Navigace mobilních robotů v neznámém prostředí s využitím měření vzdáleností

The ability of a robot to navigate itself in the environment is a crucial step towards its autonomy. Navigation as a subtask of the development of autonomous robots is the subject of this thesis, focusing on the development of a method for simultaneous localization an mapping (SLAM) of mobile robots in six degrees of freedom (DOF). As a part of this research, a platform for 3D range data acquisition based on a continuously inclined laser rangefinder was developed. This platform is presented, evaluating the measurements and also presenting the robotic equipment on which the platform can be fitted. The localization and mapping task is equal to the registration of multiple 3D images into a common frame of reference. For this purpose, a method based on the Iterative Closest Point (ICP) algorithm was developed. First, the originally implemented SLAM method is presented, focusing on the time-wise performance and the registration quality issues introduced by the implemented algorithms. In order to accelerate and improve the quality of the time-demanding 6DOF image registration, an extended method was developed. The major extension is the introduction of a factorized registration, extracting 2D representations of vertical objects called leveled maps from the 3D point sets, ensuring these representations are 3DOF invariant. The extracted representations are registered in 3DOF using ICP algorithm, allowing pre-alignment of the 3D data for the subsequent robust 6DOF ICP based registration. The extended method is presented, showing all important modifications to the original method. The developed registration method was evaluated using real 3D data acquired in different indoor environments, examining the benefits of the factorization and other extensions as well as the performance of the original ICP based method. The factorization gives promising results compared to a single phase 6DOF registration in vertically structured environments. Also, the disadvantages of the method are discussed, proposing possible solutions. Finally, the future prospects of the research are presented.Schopnost lokalizace a navigace je podmínkou autonomního provozu mobilních robotů. Předmětem této disertační práce jsou navigační metody se zaměřením na metodu pro simultánní lokalizaci a mapování (SLAM) mobilních robotů v šesti stupních volnosti (6DOF). Nedílnou součástí tohoto výzkumu byl vývoj platformy pro sběr 3D vzdálenostních dat s využitím kontinuálně naklápěného laserového řádkového scanneru. Tato platforma byla vyvinuta jako samostatný modul, aby mohla být umístěna na různé šasi mobilních robotů. Úkol lokalizace a mapování je ekvivalentní registraci více 3D obrazů do společného souřadného systému. Pro tyto účely byla vyvinuta metoda založená na algoritmu Iterative Closest Point Algorithm (ICP). Původně implementovaná verze navigační metody využívá ICP s akcelerací pomocí kd-stromů přičemž jsou zhodnoceny její kvalitativní a výkonnostní aspekty. Na základě této analýzy byly vyvinuty rozšíření původní metody založené na ICP. Jednou z hlavních modifikací je faktorizace registračního procesu, kdy tato faktorizace je založena na redukci dat: vytvoření 2D „leveled“ map (ve smyslu jednoúrovňových map) ze 3D vzdálenostních obrazů. Pro tuto redukci je technologicky i algoritmicky zajištěna invariantnost těchto map vůči třem stupňům volnosti. Tyto redukované mapy jsou registrovány pomocí ICP ve zbylých třech stupních volnosti, přičemž získaná transformace je aplikována na 3D data za účelem před-registrace 3D obrazů. Následně je provedena robustní 6DOF registrace. Rozšířená metoda je v disertační práci v popsána spolu se všemi podstatnými modifikacemi. Vyvinutá metoda byla otestována a zhodnocena s využitím skutečných 3D vzdálenostních dat naměřených v různých vnitřních prostředích. Jsou zhodnoceny přínosy faktorizace a jiných modifikací ve srovnání s původní jednofázovou 6DOF registrací, také jsou zmíněny nevýhody implementované metody a navrženy způsoby jejich řešení. Nakonec následuje návrh budoucího výzkumu a diskuse o možnostech dalšího rozvoje.

Providing Diversity in K-Nearest Neighbor Query Results

Given a point query Q in multi-dimensional space, K-Nearest Neighbor (KNN) queries return the K closest answers according to given distance metric in the database with respect to Q. In this scenario, it is possible that a majority of the answers may be very similar to some other, especially when the data has clusters. For a variety of applications, such homogeneous result sets may not add value to the user. In this paper, we consider the problem of providing diversity in the results of KNN queries, that is, to produce the closest result set such that each answer is sufficiently different from the rest. We first propose a user-tunable definition of diversity, and then present an algorithm, called MOTLEY, for producing a diverse result set as per this definition. Through a detailed experimental evaluation on real and synthetic data, we show that MOTLEY can produce diverse result sets by reading only a small fraction of the tuples in the database. Further, it imposes no additional overhead on the evaluation of traditional KNN queries, thereby providing a seamless interface between diversity and distance.Comment: 20 pages, 11 figure

