Algorithms for cartographic visualization

Maps are effective tools for communicating information to the general public and help people to make decisions in, for example, navigation, spatial planning and politics. The mapmaker chooses the details to put on a map and the symbols to represent them. Not all details need to be geographic: thematic maps, which depict a single theme or attribute, such as population, income, crime rate, or migration, can very effectively communicate the spatial distribution of the visualized attribute. The vast amount of data currently available makes it infeasible to design all maps manually, and calls for automated cartography. In this thesis we presented efficient algorithms for the automated construction of various types of thematic maps. In Chapter 2 we studied the problem of drawing schematic maps. Schematic maps are a well-known cartographic tool; they visualize a set of nodes and edges (for example, highway or metro networks) in simplified form to communicate connectivity information as effectively as possible. Many schematic maps deviate substantially from the underlying geography since edges and vertices of the original network are moved in the simplification process. This can be a problem if we want to integrate the schematized network with a geographic map. In this scenario the schematized network has to be drawn with few orientations and links, while critical features (cities, lakes, etc.) of the base map are not obscured and retain their correct topological position with respect to the network. We developed an efficient algorithm to compute a collection of non-crossing paths with fixed orientations using as few links as possible. This algorithm approximates the optimal solution to within a factor that depends only on the number of allowed orientations. We can also draw the roads with different thicknesses, allowing us to visualize additional data related to the roads such as trafic volume. In Chapter 3 we studied methods to visualize quantitative data related to geographic regions. We first considered rectangular cartograms. Rectangular cartograms represent regions by rectangles; the positioning and adjacencies of these rectangles are chosen to suggest their geographic locations to the viewer, while their areas are chosen to represent the numeric values being communicated by the cartogram. One drawback of rectangular cartograms is that not every rectangular layout can be used to visualize all possible area assignments. Rectangular layouts that do have this property are called area-universal. We show that area-universal layouts are always one-sided, and we present algorithms to find one-sided layouts given a set of adjacencies. Rectangular cartograms often provide a nice visualization of quantitative data, but cartograms deform the underlying regions according to the data, which can make the map virtually unrecognizable if the data value differs greatly from the original area of a region or if data is not available at all for a particular region. A more direct method to visualize the data is to place circular symbols on the corresponding region, where the areas of the symbols correspond to the data. However, these maps, so-called symbol maps, can appear very cluttered with many overlapping symbols if large data values are associated with small regions. In Chapter 4 we proposed a novel type of quantitative thematic map, called necklace map, which overcomes these limitations. Instead of placing the symbols directly on a region, we place the symbols on a closed curve, the necklace, which surrounds the map. The location of a symbol on the necklace should be chosen in such a way that the relation between symbol and region is as clear as possible. Necklace maps appear clear and uncluttered and allow for comparatively large symbol sizes. We developed algorithms to compute necklace maps and demonstrated our method with experiments using various data sets and maps. In Chapter 5 and 6 we studied the automated creation of ow maps. Flow maps are thematic maps that visualize the movement of objects, such as people or goods, between geographic regions. One or more sources are connected to several targets by lines whose thickness corresponds to the amount of ow between a source and a target. Good ow maps reduce visual clutter by merging (bundling) lines smoothly and by avoiding self-intersections. We developed a new algorithm for drawing ow trees, ow maps with a single source. Unlike existing methods, our method merges lines smoothly and avoids self-intersections. Our method is based on spiral trees, a new type of Steiner trees that we introduced. Spiral trees have an angle restriction which makes them appear smooth and hence suitable for drawing ow maps. We study the properties of spiral trees and give an approximation algorithm to compute them. We also show how to compute ow trees from spiral trees and we demonstrate our approach with extensive experiments

