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A centralized heterogeneous formation flight position control scheme has been formulated using an explicit model following design, based on a Linear Quadratic Regulator Proportional Integral (LQR PI) controller. The leader quadcopter is a stable reference model with desired dynamics whose output is perfectly tracked by the two wingmen quadcopters. The leader itself is controlled through the pole placement control method with desired stability characteristics, while the two followers are controlled through a robust and adaptive LQR PI control method. Selected 3-D formation geometry and static stability are maintained under a number of possible perturbations. With this control scheme, formation geometry may also be switched to any arbitrary shape during flight, provided a suitable collision avoidance mechanism is incorporated. In case of communication loss between the leader and any of the followers, the other follower provides the data, received from the leader, to the affected follower. The stability of the closed-loop system has been analyzed using singular values. The proposed approach for the tightly coupled formation flight of mini unmanned aerial vehicles has been validated with the help of extensive simulations using MATLAB/Simulink, which provided promising results.
In the present work, a simulation system is proposed that can be used as an educational tool by physicians in training basic skills of minimally invasive vascular interventions. In order to accomplish this objective, initially the physical model of the wire proposed by Konings has been improved. As a result, a simpler and more stable method was obtained to calculate the equilibrium configuration of the wire. In addition, a geometrical method is developed to perform relaxations. It is particularly useful when the wire is hindered in the physical method because of the boundary conditions. Then a recipe is given to merge the physical and the geometrical methods, resulting in efficient relaxations. Moreover, tests have shown that the shape of the virtual wire agrees with the experiment. The proposed algorithm allows real-time executions, and furthermore, the hardware to assemble the simulator has a low cost.
3D point clouds are a de facto standard for 3D documentation and modelling. The advances in laser scanning technology broadens the usability and access to 3D measurement systems. 3D point clouds are used in many disciplines such as robotics, 3D modelling, archeology and surveying. Scanners are able to acquire up to a million of points per second to represent the environment with a dense point cloud. This represents the captured environment with a very high degree of detail. The combination of laser scanning technology with photography adds color information to the point clouds. Thus the environment is represented more realistically. Full 3D models of environments, without any occlusion, require multiple scans. Merging point clouds is a challenging process. This thesis presents methods for point cloud registration based on the panorama images generated from the scans. Image representation of point clouds introduces 2D image processing methods to 3D point clouds. Several projection methods for the generation of panorama maps of point clouds are presented in this thesis. Additionally, methods for point cloud reduction and compression based on the panorama maps are proposed. Due to the large amounts of data generated from the 3D measurement systems these methods are necessary to improve the point cloud processing, transmission and archiving. This thesis introduces point cloud processing methods as a novel framework for the digitisation of archeological excavations. The framework replaces the conventional documentation methods for excavation sites. It employs point clouds for the generation of the digital documentation of an excavation with the help of an archeologist on-site. The 3D point cloud is used not only for data representation but also for analysis and knowledge generation. Finally, this thesis presents an autonomous indoor mobile mapping system. The mapping system focuses on the sensor placement planning method. Capturing a complete environment requires several scans. The sensor placement planning method solves for the minimum required scans to digitise large environments. Combining this method with a navigation system on a mobile robot platform enables it to acquire data fully autonomously. This thesis introduces a novel hole detection method for point clouds to detect obscured parts of a captured environment. The sensor placement planning method selects the next scan position with the most coverage of the obscured environment. This reduces the required number of scans. The navigation system on the robot platform consist of path planning, path following and obstacle avoidance. This guarantees the safe navigation of the mobile robot platform between the scan positions. The sensor placement planning method is designed as a stand alone process that could be used with a mobile robot platform for autonomous mapping of an environment or as an assistant tool for the surveyor on scanning projects.
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.
Small satellites contribute significantly in the rapidly evolving innovation in space engineering, in particular in distributed space systems for global Earth observation and communication services. Significant mass reduction by miniaturization, increased utilization of commercial high-tech components, and in particular standardization are the key drivers for modern miniature space technology.
This thesis addresses key fields in research and development on miniature satellite technology regarding efficiency, flexibility, and robustness. Here, these challenges are addressed by the University of Wuerzburg’s advanced pico-satellite bus, realizing a generic modular satellite architecture and standardized interfaces for all subsystems. The modular platform ensures reusability, scalability, and increased testability due to its flexible subsystem interface which allows efficient and compact integration of the entire satellite in a plug-and-play manner.