A well-separated pairs decomposition algorithm for k-d trees implemented on multi-core architectures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Variations of k-d trees represent a fundamental data structure used in Computational Geometry with numerous applications in science. For example particle track tting in the software of the LHC experiments, and in simulations of N-body systems in the study of dynamics of interacting galaxies, particle beam physics, and molecular dynamics in biochemistry. The many-body tree methods devised by Barnes and Hutt in the 1980s and the Fast Multipole Method introduced in 1987 by Greengard and Rokhlin use variants of k-d trees to reduce the computation time upper bounds to O(n log n) and even O(n) from O(n2). We present an algorithm that uses the principle of well-separated pairs decomposition to always produce compressed trees in O(n log n) work. We present and evaluate parallel implementations for the algorithm that can take advantage of multi-core architectures.The Science and Technology Facilities Council, UK

Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm

The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, pre-defined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in maze navigation and hexapod locomotion tasks

Efficient geometric algorithms for preference top-k queries, stochastic line arrangements, and proximity problems

University of Minnesota Ph.D. dissertation. June 2017. Major: Computer Science. Advisor: Ravi Janardan. 1 computer file (PDF); x, 150 pages.Problems arising in diverse real-world applications can often be modeled by geometric objects such as points, lines, and polygons. The goal of this dissertation research is to design efficient algorithms for such geometric problems and provide guarantees on their performance via rigorous theoretical analysis. Three related problems are discussed in this thesis. The first problem revisits the well-known problem of answering preference top-k queries, which arise in a wide range of applications in databases and computational geometry. Given a set of n points, each with d real-valued attributes, the goal is to organize the points into a suitable data structure so that user preference queries can be answered efficiently. A query consists of a d-dimensional vector w, representing a user's preference for each attribute, and an integer k, representing the number of data points to be retrieved. The answer to a query is the k highest-scoring points relative to w, where the score of a point, p, is designed to reflect how well it captures, in aggregate, the user's preferences for the different attributes. This thesis contributes efficient exact solutions in low dimensions (2D and 3D), and a new sampling-based approximation algorithm in higher dimensions. The second problem extends the fundamental geometric concept of a line arrangement to stochastic data. A line arrangement in the plane is a partition of the plane into vertices, edges, and faces. Surprisingly, diverse problems, including the preference top-k query and k-order Voronoi Diagram, essentially boil down to answering questions about the set of k-topmost lines at some abscissa. This thesis considers line arrangements in a new setting, where each line has an associated existence probability representing uncertainty that is inherent in real-world data. An upper-bound is derived on the expected number of changes in the set of k-topmost lines, taken over the entire x-axis, and a worst-case upper bound is given for k = 1. Also, given is an efficient algorithm to compute the most likely k-topmost lines in the arrangement. Applications of this problem including the most likely Voronoi Diagram in R^1 and stochastic preference top-k query are discussed. The third problem discussed is geometric proximity search in both the stochastic setting and the query-retrieval setting. Under the stochastic setting, the thesis considers two fundamental problems, namely, the stochastic closest pair problem and the k most likely nearest neighbor search. In both problems, the data points are assumed to lie on a tree embedded in R^2 and distances are measured along the tree (a so-called tree space). For the former, efficient solutions are given to compute the probability that the closest pair distance of a realization of the input is at least l and to compute the expected closest pair distance. For the latter, the thesis generalizes the concept of most likely Voronoi Diagram from R^1 to tree space and bounds its combinatorial complexity. A data structure for the diagram and an algorithm to construct it are also given. For the query-retrieval version which is considered in R^2, the goal is to retrieve the closest pair within a user-specified query range. The contributions here include efficient data structures and algorithms that have fast query time while using linear or near-linear space for a variety of query shapes. In addition, a generic framework is presented, which returns a closest pair that is no farther apart than the closest pair in a suitably shrunken version of the query range

On Truncations of the Exact Renormalization Group

We investigate the Exact Renormalization Group (ERG) description of ($Z_2$ invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations $n=2,3,\dots$, obtained by expanding about the field $\varphi=0$ and discarding all powers $\varphi^{2n+2}$ and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.Comment: 15 pages (with figures), Plain TeX, uses psfig, 5 postscript figures appended as uuencoded compressed tar file, SHEP 93/94-23, CERN-TH.7281/94. (Corrections of typos, and small additions to improve readability: version to be published in Phys. Lett. B