Visibility-Based Pursuit-Evasion In The Plane

As technological advances further increase the amount of memory and computing power available to mobile robots, we are seeing an unprecedented explosion in the utilization of deployable robots for various tasks. The speed at which robots begin to enter various domains is largely dependent on the availability of robust and efficient algorithms that are capable of solving the complex planning problems inherent to the given domain. One such domain which is experiencing unprecedented growth in recent years requires a robot to detect and/or track a mobile agent or group of agents. In these scenarios, there are typically two players with diametrically opposed goals. For matters of security, we have a guard and an intruder. The guard’s goal is to ensure that if an intruder enters the premises they are caught in a timely manner. Analogously, the intruder wishes to evade detection for as long as possible. Search and rescue operations are often framed as a two-player game between rescuers and survivors. Though the survivors are unlikely to behave antagonistically, an agnostic model is useful for the rescuers to guarantee that the survivors are found, regardless of their movements. Both of these tasks, are at their core, pursuit-evasion problems. There are many variants of the pursuit-evasion problem, the common theme amongst them is that one group of agents, the “pursuers”, attempts to track members of another group, the “evaders”. Geometric formulations of the pursuit-evasion problem require a pursuer(s) to systematically search an environment to locate one or more evaders ensuring that all evaders will be captured by the pursuer(s) in a finite time. The visibility-based pursuit-evasion problem is a geometric variant of the pursuit-evasion problem that defines a visibility-region which corresponds to the region of the environment that the pursuer(s) can actively perceive. If an evader lies within this visibility region then it is captured (detected). This thesis contains four novel contributions that solve various visibility-based pursuit-evasion problems. The first contribution is an algorithm that computes the optimal (minimal path length) pursuer trajectory for a single pursuer. The second contribution is an algorithm that generates a joint motion strategy for multiple pursuers. Motivated by the result of the second contribution, the third result is a sampling-based algorithm for the multiple pursuer scenario. The fourth contribution is a complete algorithm that computes a trajectory for a pursuer that has a very limited sensor footprint

Robotic Machining Fundamentals for Casting Defect Removal

In the past half century, industrial robots have developed a strong presence in manufacturing. They now commonly perform tasks such as materials handling, assembly, welding, and painting. Unfortunately robotic machining tasks have seen limited deployments. The majority of machining robots are designed for soft materials like wood or plastic and only apply repetitive cutting trajectories to create a particular geometry. The current systems fail to work for less predictable tasks with harder materials. In response, this thesis presents a novel robotic machining system for casting defect removal. Removing defects from metal castings requires flexibility to a high variance in workpiece geometry, defect locations, and defect geometry. With the proposed methods, a six-axis industrial robot arm efficiently maneuvers custom tools between sorted target locations. It applies surface-aligned custom tool paths to localized surfaces, producing cut geometries appropriate for post-removal welding. The final system serves as the basis for a full-scale application that will reduce human error and injury and improve the efficiency and effectiveness of casting manufacturing

Component-based synthesis of motion planning algorithms

Combinatory Logic Synthesis generates data or runnable programs according to formal type specifications. Synthesis results are composed based on a user-specified repository of components, which brings several advantages for representing spaces of high variability. This work suggests strategies to manage the resulting variations by proposing a domain-specific brute-force search and a machine learning-based optimization procedure. The brute-force search involves the iterative generation and evaluation of machining strategies. In contrast, machine learning optimization uses statistical models to enable the exploration of the design space. The approaches involve synthesizing programs and meta-programs that manipulate, run, and evaluate programs. The methodologies are applied to the domain of motion planning algorithms, and they include the configuration of programs belonging to different algorithmic families. The study of the domain led to the identification of variability points and possible variations. Proof-of-concept repositories represent these variability points and incorporate them into their semantic structure. The selected algorithmic families involve specific computation steps or data structures, and corresponding software components represent possible variations. Experimental results demonstrate that CLS enables synthesis-driven domain-specific optimization procedures to solve complex problems by exploring spaces of high variability.Combinatory Logic Synthesis (CLS) generiert Daten oder lauffähige Programme anhand von formalen Typspezifikationen. Die Ergebnisse der Synthese werden auf Basis eines benutzerdefinierten Repositories von Komponenten zusammengestellt, was diverse Vorteile für die Beschreibung von Räumen mit hoher Variabilität mit sich bringt. Diese Arbeit stellt Strategien für den Umgang mit den resultierenden Variationen vor, indem eine domänen-spezifische Brute-Force Suche und ein maschinelles Lernverfahren für die Untersuchung eines Optimierungsproblems aufgezeigt werden. Die Brute-Force Suche besteht aus der iterativen Generierung und Evaluation von Frässtrategien. Im Gegensatz dazu nutzt der Optimierungsansatz statistische Modelle zur Erkundung des Entwurfsraums. Beide Ansätze synthetisieren Programme und Metaprogramme, welche Programme bearbeiten, ausführen und evaluieren. Diese Methoden werden auf die Domäne der Bewegungsplanungsalgorithmen angewendet und sie beinhalten die Konfiguration von Programmen, welche zu unterschiedlichen algorithmischen Familien gehören. Die Untersuchung der Domäne führte zur Identifizierung der Variabilitätspunkte und der möglichen Variationen. Entsprechende Proof of Concept Implementierungen in Form von Repositories repräsentieren jene Variabilitätspunkte und beziehen diese in ihre semantische Struktur ein. Die gewählten algorithmischen Familien sehen bestimmte Berechnungsschritte oder Datenstrukturen vor, und entsprechende Software Komponenten stellen mögliche Variationen dar. Versuchsergebnisse belegen, dass CLS synthese-getriebene domänenspezifische Optimierungsverfahren ermöglicht, welche komplexe Probleme durch die Exploration von Räumen hoher Variabilität lösen