Beside systematic design for testability, a high degree of operational robustness is achieved by the consequent implementation of redundancy of crucial subsystems. This is combined with efficient fault detection, isolation and recovery mechanisms. Thus, the UWE-3 platform, and in particular the on-board data handling system and the electrical power system, offers one of the most efficient pico-satellite architectures launched in recent years and provides a solid basis for future extensions.
The in-orbit performance results of the pico-satellite UWE-3 are presented and summarize successful operations since its launch in 2013. Several software extensions and adaptations have been uploaded to UWE-3 increasing its capabilities. Thus, a very flexible platform for in-orbit software experiments and for evaluations of innovative concepts was provided and tested.
Graphs are a frequently used tool to model relationships among entities. A graph is a binary relation between objects, that is, it consists of a set of objects (vertices) and a set of pairs of objects (edges).
Networks are common examples of modeling data as a graph. For example, relationships between persons in a social network, or network links between computers in a telecommunication network can be represented by a graph.
The clearest way to illustrate the modeled data is to visualize the graphs. The field of Graph Drawing deals with the problem of finding algorithms to automatically generate graph visualizations. The task is to find a "good" drawing, which can be measured by different criteria such as number of crossings between edges or the used area. In this thesis, we study Angular Schematization in Graph Drawing. By this, we mean drawings
with large angles (for example, between the edges at common vertices or at crossing points).
The thesis consists of three parts. First, we deal with the placement of boxes. Boxes are axis-parallel rectangles that can, for example, contain text.
They can be placed on a map to label important sites, or can be used to describe semantic relationships between words in a word network. In the second part of the thesis, we consider graph drawings visually guide the
viewer. These drawings generally induce large angles between edges that meet at a vertex. Furthermore, the edges are drawn crossing-free and in a way that
makes them easy to follow for the human eye. The third and final part is devoted to crossings with large angles. In drawings with crossings, it is important to have large angles between edges at their crossing point, preferably right angles.
The development of ICT infrastructures has facilitated the emergence of new paradigms for looking at society and the environment over the last few years. Participatory environmental sensing, i.e. directly involving citizens in environmental monitoring, is one example, which is hoped to encourage learning and enhance awareness of environmental issues. In this paper, an analysis of the behaviour of individuals involved in noise sensing is presented. Citizens have been involved in noise measuring activities through the WideNoise smartphone application. This application has been designed to record both objective (noise samples) and subjective (opinions, feelings) data. The application has been open to be used freely by anyone and has been widely employed worldwide. In addition, several test cases have been organised in European countries. Based on the information submitted by users, an analysis of emerging awareness and learning is performed. The data show that changes in the way the environment is perceived after repeated usage of the application do appear. Specifically, users learn how to recognise different noise levels they are exposed to. Additionally, the subjective data collected indicate an increased user involvement in time and a categorisation effect between pleasant and less pleasant environments.
Background
Information extraction techniques that get structured representations out of unstructured data make a large amount of clinically relevant information about patients accessible for semantic applications. These methods typically rely on standardized terminologies that guide this process. Many languages and clinical domains, however, lack appropriate resources and tools, as well as evaluations of their applications, especially if detailed conceptualizations of the domain are required. For instance, German transthoracic echocardiography reports have not been targeted sufficiently before, despite of their importance for clinical trials. This work therefore aimed at development and evaluation of an information extraction component with a fine-grained terminology that enables to recognize almost all relevant information stated in German transthoracic echocardiography reports at the University Hospital of Würzburg.
Methods
A domain expert validated and iteratively refined an automatically inferred base terminology. The terminology was used by an ontology-driven information extraction system that outputs attribute value pairs. The final component has been mapped to the central elements of a standardized terminology, and it has been evaluated according to documents with different layouts.
Results
The final system achieved state-of-the-art precision (micro average.996) and recall (micro average.961) on 100 test documents that represent more than 90 % of all reports. In particular, principal aspects as defined in a standardized external terminology were recognized with f 1=.989 (micro average) and f 1=.963 (macro average). As a result of keyword matching and restraint concept extraction, the system obtained high precision also on unstructured or exceptionally short documents, and documents with uncommon layout.
Conclusions
The developed terminology and the proposed information extraction system allow to extract fine-grained information from German semi-structured transthoracic echocardiography reports with very high precision and high recall on the majority of documents at the University Hospital of Würzburg. Extracted results populate a clinical data warehouse which supports clinical research.
