Computing Time-Optimal Clearing Strategies for Pursuit-Evasion Problems with Linear Programming

This paper addresses and solves the problem of finding optimal clearing strategies for a team of robots in an environment given as a graph. The graph-clear model is used in which sweeping of locations, and their recontamination by intruders, is modelled over a surveillance graph. Optimization of strategies is carried out for shortest total travel distance and time taken by the robot team and under constraints of clearing costs of locations. The physical constraints of access and timely movements by the robots are also accounted for, as well as the ability of the robots to prevent recontamination of already cleared areas. The main result of the paper is that this complex problem can be reduced to a computable LP problem. To further reduce complexity, an algorithm is presented for the case when graph clear strategies are a priori available by using other methods, for instance by model checking

Contributions to Game Theory and Management. Vol. III. Collected papers presented on the Third International Conference Game Theory and Management.

The collection contains papers accepted for the Third International Conference Game Theory and Management (June 24-26, 2009, St. Petersburg University, St. Petersburg, Russia). The presented papers belong to the field of game theory and its applications to management. The volume may be recommended for researches and post-graduate students of management, economic and applied mathematics departments.

Multi-agent persistent surveillance under temporal logic constraints

This thesis proposes algorithms for the deployment of multiple autonomous agents for persistent surveillance missions requiring repeated, periodic visits to regions of interest. Such problems arise in a variety of domains, such as monitoring ocean conditions like temperature and algae content, performing crowd security during public events, tracking wildlife in remote or dangerous areas, or watching traffic patterns and road conditions. Using robots for surveillance is an attractive solution to scenarios in which fixed sensors are not sufficient to maintain situational awareness. Multi-agent solutions are particularly promising, because they allow for improved spatial and temporal resolution of sensor information. In this work, we consider persistent monitoring by teams of agents that are tasked with satisfying missions specified using temporal logic formulas. Such formulas allow rich, complex tasks to be specified, such as "visit regions A and B infinitely often, and if region C is visited then go to region D, and always avoid obstacles." The agents must determine how to satisfy such missions according to fuel, communication, and other constraints. Such problems are inherently difficult due to the typically infinite horizon, state space explosion from planning for multiple agents, communication constraints, and other issues. Therefore, computing an optimal solution to these problems is often infeasible. Instead, a balance must be struck between computational complexity and optimality. This thesis describes solution methods for two main classes of multi-agent persistent surveillance problems. First, it considers the class of problems in which persistent surveillance goals are captured entirely by TL constraints. Such problems require agents to repeatedly visit a set of surveillance regions in order to satisfy their mission. We present results for agents solving such missions with charging constraints, with noisy observations, and in the presence of adversaries. The second class of problems include an additional optimality criterion, such as minimizing uncertainty about the location of a target or maximizing sensor information among the team of agents. We present solution methods and results for such missions with a variety of optimality criteria based on information metrics. For both classes of problems, the proposed algorithms are implemented and evaluated via simulation, experiments with robots in a motion capture environment, or both

Layoutautomatisierung im analogen IC-Entwurf mit formalisiertem und nicht-formalisiertem Expertenwissen