Coverage and Time-optimal Motion Planning for Autonomous Vehicles

Autonomous vehicles are rapidly advancing with a variety of applications, such as area surveillance, environment mapping, and intelligent transportation. These applications require coverage and/or time-optimal motion planning, where the major challenges include uncertainties in the environment, motion constraints of vehicles, limited energy resources and potential failures. While dealing with these challenges in various capacities, this dissertation addresses three fundamental motion planning problems: (1) single-robot complete coverage in unknown environment, (2) multi-robot resilient and efficient coverage in unknown environment, and (3) time-optimal risk-aware motion planning for curvature-constrained vehicles. First, the ε* algorithm is developed for online coverage path planning in unknown environment using a single autonomous vehicle. It is computationally efficient, and can generate the desired back-and-forth path with less turns and overlappings. ε* prevents the local extrema problem, thus can guarantee complete coverage. Second, the CARE algorithm is developed which extends ε* for multi-robot resilient and efficient coverage in unknown environment. In case of failures, CARE guarantees complete coverage via dynamic task reallocations of other vehicles, hence provides resilience. Moreover, it reallocates idling vehicles to support others in their tasks, hence improves efficiency. Finally, the T* algorithm is developed to find the time-optimal risk-aware path for curvature-constrained vehicles. We present a novel risk function based on the concept of collision time, and integrate it with the time cost for optimization. The above-mentioned algorithms have been validated via simulations in complex scenarios and/or real experiments, and the results have shown clear advantages over existing popular approaches

Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates represent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already organizes and incorporates "vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of "routing dead-ends" that are local minima due to the difficulty of consistent coordinates attribution. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control-state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of "customer-provider" as well as "peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data structure (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when relying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for better routing performances

Optimization and Mathematical Modelling for Path Planning of Co-operative Intra-logistics Automated Vehicles

Small indoor Autonomous Vehicles have revolutionized the operation of pick-pack-and-ship warehouses. The challenges for path planning and co-operation in this domain stem from uncontrolled environments including workspaces shared with humans and human-operated vehicles. Solutions are needed which scale up to the largest existing sites with thousands of vehicles and beyond. These challenges might be familiar to anyone modelling road traffic control with the introduction of Autonomous Vehicles, but key differences in the level of decision autonomy lead to different approaches to conflict-resolution. This thesis proposes a decomposition of site-wide conflict-free motion planning into individual shortest paths though a roadmap representing the free space across the site, zone-based speed optimization to resolve conflicts in the vicinity of one intersection and individual path optimization for local obstacles. In numerical tests the individual path optimization based on clothoid basis functions created paths traversable by different vehicle configurations (steering rate limit, lateral acceleration limit and wheelbase) only by choosing an appropriate maximum longitudinal speed. Using two clothoid segments per convex region was sufficient to reach any goal, and the problem could be solved reliably and quickly with sequential quadratic programming due to the approximate graph method used to determine a good sequence of obstacle-free regions to the local goal. A design for zone-based intersection management, obtained by minimizing a linear objective subject to quadratic constraints was refined by the addition of a messaging interface compatible with the path adaptations based on clothoids. A new approximation of the differential constraints was evaluated in a multi-agent simulation of an elementary intersection layout. The proposed FIFO ordering heuristic converted the problem into a linear program. Interior point methods either found a solution quickly or showed that the problem was infeasible, unlike a quadratic constraint formulation with ordering flexibility. Subsequent tests on more complex multi-lane intersection geometries showed the quadratic constraint formulation converged to significantly better solutions than FIFO at the cost of longer and unpredictable search time. Both effects were magnified as the number of vehicles increased. To properly address site-wide conflict-free motion planning, it is essential that the local solutions are compatible with each other at the zone boundaries. The intersection management design was refined with new boundary constraints to ensure compatibility and smooth transitions without the need for a backup system. In numerical tests it was found that the additional boundary constraints were sufficient to ensure smooth transitions on an idealized map including two intersections

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes