Coupling schemes and inexact Newton for multi-physics and coupled optimization problems

This work targets mathematical solutions and software for complex numerical simulation and optimization problems. Characteristics are the combination of different models and software modules and the need for massively parallel execution on supercomputers. We consider two different types of multi-component problems in Part I and Part II of the thesis: (i) Surface coupled fluid- structure interactions and (ii) analysis of medical MR imaging data of brain tumor patients. In (i), we establish highly accurate simulations by combining different aspects such as fluid flow and arterial wall deformation in hemodynamics simulations or fluid flow, heat transfer and mechanical stresses in cooling systems. For (ii), we focus on (a) facilitating the transfer of information such as functional brain regions from a statistical healthy atlas brain to the individual patient brain (which is topologically different due to the tumor), and (b) to allow for patient specific tumor progression simulations based on the estimation of biophysical parameters via inverse tumor growth simulation (given a single snapshot in time, only). Applications and specific characteristics of both problems are very distinct, yet both are hallmarked by strong inter-component relations and result in formidable, very large, coupled systems of partial differential equations. Part I targets robust and efficient quasi-Newton methods for black-box surface-coupling of parti- tioned fluid-structure interaction simulations. The partitioned approach allows for great flexibility and exchangeable of sub-components. However, breaking up multi-physics into single components requires advanced coupling strategies to ensure correct inter-component relations and effectively tackle instabilities. Due to the black-box paradigm, solver internals are hidden and information exchange is reduced to input/output relations. We develop advanced quasi-Newton methods that effectively establish the equation coupling of two (or more) solvers based on solving a non-linear fixed-point equation at the interface. Established state of the art methods fall short by either requiring costly tuning of problem dependent parameters, or becoming infeasible for large scale problems. In developing parameter-free, linear-complexity alternatives, we lift the robustness and parallel scalability of quasi-Newton methods for partitioned surface-coupled multi-physics simulations to a new level. The developed methods are implemented in the parallel, general purpose coupling tool preCICE. Part II targets MR image analysis of glioblastoma multiforme pathologies and patient specific simulation of brain tumor progression. We apply a joint medical image registration and biophysical inversion strategy, targeting at facilitating diagnosis, aiding and supporting surgical planning, and improving the efficacy of brain tumor therapy. We propose two problem formulations and decompose the resulting large-scale, highly non-linear and non-convex PDE-constrained optimization problem into two tightly coupled problems: inverse tumor simulation and medical image registration. We deduce a novel, modular Picard iteration-type solution strategy. We are the first to successfully solve the inverse tumor-growth problem based on a single patient snapshot with a gradient-based approach. We present the joint inversion framework SIBIA, which scales to very high image resolutions and parallel execution on tens of thousands of cores. We apply our methodology to synthetic and actual clinical data sets and achieve excellent normal-to-abnormal registration quality and present a proof of concept for a very promising strategy to obtain clinically relevant biophysical information. Advanced inexact-Newton methods are an essential tool for both parts. We connect the two parts by pointing out commonalities and differences of variants used in the two communities in unified notation

