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This work focuses on coordination methods and the control of motion in groups of nonholonomic wheeled mobile robots, in particular of the car-like type. These kind of vehicles are particularly restricted in their mobility. In the main part of this work the two problems of formation motion coordination and of rendezvous in distributed multi-vehicle systems are considered. We introduce several enhancements to an existing motion planning approach for formations of nonholonomic mobile robots. Compared to the original method, the extended approach is able to handle time-varying reference speeds as well as adjustments of the formation's shape during reference trajectory segments with continuously differentiable curvature. Additionally, undesired discontinuities in the speed and steering profiles of the vehicles are avoided. Further, the scenario of snow shoveling on an airfield by utilizing multiple formations of autonomous snowplows is discussed. We propose solutions to the subproblems of motion planning for the formations and tracking control for the individual vehicles. While all situations that might occur have been tested in a simulation environment, we also verified the developed tracking controller in real robot hardware experiments. The task of the rendezvous problem in groups of car-like robots is to drive all vehicles to a common position by means of decentralized control laws. Typically there exists no direct interaction link between all of the vehicles. In this work we present decentralized rendezvous control laws for vehicles with free and with bounded steering. The convergence properties of the approaches are analyzed by utilizing Lyapunov based techniques. Furthermore, they are evaluated within various simulation experiments, while the bounded steering case is also verified within laboratory hardware experiments. Finally we introduce a modification to the bounded steering system that increases the convergence speed at the expense of a higher traveled distance of the vehicles.
Die Realisierung einer koordinierten und effektiven Fortbewegung für einen mobilen Roboter in natürlichen, sich kontinuierlich verändernden Umgebungen unter sich ebenso bewegenden Hindernissen ist eine komplexe Aufgabe, die die Lösung einer Reihe von Unterproblemen voraussetzt. Die vorliegende Arbeit beschäftigt sich sowohl mit den Themen der Wahrnehmung und Fortbewegung in veränderlichen Umgebungen, als auch mit Methoden zur Analyse der Hindernisbewegungen in Zusammenhang mit der Roboterbewegung selbst. Die Wahrnehmung wird in erster Linie anhand von Laserscannern betrachtet, und ein entsprechendes Verfahren zur Hindernisdetektion und -verfolung wird vorgestellt. Dabei werden Verfahren der globalen Netzwerkoptimierung eingesetzt, um Korrespondenzen zwischen Objekten aus den Einzelbildern herzustellen, was sich positiv auf die Robustheit gegenüber Störungen durch sporadische kleine Objekte auswirkt. Die Navigation basiert auf einer Adaption des sog. "Velocity Obstacle" Ansatzes auf die vorhandene Fahrzeugkinematik, und eine kooperative Bewegungskoordination (Roboter begleitet Mensch) wird durch eine geeignete Auswahlregel für kollisionsfreie Geschwindigkeiten realisiert. Anschließend werden verschiedene Distanzmaße eingeführt, anhand derer sich etwa der Pfad des Roboters mit dem Pfad seiner Begleitperson vergleichen lässt. Weiter wird eine Klassifizierung von Situationen vorgenommen, in die der Roboter potentiell involviert sein kann, und nach einer Übersicht über existierende Ansätze zur automatischen Intentionserkennung wird ein praktikabler Ansatz zur Erkennung gezielter Behinderungen eines mobilen Roboters vorgestellt. Die Arbeit schließt mit einem neuen Ansatz der Bewegungsplanung in dynamischen Umgebungen, der auf rekursiven Modellen des Roboters von seinem Gegenüber basiert, d.h. der Roboter berechnet zunächst, wie er sich in der Situation des (intelligenten, beweglichen) Hindernisses fortbewegen würde, und bezieht dies in die Entscheidung über die eigene Fortbewegung mit ein. Je nach Rekursionstiefe entstehen hierdurch Verhaltensweisen unterschiedlichen Charakters für den Roboter.