A binary tanglegram is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential that both trees are drawn without edge crossings and that the inter-tree edges have as few crossings as possible. It is known that finding a tanglegram with the minimum number of crossings is NP-hard and that the problem is fixed-parameter tractable with respect to that number.
We prove that under the Unique Games Conjecture there is no constant-factor approximation for binary trees. We show that the problem is NP-hard even if both trees are complete binary trees. For this case we give an O(n 3)-time 2-approximation and a new, simple fixed-parameter algorithm. We show that the maximization version of the dual problem for binary trees can be reduced to a version of MaxCut for which the algorithm of Goemans and Williamson yields a 0.878-approximation.
Knowledge-based systems (KBS) face an ever-increasing interest in various disciplines and contexts. Yet, the former aim to construct the ’perfect intelligent software’ continuously shifts to user-centered, participative solutions. Such systems enable users to contribute their personal knowledge to the problem solving process for increased efficiency and an ameliorated user experience. More precisely, we define non-functional key requirements of participative KBS as: Transparency (encompassing KBS status mediation), configurability (user adaptability, degree of user control/exploration), quality of the KB and UI, and evolvability (enabling the KBS to grow mature with their users). Many of those requirements depend on the respective target users, thus calling for a more user-centered development. Often, also highly expertise domains are targeted — inducing highly complex KBs — which requires a more careful and considerate UI/interaction design. Still, current KBS engineering (KBSE) approaches mostly focus on knowledge acquisition (KA) This often leads to non-optimal, little reusable, and non/little evaluated KBS front-end solutions.
In this thesis we propose a more encompassing KBSE approach. Due to the strong mutual influences between KB and UI, we suggest a novel form of intertwined UI and KB development. We base the approach on three core components for encompassing KBSE:
(1) Extensible prototyping, a tailored form of evolutionary prototyping; this builds on mature UI prototypes and offers two extension steps for the anytime creation of core KBS prototypes (KB + core UI) and fully productive KBS (core KBS prototype + common framing functionality). (2) KBS UI patterns, that define reusable solutions for the core KBS UI/interaction; we provide a basic collection of such patterns in this work. (3) Suitable usability instruments for the assessment of the KBS artifacts. Therewith, we do not strive for ’yet another’ self-contained KBS engineering methodology. Rather, we motivate to extend existing approaches by the proposed key components. We demonstrate this based on an agile KBSE model.
For practical support, we introduce the tailored KBSE tool ProKEt. ProKEt offers a basic selection of KBS core UI patterns and corresponding configuration options out of the box; their further adaption/extension is possible on various levels of expertise. For practical usability support, ProKEt offers facilities for quantitative and qualitative data collection. ProKEt explicitly fosters the suggested, intertwined development of UI and KB. For seamlessly integrating KA activities, it provides extension points for two selected external KA tools: For KnowOF, a standard office based KA environment. And for KnowWE, a semantic wiki for collaborative KA. Therewith, ProKEt offers powerful support for encompassing, user-centered KBSE.
Finally, based on the approach and the tool, we also developed a novel KBS type: Clarification KBS as a mashup of consultation and justification KBS modules. Those denote a specifically suitable realization for participative KBS in highly expertise contexts and consequently require a specific design. In this thesis, apart from more common UI solutions, we particularly also introduce KBS UI patterns especially tailored towards Clarification KBS.
At the center of the Internet’s protocol stack stands the Internet Protocol (IP) as a common denominator that enables all communication. To make routing efficient, resilient, and scalable, several aspects must be considered. Care must be taken that traffic is well balanced to make efficient use of the existing network resources, both in failure free operation and in failure scenarios.
Finding the optimal routing in a network is an NP-complete problem. Therefore, routing optimization is usually performed using heuristics. This dissertation shows that a routing optimized with one objective function is often not good when looking at other objective functions. It can even be worse than unoptimized routing with respect to that objective function. After looking at failure-free routing and traffic distribution in different failure scenarios, the analysis is extended to include the loop-free alternate (LFA) IP fast reroute mechanism. Different application scenarios of LFAs are examined and a special focus is set on the fact that LFAs usually cannot protect all traffic in a network even against single link failures. Thus, the routing optimization for LFAs is targeted on both link utilization and failure coverage. Finally, the pre-congestion notification mechanism PCN for network admission control and overload protection is analyzed and optimized. Different design options for implementing the protocol are compared, before algorithms are developed for the calculation and optimization of protocol parameters and PCN-based routing.
The second part of the thesis tackles a routing problem that can only be resolved on a global scale. The scalability of the Internet is at risk since a major and intensifying growth of the interdomain routing tables has been observed. Several protocols and architectures are analyzed that can be used to make interdomain routing more scalable. The most promising approach is the locator/identifier (Loc/ID) split architecture which separates routing from host identification. This way, changes in connectivity, mobility of end hosts, or traffic-engineering activities are hidden from the routing in the core of the Internet and the routing tables can be kept much smaller. All of the currently proposed Loc/ID split approaches have their downsides. In particular, the fact that most architectures use the ID for routing outside the Internet’s core is a poor design, which inhibits many of the possible features of a new routing architecture. To better understand the problems and to provide a solution for a scalable routing design that implements a true Loc/ID split, the new GLI-Split protocol is developed in this thesis, which provides separation of global and local routing and uses an ID that is independent from any routing decisions.
Besides GLI-Split, several other new routing architectures implementing Loc/ID split have been proposed for the Internet. Most of them assume that a mapping system is queried for EID-to-RLOC mappings by an intermediate node at the border of an edge network. When the mapping system is queried by an intermediate node, packets are already on their way towards their destination, and therefore, the mapping system must be fast, scalable, secure, resilient, and should be able to relay packets without locators to nodes that can forward them to the correct destination. The dissertation develops a classification for all proposed mapping system architectures and shows their similarities and differences. Finally, the fast two-level mapping system FIRMS is developed. It includes security and resilience features as well as a relay service for initial packets of a flow when intermediate nodes encounter a cache miss for the EID-to-RLOC mapping.
A simple test setup has been developed at Institute of Aerospace Information Technology, University of Würzburg, Germany to realize basic functionalities for formation flight of quadrocopters. The test environment is planned to be utilized for developing and validating the algorithms for formation flying capability in real environment as well as for education purpose. An already existing test bed for single quadrocopter was extended with necessary inter-communication and distributed control mechanism to test the algorithms for formation flights in 2 degrees of freedom (roll / pitch). This study encompasses the domain of communication, control engineering and embedded systems programming. Bluetooth protocol has been used for inter-communication between two quadrocopters. A simple approach of PID control in combination with Kalman filter has been exploited. MATLAB Instrument Control Toolbox has been used for data display, plotting and analysis. Plots can be drawn in real-time and received information can also be stored in the form of files for later use and analysis. The test setup has been developed indigenously and at considerably low cost. Emphasis has been placed on simplicity to facilitate students learning process. Several lessons have been learnt during the course of development of this setup. Proposed setup is quite flexible that can be modified as per changing requirements.
Object six Degrees of Freedom (6DOF) pose estimation is a fundamental problem in many practical robotic applications, where the target or an obstacle with a simple or complex shape can move fast in cluttered environments. In this thesis, a 6DOF pose estimation algorithm is developed based on the fused data from a time-of-flight camera and a color camera. The algorithm is divided into two stages, an annealed particle filter based coarse pose estimation stage and a gradient decent based accurate pose optimization stage. In the first stage, each particle is evaluated with sparse representation. In this stage, the large inter-frame motion of the target can be well handled. In the second stage, the range data based conventional Iterative Closest Point is extended by incorporating the target appearance information and used for calculating the accurate pose by refining the coarse estimate from the first stage. For dealing with significant illumination variations during the tracking, spherical harmonic illumination modeling is investigated and integrated into both stages. The robustness and accuracy of the proposed algorithm are demonstrated through experiments on various objects in both indoor and outdoor environments. Moreover, real-time performance can be achieved with graphics processing unit acceleration.
This technical report introduces the Descartes Modeling Language (DML), a new architecture-level modeling language for modeling Quality-of-Service (QoS) and resource management related aspects of modern dynamic IT systems, infrastructures and services. DML is designed to serve as a basis for self-aware resource management during operation ensuring that system QoS requirements are continuously satisfied while infrastructure resources are utilized as efficiently as possible.
In many cases, problems, data, or information can be modeled as graphs. Graphs can be used as a tool for modeling in any case where connections between distinguishable objects occur. Any graph consists of a set of objects, called vertices, and a set of connections, called edges, such that any edge connects a pair of vertices. For example, a social network can be modeled by a graph by
transforming the users of the network into vertices and friendship relations between users into edges. Also physical networks like computer networks or transportation networks, for example, the metro network of a city, can be seen as graphs.