After more than three decades of electronic design automation, most layouts for analog integrated circuits are still handcrafted in a laborious manual fashion today. Obverse to the highly automated synthesis tools in the digital domain (coping with the quantitative difficulty of packing more and more components onto a single chip – a desire well known as More Moore), analog layout automation struggles with the many diverse and heavily correlated functional requirements that turn the analog design problem into a More than Moore challenge. Facing this qualitative complexity, seasoned layout engineers rely on their comprehensive expert knowledge to consider all design constraints that uncompromisingly need to be satisfied. This usually involves both formally specified and nonformally communicated pieces of expert knowledge, which entails an explicit and implicit consideration of design constraints, respectively. Existing automation approaches can be basically divided into optimization algorithms (where constraint consideration occurs explicitly) and procedural generators (where constraints can only be taken into account implicitly). As investigated in this thesis, these two automation strategies follow two fundamentally different paradigms denoted as top-down automation and bottom-up automation. The major trait of top-down automation is that it requires a thorough formalization of the problem to enable a self-intelligent solution finding, whereas a bottom-up automatism –controlled by parameters– merely reproduces solutions that have been preconceived by a layout expert in advance. Since the strengths of one paradigm may compensate the weaknesses of the other, it is assumed that a combination of both paradigms –called bottom-up meets top-down– has much more potential to tackle the analog design problem in its entirety than either optimization-based or generator-based approaches alone. Against this background, the thesis at hand presents Self-organized Wiring and Arrangement of Responsive Modules (SWARM), an interdisciplinary methodology addressing the design problem with a decentralized multi-agent system. Its basic principle, similar to the roundup of a sheep herd, is to let responsive mobile layout modules (implemented as context-aware procedural generators) interact with each other inside a user-defined layout zone. Each module is allowed to autonomously move, rotate and deform itself, while a supervising control organ successively tightens the layout zone to steer the interaction towards increasingly compact (and constraint compliant) layout arrangements. Considering various principles of self-organization and incorporating ideas from existing decentralized systems, SWARM is able to evoke the phenomenon of emergence: although each module only has a limited viewpoint and selfishly pursues its personal objectives, remarkable overall solutions can emerge on the global scale. Several examples exhibit this emergent behavior in SWARM, and it is particularly interesting that even optimal solutions can arise from the module interaction. Further examples demonstrate SWARM’s suitability for floorplanning purposes and its application to practical place-and-route problems. The latter illustrates how the interacting modules take care of their respective design requirements implicitly (i.e., bottom-up) while simultaneously paying respect to high level constraints (such as the layout outline imposed top-down by the supervising control organ). Experimental results show that SWARM can outperform optimization algorithms and procedural generators both in terms of layout quality and design productivity. From an academic point of view, SWARM’s grand achievement is to tap fertile virgin soil for future works on novel bottom-up meets top-down automatisms. These may one day be the key to close the automation gap in analog layout design.Nach mehr als drei Jahrzehnten Entwurfsautomatisierung werden die meisten Layouts für analoge integrierte Schaltkreise heute immer noch in aufwändiger Handarbeit entworfen. Gegenüber den hochautomatisierten Synthesewerkzeugen im Digitalbereich (die sich mit dem quantitativen Problem auseinandersetzen, mehr und mehr Komponenten auf einem einzelnen Chip unterzubringen – bestens bekannt als More Moore) kämpft die analoge Layoutautomatisierung mit den vielen verschiedenen und stark korrelierten funktionalen Anforderungen, die das analoge Entwurfsproblem zu einer More than Moore Herausforderung machen. Angesichts dieser qualitativen Komplexität bedarf es des umfassenden Expertenwissens erfahrener Layouter um sämtliche Entwurfsconstraints, die zwingend eingehalten werden müssen, zu berücksichtigen. Meist beinhaltet dies formal spezifiziertes als auch nicht-formal übermitteltes Expertenwissen, was eine explizite bzw. implizite Constraint Berücksichtigung nach sich zieht. Existierende Automatisierungsansätze können grundsätzlich unterteilt werden in Optimierungsalgorithmen (wo die Constraint Berücksichtigung explizit erfolgt) und prozedurale Generatoren (die Constraints nur implizit berücksichtigen können). Wie in dieser Arbeit eruiert wird, folgen diese beiden Automatisierungsstrategien zwei grundlegend unterschiedlichen Paradigmen, bezeichnet als top-down Automatisierung und bottom-up Automatisierung. Wesentliches Merkmal der top-down Automatisierung ist die Notwendigkeit einer umfassenden Problemformalisierung um eine eigenintelligente Lösungsfindung zu ermöglichen, während ein bottom-up Automatismus –parametergesteuert– lediglich Lösungen reproduziert, die vorab von einem Layoutexperten vorgedacht wurden. Da die Stärken des einen Paradigmas die Schwächen des anderen ausgleichen können, ist anzunehmen, dass eine Kombination beider Paradigmen –genannt bottom-up meets top down– weitaus mehr Potenzial hat, das analoge Entwurfsproblem in seiner Gesamtheit zu lösen als optimierungsbasierte oder generatorbasierte Ansätze für sich allein. Vor diesem Hintergrund stellt die vorliegende Arbeit Self-organized Wiring and Arrangement of Responsive Modules (SWARM) vor, eine interdisziplinäre Methodik, die das Entwurfsproblem mit einem dezentralisierten Multi-Agenten-System angeht. Das Grundprinzip besteht darin, ähnlich dem Zusammentreiben einer Schafherde, reaktionsfähige mobile Layoutmodule (realisiert als kontextbewusste prozedurale Generatoren) in einer benutzerdefinierten Layoutzone interagieren zu lassen. Jedes Modul darf sich selbständig bewegen, drehen und verformen, wobei ein übergeordnetes Kontrollorgan die Zone schrittweise verkleinert, um die Interaktion auf zunehmend kompakte (und constraintkonforme) Layoutanordnungen hinzulenken. Durch die Berücksichtigung diverser Selbstorganisationsgrundsätze und die Einarbeitung von Ideen bestehender dezentralisierter Systeme ist SWARM in der Lage, das Phänomen der Emergenz hervorzurufen: obwohl jedes Modul nur eine begrenzte Sichtweise hat und egoistisch seine eigenen Ziele verfolgt, können sich auf globaler Ebene bemerkenswerte Gesamtlösungen herausbilden. Mehrere Beispiele veranschaulichen dieses emergente Verhalten in SWARM, wobei besonders interessant ist, dass sogar optimale Lösungen aus der Modulinteraktion entstehen können. Weitere Beispiele demonstrieren SWARMs Eignung zwecks Floorplanning sowie die Anwendung auf praktische Place-and-Route Probleme. Letzteres verdeutlicht, wie die interagierenden Module ihre jeweiligen Entwurfsanforderungen implizit (also: bottom-up) beachten, während sie gleichzeitig High-Level-Constraints berücksichtigen (z.B. die Layoutkontur, die top-down vom übergeordneten Kontrollorgan auferlegt wird). Experimentelle Ergebnisse zeigen, dass Optimierungsalgorithmen und prozedurale Generatoren von SWARM sowohl bezüglich Layoutqualität als auch Entwurfsproduktivität übertroffen werden können. Aus akademischer Sicht besteht SWARMs große Errungenschaft in der Erschließung fruchtbaren Neulands für zukünftige Arbeiten an neuartigen bottom-up meets top-down Automatismen. Diese könnten eines Tages der Schlüssel sein, um die Automatisierungslücke im analogen Layoutentwurf zu schließen