Imagine a technology that automatically creates a full 3D thermal model of an environment and detects temperature peaks in it. For better orientation in the model it is enhanced with color information. The current state of the art for analyzing temperature related issues is thermal imaging. It is relevant for energy efficiency but also for securing important infrastructure such as power supplies and temperature regulation systems. Monitoring and analysis of the data for a large building is tedious as stable conditions need to be guaranteed for several hours and detailed notes about the pose and the environment conditions for each image must be taken. For some applications repeated measurements are necessary to monitor changes over time. The analysis of the scene is only possible through expertise and experience.
This thesis proposes a robotic system that creates a full 3D model of the environment with color and thermal information by combining thermal imaging with the technology of terrestrial laser scanning. The addition of a color camera facilitates the interpretation of the data and allows for other application areas. The data from all sensors collected at different positions is joined in one common reference frame using calibration and scan matching. The first part of the thesis deals with 3D point cloud processing with the emphasis on accessing point cloud data efficiently, detecting planar structures in the data and registering multiple point clouds into one common coordinate system. The second part covers the autonomous exploration and data acquisition with a mobile robot with the objective to minimize the unseen area in 3D space. Furthermore, the combination of different modalities, color images, thermal images and point cloud data through calibration is elaborated. The last part presents applications for the the collected data. Among these are methods to detect the structure of building interiors for reconstruction purposes and subsequent detection and classification of windows. A system to project the gathered thermal information back into the scene is presented as well as methods to improve the color information and to join separately acquired point clouds and photo series.
A full multi-modal 3D model contains all the relevant geometric information about the recorded scene and enables an expert to fully analyze it off-site. The technology clears the path for automatically detecting points of interest thereby helping the expert to analyze the heat flow as well as localize and identify heat leaks. The concept is modular and neither limited to achieving energy efficiency nor restricted to the use in combination with a mobile platform. It also finds its application in fields such as archaeology and geology and can be extended by further sensors.
Network planning has come to great importance during the past decades. Today's telecommunication, traffic systems, and logistics would not have been evolved to the current state without careful analysis of the underlying network problems and precise implementation of the results obtained from those examinations. Graphs with node and arc attributes are a very useful tool to model realistic applications, while on the other hand they are well understood in theory. We investigate network design problems which are motivated particularly from applications in communication networks and logistics. Those problems include the search for homogeneous subgraphs in edge labeled graphs where either the total number of labels or the reload cost are subject to optimize. Further, we investigate some variants of the dial a ride problem. On the other hand, we use node and edge upgrade models to deal with the fact that in many cases one prefers to change existing networks rather than implementing a newly computed solution from scratch. We investigate the construction of bottleneck constrained forests under a node upgrade model, as well as several flow cost problems under a edge based upgrade model. All problems are examined within a framework of multi-criteria optimization. Many of the problems can be shown to be NP-hard, with the consequence that, under the widely accepted assumption that P is not equal to NP, there cannot exist efficient algorithms for solving the problems. This motivates the development of approximation algorithms which compute near-optimal solutions with provable performance guarantee in polynomial time.
