L'objectif de la restauration sismique consiste à inverser les déformations pour fournir une image résultante qui représente le système de dépôt géologique tel qu'il était dans un état antérieur. Classiquement, ce procédé permet de tester la cohérence des hypothèses d'interprétations formulées par les géophysiciens sur les images initiales. Dans notre contribution, nous fournissons un outil qui permet de générer rapidement des images restaurées et qui aide donc les géophysiciens à reconnaître et identifier les caractéristiques géologiques qui peuvent être très fortement modifiées et donc difficilement identifiables dans l'image observée d'origine. Cette application permet alors d'assister ces géophysiciens pour la formulation d'hypothèses d'interprétation des images sismiques. L'approche que nous introduisons est basée sur un processus de minimisation qui exprime les déformations géologiques en termes de contraintes géométriques. Nous utilisons une approche itérative de Gauss-Newton qui converge rapidement pour résoudre le système. Dans une deuxième partie de notre travail nous montrons différents résultats obtenus dans des cas concrets afin d'illustrer le processus de restauration d'image sismique sur des données réelles et de montrer comment la version restaurée peut être utilisée dans un cadre d'interprétation géologique. / We present a new method for seismic image restoration. When observed, a seismic image is the result of an initial deposit system that has been transformed by a set of successive geological deformations (folding, fault slip, etc) that occurred over a large period of time. The goal of seismic restoration consists in inverting the deformations to provide a resulting image that depicts the geological deposit system as it was in a previous state. With our contribution, providing a tool that quickly generates restored images helps the geophysicists to recognize geological features that may be too strongly altered in the observed image. The proposed approach is based on a minimization process that expresses geological deformations in terms of geometrical constraints. We use a quickly-converging Gauss-Newton approach to solve the system. We provide results to illustrate the seismic image restoration process on real data and present how the restored version can be used in a geological interpretation framework.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-04T13:26:23Z No. of bitstreams: 1 Magali Teresopolis Reis Amaral.pdf: 5438608 bytes, checksum: a3ca949533ae94adaf7883fd465a627a (MD5) / Made available in DSpace on 2016-08-04T13:26:23Z (GMT). No. of bitstreams: 1 Magali Teresopolis Reis Amaral.pdf: 5438608 bytes, checksum: a3ca949533ae94adaf7883fd465a627a (MD5) Previous issue date: 2008-08-18 / The adjustment of the weight-age growth curves for animals plays an important role in animal production planning. These adjusted growth curves must be coherent with the biological interpretation of animal growth, which often demands imposition of constraints on model parameters.The inference of the parameters of nonlinear models with constraints, using classical techniques, presents various difficulties. In order to bypass those difficulties, a bayesian approach for adjustment of the growing curves is proposed. In this respect the bayesian proposed approach introduces restrictions on model parameters through choice of the prior density. Due to the nonlinearity, the posterior density of those parameters does not have a kernel that can be identified among the traditional distributions, and their moments can only be obtained using numerical techniques. In this work the MCMC simulation (Monte Carlo chain Markov) was implemented to obtain a summary of the posterior density. Besides, selection model criteria were used for the observed data, based on generated samples of the posterior density.The main purpose of this work is to show that the bayesian approach can be of practical use, and to compare the bayesian inference of the estimated parameters considering noninformative prior density (from Jeffreys), with the classical inference obtained by the Gauss-Newton method. Therefore it was possible to observe that the calculation of the confidence intervals based on the asymptotic theory fails, indicating non significance of certain parameters of some models, while in the bayesian approach the intervals of credibility do not present this problem. The programs in this work were implemented in R language,and to illustrate the utility of the proposed method, analysis of real data was performed, from an experiment of evaluation of system of crossing among cows from different herds, implemented by Embrapa Pecuária Sudeste. The data correspond to 12 measurements of weight of animals between 8 and 19 months old, from the genetic groups of the races Nelore and Canchim, belonging to the genotype AALLAB (Paz 2002). The results reveal excellent applicability of the bayesian method, where the model of Richard presented difficulties of convergence both in the classical and in the bayesian approach (with non informative prior). On the other hand the logistic model provided the best adjustment of the data for both methodologies when opting for non informative and informative prior density. / O ajuste de curva de crescimento peso-idade para animais tem um papel importante no planejamento da produção animal. No entanto, as curvas de crescimento ajustadas devem ser coerentes com as interpretações biológicas do crescimento do animal, o que exige muitas vezes que sejam impostas restrições aos parâmetros desse modelo.A inferência de parâmetros de modelos não lineares sujeito a restrições, utilizando técnicas clássicas apresenta diversas dificuldades. Para contornar estas dificuldades, foi proposta uma abordagem bayesiana para ajuste de curvas de crescimento. Neste sentido,a abordagem bayesiana proposta introduz as restrições nos parâmetros dos modelos através das densidades de probabilidade a priori adotadas. Devido à não linearidade, as densidades a posteriori destes parâmetros não têm um núcleo que possa ser identificado entre as distribuições tradicionalmente conhecidas e os seus momentos só podem ser obtidos numericamente. Neste trabalho, as técnicas de simulação de Monte Carlo Cadeia de Markov (MCMC) foram implementadas para obtenção de um sumário das densidades a posteriori. Além disso, foram utilizados critérios de seleção do melhor modelo para um determinado conjunto de dados baseados nas amostras geradas das densidades a posteriori.O objetivo principal deste trabalho é mostrar a viabilidade da abordagem bayesiana e comparar a inferência bayesiana dos parâmetros estimados, considerando-se densidades a priori não informativas (de Jeffreys), com a inferência clássica das estimativas obtidas pelo método de Gauss-Newton. Assim, observou-se que o cálculo de intervalos de confiança, baseado na teoria assintótica, falha, levando a não significância de certos parâmetros de alguns modelos. Enquanto na abordagem bayesiana os intervalos de credibilidade não apresentam este problema. Os programas utilizados foram implementados no R e para ilustração da aplicabilidade do método proposto, foram realizadas análises de dados reais oriundos de um experimento de avaliação de sistema de cruzamento entre raças bovinas de corte, executado na Embrapa Pecuária Sudeste. Os dados correspondem a 12 mensurações de peso dos 8 aos 19 meses de idade do grupo genético das raças Nelore e Canchim, pertencente ao grupo de genotípico AALLAB, ver (Paz 2002). Os resultados revelaram excelente aplicabilidade do método bayesiano, destacando que o modelo de Richard apresentou dificuldades de convergência tanto na abordagem clássica como bayesiana (com priori não informativa). Por outro lado o modelo Logístico foi quem melhor se ajustou aos dados em ambas metodologias quando se optou por densidades a priori não informativa e informativa.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-05T14:28:50Z No. of bitstreams: 2 Dissertação - Ademir Alves Aguiar - 2014.pdf: 1975016 bytes, checksum: 31320b5840b8b149afedc97d0e02b49b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-06T10:38:03Z (GMT) No. of bitstreams: 2 Dissertação - Ademir Alves Aguiar - 2014.pdf: 1975016 bytes, checksum: 31320b5840b8b149afedc97d0e02b49b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-03-06T10:38:03Z (GMT). No. of bitstreams: 2 Dissertação - Ademir Alves Aguiar - 2014.pdf: 1975016 bytes, checksum: 31320b5840b8b149afedc97d0e02b49b (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-12-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation we present a semi-local convergence analysis for the Gauss-Newton method to solve a special class of systems of non-linear equations, under the hypothesis that the derivative of the non-linear operator satisfies a majorant condition. The proofs and conditions of convergence presented in this work are simplified by using a simple majorant condition. Another tool of demonstration that simplifies our study is to identify regions where the iteration of Gauss-Newton is “well-defined”. Moreover, special cases of the general theory are presented as applications. / Nesta dissertação apresentamos uma análise de convergência semi-local do método de Gauss-Newton para resolver uma classe especial de sistemas de equações não-lineares, sob a hipótese que a derivada do operador não-linear satisfaz uma condição majorante. As demonstrações e condições de convergência apresentadas neste trabalho são simplificadas pelo uso de uma simples condição majorante. Outra ferramenta de demonstração que simplifica o nosso estudo é a identificação de regiões onde a iteração de Gauss-Newton está “bem-definida”. Além disso, casos especiais da teoria geral são apresentados como aplicações.