For making graphs and, thereby, the data that is modeled, well-understandable for users, we need a visualization. Graph drawing deals with algorithms for visualizing graphs. In this thesis, especially the use of crossings and curves is investigated for graph drawing problems under additional constraints. The constraints that occur in the problems investigated in this thesis especially restrict the positions of (a part of) the vertices; this is done either as a hard constraint or as an optimization criterion.
Routing is one of the most important issues in any communication network. It defines on which path packets are transmitted from the source of a connection to the destination. It allows to control the distribution of flows between different locations in the network and thereby is a means to influence the load distribution or to reach certain constraints imposed by particular applications. As failures in communication networks appear regularly and cannot be completely avoided, routing is required to be resilient against such outages, i.e., routing still has to be able to forward packets on backup paths even if primary paths are not working any more.
Throughout the years, various routing technologies have been introduced that are very different in their control structure, in their way of working, and in their ability to handle certain failure cases. Each of the different routing approaches opens up their own specific questions regarding configuration, optimization, and inclusion of resilience issues. This monograph investigates, with the example of three particular routing technologies, some concrete issues regarding the analysis and optimization of resilience. It thereby contributes to a better general, technology-independent understanding of these approaches and of their diverse potential for the use in future network architectures.
The first considered routing type, is decentralized intra-domain routing based on administrative IP link costs and the shortest path principle. Typical examples are common today's intra-domain routing protocols OSPF and IS-IS. This type of routing includes automatic restoration abilities in case of failures what makes it in general very robust even in the case of severe network outages including several failed components. Furthermore, special IP-Fast Reroute mechanisms allow for a faster reaction on outages. For routing based on link costs, traffic engineering, e.g. the optimization of the maximum relative link load in the network, can be done indirectly by changing the administrative link costs to adequate values.
The second considered routing type, MPLS-based routing, is based on the a priori configuration of primary and backup paths, so-called Label Switched Paths. The routing layout of MPLS paths offers more freedom compared to IP-based routing as it is not restricted by any shortest path constraints but any paths can be setup. However, this in general involves a higher configuration effort.
Finally, in the third considered routing type, typically centralized routing using a Software Defined Networking (SDN) architecture, simple switches only forward packets according to routing decisions made by centralized controller units. SDN-based routing layouts offer the same freedom as for explicit paths configured using MPLS. In case of a failure, new rules can be setup by the controllers to continue the routing in the reduced topology. However, new resilience issues arise caused by the centralized architecture. If controllers are not reachable anymore, the forwarding rules in the single nodes cannot be adapted anymore. This might render a rerouting in case of connection problems in severe failure scenarios infeasible.
With the introduction of OpenFlow by the Stanford University in 2008, a process began in the area of network research, which questions the predominant approach of fully distributed network control. OpenFlow is a communication protocol that allows the externalization of the network control plane from the network devices, such as a router, and to realize it as a logically-centralized entity in software. For this concept, the term "Software Defined Networking" (SDN) was coined during scientific discourse.
For the network operators, this concept has several advantages. The two most important can be summarized under the points cost savings and flexibility. Firstly, it is possible through the uniform interface for network hardware ("Southbound API"), as implemented by OpenFlow, to combine devices and software from different manufacturers, which increases the innovation and price pressure on them. Secondly, the realization of the network control plane as a freely programmable software with open interfaces ("Northbound API") provides the opportunity to adapt it to the individual circumstances of the operator's network and to exchange information with the applications it serves. This allows the network to be more flexible and to react more quickly to changing circumstances as well as transport the traffic more effectively and tailored to the user’s "Quality of Experience" (QoE).
The approach of a separate network control layer for packet-based networks is not new and has already been proposed several times in the past. Therefore, the SDN approach has raised many questions about its feasibility in terms of efficiency and applicability. These questions are caused to some extent by the fact that there is no generally accepted definition of the SDN concept to date. It is therefore a part of this thesis to derive such a definition. In addition, several of the open issues are investigated. This Investigations follow the three aspects: Performance Evaluation of Software Defined Networking, applications on the SDN control layer, and the usability of SDN Northbound-API for creation application-awareness in network operation.
Performance Evaluation of Software Defined Networking: The question of the efficiency of an SDN-based system was from the beginning one of the most important. In this thesis, experimental measurements of the performance of OpenFlow-enabled switch hardware and control software were conducted for the purpose of answering this question. The results of these measurements were used as input parameters for establishing an analytical model of the reactive SDN approach. Through the model it could be determined that the performance of the software control layer, often called "Controller", is crucial for the overall performance of the system, but that the approach is generally viable. Based on this finding a software for analyzing the performance of SDN controllers was developed. This software allows the emulation of the forwarding layer of an SDN network towards the control software and can thus determine its performance in different situations and configurations. The measurements with this software showed that there are quite significant differences in the behavior of different control software implementations. Among other things it has been shown that some show different characteristics for various switches, in particular in terms of message processing speed. Under certain circumstances this can lead to network failures.