Die Dissertation befaßt sich mit der Entwicklung einer multimedialen, datenbankgestützten Lehr- und Lernplattform. Die entwickelten Module ermöglichen und erweitern nicht nur die Möglichkeit des Selbststudiums für den Studenten sondern erleichtern auch die Arbeit der Dozenten. Außerdem wird auch die Zusammenarbeit und der Austausch von Lernobjekten zwischen verschiedenen Institutionen ermöglicht. In der Lehr- und Lernplattform können verschiedene Lernobjekt-Typen verwaltet werden. Exemplarisch wurden die Typen Bilder, 3D-Animationen, Vorlesungen, Lerntexte, Fallbeispiele und Quizelemente integriert. Die Lehr- und Lernplattform besteht aus drei Bausteinen: 1. In der Lernobjekt-Datenbank werden alle Lernobjekt-Typen und Lernobjekte verwaltet. 2. Autorenwerkzeuge dienen zur Erstellung von Lernobjekten. 3. In der Lernplattform werden die Lernobjekte den Studenten zum (Selbst-)Lernen präsentiert. Neben den Vorteilen, die der Einsatz von E-Learning im allgemeinen bietet, wie die flexible Lernorganisation oder die Nutzung von Lerninhalten unabhängig von Ort und Zeit, zeichnet sich die entwickelte Lehr- und Lernplattform besonders durch folgende Punkte aus: Generierung von Lerninhalten höherer Qualität durch multizentrische Expertenbündelung und Arbeitsteilung, Erweiterbarkeit auf andere, neue Lernobjekt-Typen, Verwaltbarkeit, Konsistenz, Flexibilität, geringer Verwaltungsaufwand, Navigationsmöglichkeiten für den Studenten, Personalisierbarkeit und Konformität zu internationalen Standards. Sowohl bei der Modellierung als auch bei der Umsetzung wurde darauf geachtet, möglichst gut die Anforderungen der Dermatologie bei gleichzeitiger Erweiterbarkeit auf andere, ähnliche Szenarien zu erfüllen. Besonders einfach sollte die Anpassung der Plattform für andere bildorientierte Disziplinen sein.
Practical optimization problems often comprise several incomparable and conflicting objectives. When booking a trip using several means of transport, for instance, it should be fast and at the same time not too expensive. The first part of this thesis is concerned with the algorithmic solvability of such multiobjective optimization problems. Several solution notions are discussed and compared with respect to their difficulty. Interestingly, these solution notions are always equally difficulty for a single-objective problem and they differ considerably already for two objectives (unless P = NP). In this context, the difference between search and decision problems is also investigated in general. Furthermore, new and improved approximation algorithms for several variants of the traveling salesperson problem are presented. Using tools from discrepancy theory, a general technique is developed that helps to avoid an obstacle that is often hindering in multiobjective approximation: The problem of combining two solutions such that the new solution is balanced in all objectives and also mostly retains the structure of the original solutions. The second part of this thesis is dedicated to several aspects of systems of equations for (formal) languages. Firstly, conjunctive and Boolean grammars are studied, which are extensions of context-free grammars by explicit intersection and complementation operations, respectively. Among other results, it is shown that one can considerably restrict the union operation on conjunctive grammars without changing the generated language. Secondly, certain circuits are investigated whose gates do not compute Boolean values but sets of natural numbers. For these circuits, the equivalence problem is studied, i.\,e.\ the problem of deciding whether two given circuits compute the same set or not. It is shown that, depending on the allowed types of gates, this problem is complete for several different complexity classes and can thus be seen as a parametrized) representative for all those classes.
Given points in the plane, connect them using minimum ink. Though the task seems simple, it turns out to be very time consuming. In fact, scientists believe that computers cannot efficiently solve it. So, do we have to resign? This book examines such NP-hard network-design problems, from connectivity problems in graphs to polygonal drawing problems on the plane. First, we observe why it is so hard to optimally solve these problems. Then, we go over to attack them anyway. We develop fast algorithms that find approximate solutions that are very close to the optimal ones. Hence, connecting points with slightly more ink is not hard.
Consider the situation where two or more images are taken from the same object. After taking the first image, the object is moved or rotated so that the second recording depicts it in a different manner. Additionally, take heed of the possibility that the imaging techniques may have also been changed. One of the main problems in image processing is to determine the spatial relation between such images. The corresponding process of finding the spatial alignment is called “registration”. In this work, we study the optimization problem which corresponds to the registration task. Especially, we exploit the Lie group structure of the set of transformations to construct efficient, intrinsic algorithms. We also apply the algorithms to medical registration tasks. However, the methods developed are not restricted to the field of medical image processing. We also have a closer look at more general forms of optimization problems and show connections to related tasks.