We are examining iteratively regularized methods for solving nonlinear inverse problems. Of particular interest for these types of methods are application problems which are unstable. For these application problems, special methods of numerical analysis are necessary, since classical algorithms tend to be divergent.

No description available.

In this age, there are many applications of inverse problems to lots of areas ranging from astronomy, geoscience and so on. For example, image reconstruction and deblurring require the use of methods to solve inverse problems. Since the problems are subject to many factors and noise, we can't simply apply general inversion methods. Furthermore in the problems of interest, the number of unknown variables is huge, and some may depend nonlinearly on the data, such that we must solve nonlinear problems. It is quite different and significantly more challenging to solve nonlinear problems than linear inverse problems, and we need to use more sophisticated methods to solve these kinds of problems. / Master of Science / In various research areas, there are many required measurements which can't be observed due to physical and economical reasons. Instead, these unknown measurements can be recovered by known measurements. This phenomenon can be modeled and be solved by mathematics.

Cable-driven parallel robots (CDPRs) are parallel robots in which cables are used instead of rigid connecting elements. An important task here, as in other areas of robotics, are kinematic calculations. The state of the CDPR can be described either in Cartesian workspace coordinates as a pose or in the joint space via the cable lengths. The calculation of the cable lengths from a given platform pose is relatively simple for CDPRs. In contrast, the forward kinematics, that is, the calculation of the pose from the cable lengths, is complex due to the parallel topology and often cannot be solved analytically. In addition, CDPR systems are often designed redundantly, with more cables than Cartesian degrees of freedom. This redundancy causes that the solution of the forward kinematics can be considered as a fitting problem, where for measured cable lengths, the solution with minimum error norm is sought. In this paper, an approach based on the Gauss–Newton method is presented. It is described how a computationally efficient implementation is possible when using quaternions under consideration of the unit quaternion constraints.

The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems. / Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.