Microwave Imaging of The Neck by Means of Inverse-Scattering Techniques

In recent decades, in the field of applied electromagnetism, there has been a significant interest in the development of non-invasive diagnostic methods through the use of electromagnetic waves, especially at microwave frequencies [1]. Microwave imaging (MWI) - considered for a long period an emerging technique - has potential- ities in numerous, and constantly increasing, applications in different areas, ranging from civil and industrial engineering, with non-destructive testing and evaluations (example e.g., monitoring contamination in food, sub-surface imaging based on both terrestrial and space platforms; detection of cracks and defects in structures and equipments of various kinds; antennas diagnostics, etc. ), up to the biomedical field [2], [3], [4], [5], [6], [7]. One of the first applications of microwave imaging (MWI) in the medical field was the detection of breast tumors [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. Subsequently, brain stroke detection has received great attention [18],[19], [20], too. Other possible clinical applications include imaging of torso, arms, and other body parts [21], [22], [23], [24]. The standard diagnostic method are computerized tomography (CT), nuclear magnetic resonance (NMR) and X-rays. Although these consolidated techniques are able to provide extraordinary diagnostic results, some limitations still exist that stimulate the continuous research of new imaging solutions. In this context, MWI can be overcome some limitations of these techniques, such as the ionizing radiations in the CT and X-rays or the disadvantages of being expensive, in the NMR case. This motivates the study of MWI methods and systems, at least as a complementary diagnostic tools. The aim of electromagnetic diagnostic techniques is to determine physical param- eters (such as the electrical conductivity and the dielectric permittivity of materials) and/or geometrics of the objects under test, which are suppose contained within a certain space region, sometimes denoted as "investigation domain". In particular, by means of a properly designed transmitting antenna, the object under test is illuminated by an electromagnetic radiation. The interaction between the incident radiation and the target causes the so-called electromagnetic scattering phenomena. The field generated by this interaction can be measured around the object by means of one or more receiving antennas, placed in what is sometimes defined as the "ob- servation domain". Starting from the measured values of the scattering field, it is possible to reconstruct the fundamental properties of the test object by solving an inverse electromagnetic scattering problem. As it is well known, the inverse problem is non-linear and strongly ill-posed, unless specific approximations are used, which can be applied in specific situations. In several cases, two-dimensional configurations (2D) can be assumed, i.e., the inspected target has a cylindrical shape, at least as a first approximation. More- over, often the target is illuminated by antennas capable of generating a transverse magnetic (TM) electromagnetic field [25]. These assumptions reduces the problem from a vector and three-dimensional problem to a 2D and scalar one, since it turns out that the only significant the field components are those co-polarized with the incident wave and directed along to the cylinder axis. In recent years, several methods and algorithms that allow an efficient resolution of the equations of electromagnetic inverse scattering problem have been developed. The proposed approaches can be mainly grouped into two categories: qualitative and quantitative techniques. Qualitative procedures, such as the delay-and-sum technique [26], the linear sampling method [27], and the orthogonality sampling method [28], usually provides reconstructions that allows to extract only some parameters of the targets, such as position, dimensions and shape. However, they are in most cases fast and