Applications on the SDN control layer: The core piece of software defined networking are the intelligent network applications that operate on the control layer. However, their development is still in its infancy and little is known about the technical possibilities and their limitations. Therefore, the relationship between an SDN-based and classical implementation of a network function is investigated in this thesis. This function is the monitoring of network links and the traffic they carry. A typical approach for this task has been built based on Wiretapping and specialized measurement hardware and compared with an implementation based on OpenFlow switches and a special SDN control application. The results of the comparison show that the SDN version can compete in terms of measurement accuracy for bandwidth and delay estimation with the traditional measurement set-up. However, a compromise has to be found for measurements below the millisecond range.
Another question regarding the SDN control applications is whether and how well they can solve existing problems in networks. Two programs have been developed based on SDN in this thesis to solve two typical network issues. Firstly, the tool "IPOM", which enables considerably more flexibility in the study of effects of network structures for a researcher, who is confined to a fixed physical test network topology.
The second software provides an interface between the Cloud Orchestration Software "OpenNebula" and an OpenFlow controller. The purpose of this software was to investigate experimentally whether a pre-notification of the network of an impending relocation of a virtual service in a data center is sufficient to ensure the continuous operation of that service. This was demonstrated on the example of a video service.
Usability of the SDN Northbound API for creating application-awareness in network operation: Currently, the fact that the network and the applications that run on it are developed and operated separately leads to problems in network operation. SDN offers with the Northbound-API an open interface that enables the exchange between information of both worlds during operation. One aim of this thesis was to investigate whether this interface can be exploited so that the QoE experienced by the user can be maintained on high level. For this purpose, the QoE influence factors were determined on a challenging application by means of a subjective survey study. The application is cloud gaming, in which the calculation of video game environments takes place in the cloud and is transported via video over the network to the user. It was shown that apart from the most important factor influencing QoS, i.e., packet loss on the downlink, also the type of game type and its speed play a role. This demonstrates that in addition to QoS the application state is important and should be communicated to the network. Since an implementation of such a state conscious SDN for the example of Cloud Gaming was not possible due to its proprietary implementation, in this thesis the application “YouTube video streaming” was chosen as an alternative. For this application, status information is retrievable via the "Yomo" tool and can be used for network control. It was shown that an SDN-based implementation of an application-aware network has distinct advantages over traditional network management methods and the user quality can be obtained in spite of disturbances.
In this paper we study connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) by adding edges such that the resulting graph keeps the property. The aim is to add as few edges as possible. The property that we consider is planarity, both in an abstract graph-theoretic and in a geometric setting, where vertices correspond to points in the plane and edges to straight-line segments.
We show that it is NP-hard to nd a minimum-cardinality augmentation that makes a planar graph 2-edge connected. For making a planar graph 2-vertex connected this was known. We further show that both problems are hard in the geometric setting, even when restricted to trees. The problems remain hard for higher degrees of connectivity. On the other hand we give polynomial-time algorithms for the special case of convex geometric graphs.
We also study the following related problem. Given a planar (plane geometric) graph G, two vertices s and t of G, and an integer c, how many edges have to be added to G such that G is still planar (plane geometric) and contains c edge- (or vertex-) disjoint s{t paths? For the planar case we give a linear-time algorithm for c = 2. For the plane geometric case we give optimal worst-case bounds for c = 2; for c = 3 we characterize the cases that have a solution.
The present paper compares the effect of different waypoint parameters on the flight performance of a special autonomous indoor UAV (unmanned aerial vehicle) fusing ultrasonic, inertial, pressure and optical sensors for 3D positioning and controlling. The investigated parameters are the acceptance threshold for reaching a waypoint as well as the maximal waypoint step size or block size. The effect of these parameters on the flight time and accuracy of the flight path is investigated. Therefore the paper addresses how the acceptance threshold and step size influence the speed and accuracy of the autonomous flight and thus influence the performance of the presented autonomous quadrocopter under real indoor navigation circumstances.
Furthermore the paper demonstrates a drawback of the standard potential field method for navigation of such autonomous quadrocopters and points to an improvement.