Geometric Pursuit Evasion

In this dissertation we investigate pursuit evasion problems set in geometric environments. These games model a variety of adversarial situations in which a team of agents, called pursuers, attempts to catch a rogue agent, called the evader. In particular, we consider the following problem: how many pursuers, each with the same maximum speed as the evader, are needed to guarantee a successful capture? Our primary focus is to provide combinatorial bounds on the number of pursuers that are necessary and sufficient to guarantee capture. The first problem we consider consists of an unpredictable evader that is free to move around a polygonal environment of arbitrary complexity. We assume that the pursuers have complete knowledge of the evader's location at all times, possibly obtained through a network of cameras placed in the environment. We show that regardless of the number of vertices and obstacles in the polygonal environment, three pursuers are always sufficient and sometimes necessary to capture the evader. We then consider several extensions of this problem to more complex environments. In particular, suppose the players move on the surface of a 3-dimensional polyhedral body; how many pursuers are required to capture the evader? We show that 4 pursuers always suffice (upper bound), and that 3 are sometimes necessary (lower bound), for any polyhedral surface with genus zero. Generalizing this bound to surfaces of genus g, we prove the sufficiency of (4g + 4) pursuers. Finally, we show that 4 pursuers also suffice under the "weighted region" constraints, where the movement costs through different regions of the (genus zero) surface have (different) multiplicative weights. Next we consider a more general problem with a less restrictive sensing model. The pursuers' sensors are visibility based, only providing the location of the evader if it is in direct line of sight. We begin my making only the minimalist assumption that pursuers and the evader have the same maximum speed. When the environment is a simply-connected (hole-free) polygon of n vertices, we show that Θ(n^1/2 ) pursuers are both necessary and sufficient in the worst-case. When the environment is a polygon with holes, we prove a lower bound of Ω(n^2/3 ) and an upper bound of O(n^5/6 ) pursuers, where n includes the vertices of the hole boundaries. However, we show that with realistic constraints on the polygonal environment these bounds can be drastically improved. Namely, if the players' movement speed is small compared to the features of the environment, we give an algorithm with a worst case upper bound of O(log n) pursuers for simply-connected n-gons and O(√h + log n) for polygons with h holes. The final problem we consider takes a small step toward addressing the fact that location sensing is noisy and imprecise in practice. Suppose a tracking agent wants to follow a moving target in the two-dimensional plane. We investigate what is the tracker's best strategy to follow the target and at what rate does the distance between the tracker and target grow under worst-case localization noise. We adopt a simple but realistic model of relative error in sensing noise: the localization error is proportional to the true distance between the tracker and the target. Under this model we are able to give tight upper and lower bounds for the worst-case tracking performance, both with or without obstacles in the Euclidean plane