computationally efficient.On the contrary, quantitative methods allows in principle to retrieve the full distributions of the dielectric properties of the object under test, which allows to also obtain additional information on the materials composing the inspected scenario. Such approaches are often computationally very demanding [25]. Qualitative and quantitative approaches can be combined in order to develop hybrid algorithms [29], [30], [31], [32], [33], [34]. An example is represented by the combination of a delay-and-sum qualitative focusing technique [35], [36], [37] with a quantitative Newton scheme performing a regularization in the framework of the Lp Banach spaces [38], [39], [40]. Holographic microwave imaging techniques are other important qualitative meth- ods. In this case, the processing of data is performed by using through direct and inverse Fourier transforms in order to obtain a map of the inspected target. As previously mentioned, quantitative approaches aim at retrieving the distributions of the dielectric properties of the scene under test, although they can be significantly more time-consuming especially in 3D imaging. Among them, Newton- type approach are often considered [39], [40]. Recently, artificial neural networks (ANNs) have been considered as powerful tools for quantitative MWI. The first proposed ANNs were developed as shallow network architectures, in which one or at least two hidden layers were considered [41], [42]. Successively, deep neural networks have been proposed, in which more complex fully-connected architecture are adopted. In this framework, Convolutional Neural Networks (CNNs) have been developed as more complex topologies, for classification problems or for solving the inverse scattering problems [43], [44], [45], [46], [47], [48], [49]. In the inverse scattering problems, the CNNs often require a preliminary image retrieved by other techniques [43], [44], [47], [50], [51] and do not allow directly inver- sion from the scattered electric fields collected by the receiving antennas. Standard CNNs are developed for different applications. Examples are represented by Unet [52], ResNet [53] and VGG [54]. This Thesis is devoted to the application of MWI techniques to inspect the human neck. Several pathologic conditions can affect this part of the body, and a non-invasive and nonionizing imaging method can be useful for monitoring patients. The first pathological condition studied in this Thesis is the cervical myelopathy [55], which is a disease that damages the first part of the spinal cord, between the C3 and C7 cervical vertebrae located near the head [56]. The spinal cord has an important function in the body, since it represents the principal actor in the nervous system. For this reason, it is "protected" inside the spinal canal [57]. A first effect of cervical myelopathy is a reduction of the spinal canal sagittal diameter, which may be caused by different factors [58]. Some patients are asymptomatic and for this reason a continuous monitoring could be very helpful for evaluating the pathology progression. To this end, the application of qualitative and quantitative MWI approaches are proposed in this document. The second neck pathology studied in this Thesis is the neck tumor, in particular supraglottic laryngeal carcinoma [59], thyroid cancer [60] and cervical lymph node metastases [61]. These kinds of tumors are frequently occurring and shown a 50% 5-year survival probability [61],[62], [63], [64]. Fully-connected neural network are proposed for neck tumor detection. The Thesis is organized as follows. In Chapter 2, the relevant concepts of the electromagnetic theory are recalled. Chapter 3 describes the developed inversion algorithms. It also reports an extensive validation considering both synthetic and experimental data. Detailed data about the imaging approach based on machine learning are provided in Chapter 4. This chapter also reports the results obtained in a set of simulations and experiments. Finally, some conclusions are drawn in Chapter 5

Crosstalk suppression in multiparameter full waveform inversion through parameter decorrelation

Multiparameter full waveform inversion (FWI) is a promising technique to estimate the elastic properties of the subsurface, but it is commonly affected by crosstalk between parameters of different nature, which impacts the convergence of the local optimization algorithms and introduces artifacts and uncertainty to the results. Hence, reducing these effects is essential to increase confidence in the estimates. This thesis is focused on proposing strategies to treat these artifacts in the model space of the density (ρ), P-wave velocity (Vp), and S-wave velocity (Vs) while considering seismic surface experiments. The crosstalk effects are described and corrected by the Hessian operator, which also affects the shape of the iso-surfaces of the objective function. Therefore, two methodologies were developed based on performing constrained re-parameterizations, aiming to find an intermediate model space with decorrelated parameter classes, i.e., where the Hessian is the identity matrix, to reach convergence to an accurate minimum point, and later transform it into the original model space. The difference between both strategies lies in the type and size of the Hessian matrix used, i.e., point-wise Hessians and point-probes Hessians, as well as in the numerical approach employed to compute the transformation matrices necessary to map between model spaces. In both strategies, the estimates of Vs were relatively accurate but the results of Vp and ρ were strongly impacted by crosstalk effects in comparison to those obtained with FWI approaches that were not re-parameterized; thus, the sought intermediate model space was not properly mapped. The decorrelation ideas were successful in certain aspects, but the challenges were related to the limitations brought by the amount of crosstalk information considered through the Hessians, the selected numerical approaches, and the type of transformation matrix computed, which was able to do a good job in some locations of the model grid or for some parameter classes, but was not general enough to produce the expected transformation in a large scale

Contribution to the study of efficient iterative methods for the numerical solution of partial differential equations

Multigrid and domain decomposition methods provide efficient algorithms for the numerical solution of partial differential equations arising in the modelling of many applications in Computational Science and Engineering. This manuscript covers certain aspects of modern iterative solution methods for the solution of large-scale problems issued from the discretization of partial differential equations. More specifically, we focus on geometric multigrid methods, non-overlapping substructuring methods and flexible Krylov subspace methods with a particular emphasis on their combination. Firstly, the combination of multigrid and Krylov subspace methods is investigated on a linear partial differential equation modelling wave propagation in heterogeneous media. Secondly, we focus on non-overlapping domain decomposition methods for a specific finite element discretization known as the hp finite element, where unrefinement/refinement is allowed both by decreasing/increasing the step size h or by decreasing/increasing the polynomial degree p of the approximation on each element. Results on condition number bounds for the domain decomposition preconditioned operators are given and illustrated by numerical results on academic problems in two and three dimensions. Thirdly, we review recent advances related to a class of Krylov subspace methods allowing variable preconditioning. We examine in detail flexible Krylov subspace methods including augmentation and/or spectral deflation, where deflation aims at capturing approximate invariant subspace information. We also present flexible Krylov subspace methods for the solution of linear systems with multiple right-hand sides given simultaneously. The efficiency of the numerical methods is demonstrated on challenging applications in seismics requiring the solution of huge linear systems of equations with multiple right-hand sides on parallel distributed memory computers. Finally, we expose current and future prospectives towards the design of efficient algorithms on extreme scale machines for the solution of problems coming from the discretization of partial differential equations

A parallel algorithm for deformable contact problems

In the field of nonlinear computational solid mechanics, contact problems deal with the deformation of separate bodies which interact when they come in touch. Usually, these problems are formulated as constrained minimization problems which may be solved using optimization techniques such as penalty method, Lagrange multipliers, Augmented Lagrangian method, etc. This classical approach is based on node connectivities between the contacting bodies. These connectivities are created through the construction of contact elements introduced for the discretization of the contact interface, which incorporate the contact constraints in the global weak form. These methods are well known and widely used in the resolution of contact problems in engineering and science. As parallel computing platforms are nowadays widely available, solving large engineering problems on high performance computers is a real possibility for any engineer or researcher. Due to the memory and compute power that contact problems require and consume, they are good candidates for parallel computation. Industrial and scientific realistic contact problems involve different physical domains and a large number of degrees of freedom, so algorithms designed to run efficiently in high performance computers are needed. Nevertheless, the parallelization of the numerical solution methods that arises from the classical optimization techniques and discretization approaches presents some drawbacks which must be considered. Mainly, for general contact cases where sliding occurs, the introduction of contact elements requires the update of the mesh graph in a fixed number of time steps. From the point of view of the domain decomposition method for parallel resolution of numerical problems this is a major drawback due to its computational expensiveness, since dynamic repartitioning must be done to redistribute the updated mesh graph to the different processors. On the other hand, some of the optimization techniques modify dynamically the number of degrees of freedom in the problem, by introducing Lagrange multipliers as unknowns. In this work we introduce a Dirichlet-Neumann type parallel algorithm for the numerical solution of nonlinear frictional contact problems, putting a strong focus on its computational implementation. Among its main characteristics it can be highlighted that there is no need to update the mesh graph during the simulation, as no contact elements are used. Also, no additional degrees of freedom are introduced into the system, since no Lagrange multipliers are required. In this algorithm the bodies in contact are treated separately, in a segregated way. The coupling between the contacting bodies is performed through boundary conditions transfer at the contact zone. From a computational point of view, this feature allows to use a multi-code approach. Furthermore, the algorithm can be interpreted as a black-box method as it solves each body separately even with different computational codes. In addition, the contact algorithm proposed in this thesis can also be formulated as a general fixed-point solver for the solution of interface problems. This generalization gives us the theoretical basis to extrapolate and implement numerical techniques that were already developed and widely tested in the field of fluid-structure interaction (FSI) problems, especially those related to convergence ensurance and acceleration. We describe the parallel implementation of the proposed algorithm and analyze its parallel behaviour and performance in both validation and realistic test cases executed in HPC machines using several processors.En el ámbito de la mecánica de contacto computacional, los problemas de contacto tratan con la deformación que sufren cuerpos separados cuando interactúan entre ellos. Comunmente, estos problemas son formulados como problemas de minimización con restricciones, que pueden ser resueltos utilizando técnicas de optimización como la penalización, los multiplicadores de Lagrange, el Lagrangiano Aumentado, etc. Este enfoque clásico está basado en la conectividad de nodos entre los cuerpos, que se realiza a través de la construcción de los elementos de contacto que surgen de la discretización de la interfaz. Estos elementos incorporan las restricciones de contacto en forma débil. Debido al consumo de memoria y a los requerimientos de potencia de cálculo que los problemas de contacto requieren, resultan ser muy buenos candidatos para su paralelización computacional. Sin embargo, tanto la paralelización de los métodos numéricos que surgen de las técnicas clásicas de optimización como los distintos enfoques para su discretización, presentan algunas desventajas que deben ser consideradas. Por un lado, el principal problema aparece ya que en los casos más generales de la mecánica de contacto ocurre un deslizamiento entre cuerpos. Por este motivo, la introducción de los elementos de contacto vuelve necesaria una actualización del grafo de la malla cada cierto número de pasos de tiempo. Desde el punto de vista del método de descomposición de dominios utilizado en la resolución paralela de problemas numéricos, esto es una gran desventaja debidoa su coste computacional. En estos casos, un reparticionamiento dinámico debe ser realizado para redistribuir el grafo actualizado de la malla entre los diferentes procesadores. Por otro lado, algunas técnicas de optimización modifican dinámicamente el número de grados de libertad del problema al introducir multiplicadores de Lagrange como incógnitas. En este trabajo presentamos un algoritmo paralelo del tipo Dirichlet-Neumann para la resolución numérica de problemas de contacto no lineales con fricción, poniendo un especial énfasis en su implementación computacional. Entre sus principales características se puede destacar que no hay necesidad de actualizar el grafo de la malla durante la simulación, ya que en este algoritmo no se utilizan elementos de contacto. Adicionalmente, ningún grado de libertad extra es introducido al sistema, ya que los multiplicadores de Lagrange no son requeridos. En este algoritmo los cuerpos en contacto son tratados de forma separada, de una manera segregada. El acople entre estos cuerpos es realizado a través del intercambio de condiciones de contorno en la interfaz de contacto. Desde un punto de vista computacional, esta característica permite el uso de un enfoque multi-código. Además, este algoritmo puede ser interpretado como un método del tipo black-box ya que permite resolver cada cuerpo por separado, aún utilizando distintos códigos computacionales. Adicionalmente, el algoritmo de contacto propuesto en esta tesis puede ser formulado como un esquema de resolución de punto fijo, empleado de forma general en la solución de problemas de interfaz. Esta generalización permite extrapolar técnicas numéricas ya utilizadas en los problemas de interacción fluido-estructura e implementarlas en la mecánica de contacto, en especial aquellas relacionadas con el aseguramiento y aceleración de la convergencia. En este trabajo describimos la implementación paralela del algoritmo propuesto y analizamos su comportamiento y performance paralela tanto en casos de validación como reales, ejecutados en computadores de alta performance utilizando varios procesadores.Postprint (published version

Updating the Lambda modes of a nuclear power reactor

[EN] Starting from a steady state configuration of a nuclear power reactor some situations arise in which the reactor configuration is perturbed. The Lambda modes are eigenfunctions associated with a given configuration of the reactor, which have successfully been used to describe unstable events in BWRs. To compute several eigenvalues and its corresponding eigenfunctions for a nuclear reactor is quite expensive from the computational point of view. Krylov subspace methods are efficient methods to compute the dominant Lambda modes associated with a given configuration of the reactor, but if the Lambda modes have to be computed for different perturbed configurations of the reactor more efficient methods can be used. In this paper, different methods for the updating Lambda modes problem will be proposed and compared by computing the dominant Lambda modes of different configurations associated with a Boron injection transient in a typical BWR reactor. (C) 2010 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politecnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2011). Updating the Lambda modes of a nuclear power reactor. Mathematical and Computer Modelling. 54(7):1796-1801. https://doi.org/10.1016/j.mcm.2010.12.013S1796180154

Information metrics for localization and mapping

Aplicat embargament des de la defensa de la tesi fins al 12/2019Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals.Postprint (published version

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

Information metrics for localization and mapping

Decades of research have made possible the existence of several autonomous systems that successfully and efficiently navigate within a variety of environments under certain conditions. One core technology that has allowed this is simultaneous localization and mapping (SLAM), the process of building a representation of the environment while localizing the robot in it. State-of-the-art solutions to the SLAM problem still rely, however, on heuristic decisions and options set by the user. In this thesis we search for principled solutions to various aspects of the localization and mapping problem with the help of information metrics. One such aspect is the issue of scalability. In SLAM, the problem size grows indefinitely as the experiment goes by, increasing computational resource demands. To maintain the problem tractable, we develop methods to build an approximation to the original network of constraints of the SLAM problem by reducing its size while maintaining its sparsity. In this thesis we propose three methods to build the topology of such approximated network, and two methods to perform the approximation itself. In addition, SLAM is a passive application. It means, it does not drive the robot. The problem of driving the robot with the aim of both accurately localizing the robot and mapping the environment is called active SLAM. In this problem two normally opposite forces drive the robot, one to new places discovering unknown regions and another to revisit previous configurations to improve localization. As opposed to heuristics, in this thesis we pose the problem as the joint minimization of both map and trajectory estimation uncertainties, and present four different active SLAM approaches based on entropy-reduction formulation. All methods presented in this thesis have been rigorously validated in both synthetic and real datasets.Dècades de recerca han fet possible l’existència de nombrosos sistemes autònoms que naveguen eficaçment i eficient per varietat d’entorns sota certes condicions. Una de les principals tecnologies que ho han fet possible és la localització i mapeig simultanis (SLAM), el procés de crear una representació de l’entorn mentre es localitza el robot en aquesta. De tota manera, els algoritmes d’SLAM de l’estat de l’art encara basen moltes decisions en heurístiques i opcions a escollir per l’usuari final. Aquesta tesi persegueix solucions fonamentades per a varietat d’aspectes del problema de localització i mappeig amb l’ajuda de mesures d’informació. Un d’aquests aspectes és l’escalabilitat. En SLAM, el problema creix indefinidament a mesura que l’experiment avança fent créixer la demanda de recursos computacionals. Per mantenir el problema tractable, desenvolupem mètodes per construir una aproximació de la xarxa de restriccions original del problema d’SLAM, reduint així el seu tamany a l’hora que es manté la seva naturalesa dispersa. En aquesta tesi, proposem tres métodes per confeccionar la topologia de l’approximació i dos mètodes per calcular l’aproximació pròpiament. A més, l’SLAM és una aplicació passiva. És a dir que no dirigeix el robot. El problema de guiar el robot amb els objectius de localitzar el robot i mapejar l’entorn amb precisió es diu SLAM actiu. En aquest problema, dues forces normalment oposades guien el robot, una cap a llocs nous descobrint regions desconegudes i l’altra a revisitar prèvies configuracions per millorar la localització. En contraposició amb mètodes heurístics, en aquesta tesi plantegem el problema com una minimització de l’incertesa tant en el mapa com en l’estimació de la trajectòria feta i presentem quatre mètodes d’SLAM actiu basats en la reducció de l’entropia. Tots els mètodes presentats en aquesta tesi han estat rigurosament validats tant en sèries de dades sintètiques com en reals

A Probabilistic Treatment To Point Cloud Matching And Motion Estimation

Probabilistic and efficient motion estimation is paramount in many robotic applications, including state estimation and position tracking. Iterative closest point (ICP) is a popular algorithm that provides ego-motion estimates for mobile robots by matching point cloud pairs. Estimating motion efficiently using ICP is challenging due to the large size of point clouds. Further, sensor noise and environmental uncertainties result in uncertain motion and state estimates. Probabilistic inference is a principled approach to quantify uncertainty but is computationally expensive and thus challenging to use in complex real-time robotics tasks. In this thesis, we address these challenges by leveraging recent advances in optimization and probabilistic inference and present four core contributions. First is SGD-ICP, which employs stochastic gradient descent (SGD) to align two point clouds efficiently. The second is Bayesian-ICP, which combines SGD-ICP with stochastic gradient Langevin dynamics to obtain distributions over transformations efficiently. We also propose an adaptive motion model that employs Bayesian-ICP to produce environment-aware proposal distributions for state estimation. The third is Stein-ICP, a probabilistic ICP technique that exploits GPU parallelism for speed gains. Stein-ICP exploits the Stein variational gradient descent framework to provide non-parametric estimates of the transformation and can model complex multi-modal distributions. The fourth contribution is Stein particle filter, capable of filtering non-Gaussian, high-dimensional dynamical systems. This method can be seen as a deterministic flow of particles from an initial to the desired state. This transport of particles is embedded in a reproducing kernel Hilbert space where particles interact with each other through a repulsive force that brings diversity among the particles