In the course of the growth of the Internet and due to increasing availability of data, over the last two decades, the field of network science has established itself as an own area of research. With quantitative scientists from computer science, mathematics, and physics working on datasets from biology, economics, sociology, political sciences, and many others, network science serves as a paradigm for interdisciplinary research.
One of the major goals in network science is to unravel the relationship between topological graph structure and a network’s function. As evidence suggests, systems from the same fields, i.e. with similar function, tend to exhibit similar structure. However, it is still vague whether a similar graph structure automatically implies likewise function. This dissertation aims at helping to bridge this gap, while particularly focusing on the role of triadic structures.
After a general introduction to the main concepts of network science, existing work devoted to the relevance of triadic substructures is reviewed. A major challenge in modeling triadic structure is the fact that not all three-node subgraphs can be specified independently
of each other, as pairs of nodes may participate in multiple of those triadic subgraphs.
In order to overcome this obstacle, we suggest a novel class of generative network models based on so called Steiner triple systems. The latter are partitions of a graph’s vertices into pair-disjoint triples (Steiner triples). Thus, the configurations on Steiner triples can be specified independently of each other without overdetermining the network’s link
structure.
Subsequently, we investigate the most basic realization of this new class of models. We call it the triadic random graph model (TRGM). The TRGM is parametrized by a probability distribution over all possible triadic subgraph patterns. In order to generate a network instantiation of the model, for all Steiner triples in the system, a pattern is drawn from the distribution and adjusted randomly on the Steiner triple. We calculate the degree distribution of the TRGM analytically and find it to be similar to a Poissonian distribution. Furthermore, it is shown that TRGMs possess non-trivial triadic structure. We discover inevitable correlations in the abundance of certain triadic subgraph
patterns which should be taken into account when attributing functional relevance to particular motifs – patterns which occur significantly more frequently than expected at random. Beyond, the strong impact of the probability distributions on the Steiner triples on the occurrence of triadic subgraphs over the whole network is demonstrated. This interdependence allows us to design ensembles of networks with predefined triadic substructure. Hence, TRGMs help to overcome the lack of generative models needed for assessing the relevance of triadic structure.
We further investigate whether motifs occur homogeneously or heterogeneously distributed over a graph. Therefore, we study triadic subgraph structures in each node’s neighborhood individually. In order to quantitatively measure structure from an individual node’s perspective, we introduce an algorithm for node-specific pattern mining for both directed unsigned, and undirected signed networks. Analyzing real-world datasets, we find that there are networks in which motifs are distributed highly heterogeneously, bound to the proximity of only very few nodes. Moreover, we observe indication for the potential sensitivity of biological systems to a targeted removal of these critical vertices. In addition, we study whole graphs with respect to the homogeneity and homophily of their node-specific triadic structure. The former describes the similarity of subgraph distributions in the neighborhoods of individual vertices. The latter quantifies whether connected vertices
are structurally more similar than non-connected ones. We discover these features to be characteristic for the networks’ origins. Moreover, clustering the vertices of graphs regarding their triadic structure, we investigate structural groups in the neural network of C. elegans, the international airport-connection network, and the global network of diplomatic sentiments between countries. For the latter we find evidence for the instability of triangles considered socially unbalanced according to sociological theories.
Finally, we utilize our TRGM to explore ensembles of networks with similar triadic substructure in terms of the evolution of dynamical processes acting on their nodes. Focusing on oscillators, coupled along the graphs’ edges, we observe that certain triad motifs impose a clear signature on the systems’ dynamics, even when embedded in a larger
network structure.
Operators of Higher Order
(1998)
Motivated by results on interactive proof systems we investigate the computational power of quantifiers applied to well-known complexity classes.
In special, we are interested in existential, universal and probabilistic bounded error quantifiers ranging over words and sets of words, i.e. oracles if we think in a Turing machine model.
In addition to the standard oracle access mechanism, we also consider quantifiers ranging over oracles to which access is restricted in a certain way.