Multi-Agent Search for a Moving and Camouflaging Target

In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer nonlinear program, which we reformulate using three linearization techniques. We develop preprocessing steps, outer approximations via lazy constraints, and bundle-based cutting plane methods to address large-scale instances. Further specializations emerge when the target moves according to a Markov chain. We carry out an extensive numerical study to show the computational efficiency of our methods and to derive insights regarding which approach should be favored for which type of problem instance

Uninsurable individual risk and the cyclical behavior of unemployment and vacancies

This paper is concerned with the business cycle dynamics in search-and-matching models of the labor market when agents are ex post heterogeneous. We focus on wealth heterogeneity that comes as a result of imperfect opportunities to insure against idiosyncratic risk. We show that this heterogeneity implies wage rigidity relative to a complete insurance economy. The fraction of wealth-poor agents prevents real wages from falling too much in recessions since small decreases in income imply large losses in utility. Analogously, wages rise less in expansions compared with the standard model because small increases are enough for poor workers to accept job offers. This mechanism reduces the volatility of wages and increases the volatility of vacancies and unemployment. This channel can be relevant if the lack of insurance is large enough so that the fraction of agents close to the borrowing constraint is significant. However, discipline in the parameterization implies an earnings variance and persistence in the unemployment state that result in a large degree of self-insurance.

Coverage & cooperation: Completing complex tasks as quickly as possible using teams of robots

As the robotics industry grows and robots enter our homes and public spaces, they are increasingly expected to work in cooperation with each other. My thesis focuses on multirobot planning, specifically in the context of coverage robots, such as robotic lawnmowers and vacuum cleaners. Two problems unique to multirobot teams are task allocation and search. I present a task allocation algorithm which balances the workload amongst all robots in the team with the objective of minimizing the overall mission time. I also present a search algorithm which robots can use to find lost teammates. It uses a probabilistic belief of a target robot’s position to create a planning tree and then searches by following the best path in the tree. For robust multirobot coverage, I use both the task allocation and search algorithms. First the coverage region is divided into a set of small coverage tasks which minimize the number of turns the robots will need to take. These tasks are then allocated to individual robots. During the mission, robots replan with nearby robots to rebalance the workload and, once a robot has finished its tasks, it searches for teammates to help them finish their tasks faster

Multi Robot Intruder Search

The aim of this work is the development and analysis of methods and algorithms to allow a multi robot system to cooperatively search a closed, 2-dimensional environment for a human intruder. The underlying problem corresponds to the game-theoretic concept of a classical pursuit evasion game, whereas the focus is set to the generation of plans for the group of pursuers. While the main aspect of of this work lies in the field of probabilistic robotics, concepts and ideas are incorporated from differential game theory, algorithmic geometry and graph theory. The probabilistic basis allows the integration of sensor error as well as nondeterministic robot motion. The main contributions of this work can be divided into three major parts: The first part deals with the development and implementation of probabilistic human models. Depending on the specific behavior of an intruder, ranging from uncooperative to unaware, different classes of intruders are identified. Models are proposed for two of these classes. For the case of a clever and uncooperative intruder who actively evades detection, we propose a model based on the concept of contamination. The second class corresponds to a person who is unaware of the pursuit. We show that simple Markov models, which are often proposed in literature, are not suited for modeling realistic human motion and develop advanced Markov models, which conform to random waypoint motion models. The second part, which is also the most extensive part of this work, deals with the problem of finding an uncooperative and clever intruder. A solution is presented, which projects the problem on a graph structure, which is then searched by a highly optimized A* planner. The solution for the corresponding graph problem is afterwards projected back to the original search space and can be executed by the robotic pursuers. By means of the models proposed in the first part, the performance and correctness of the method is shown. We present experiments in simulation as on real robots to show the practicability and efficiency of the method. The third part deals with the problem of finding an intruder who is unaware of the search. Based on the advanced Markov model previously discussed, a greedy algorithm is proposed, which aims at maximizing the probability to find the intruder in the near future. Experimental results for this method are shown and comparisons to simpler methods are given.Mehrroboter-Eindringlings-Suche Ziel dieser Arbeit ist die Entwicklung und Analyse von Methoden und Algorithmen, die einem kooperativen Mehrrobotersystem erlauben nach einem Eindringling in einer zweidimensionalen, geschlossenen Umgebung zu suchen. Das dem zugrunde liegende Problem entspricht dem spieltheoretischen Konzept eines Suche und Ausweichen Spieles (pursuit evasion game), wobei der Fokus auf der Generierung von Plänen für die Verfolger liegt. Der Hauptaspekt dieser Arbeit liegt dabei im Feld der probabilistischen Robotik, wobei Konzepte und Ideen aus dem Gebiet der differentiellen Spieltheorie, der algorithmischen Geometrie und der Graph Theorie verwendet werden. Die probabilistische Modellierung erlaubt dabei die Integration von Sensorfehlern wie auch nichtdeterministische Roboter-Bewegung. Die Arbeit gliedert sich in drei Hauptteile: Der erste Teil beschäftigt sich mit dem Entwurf und der Implementierung von probabilistischen Modellen für menschliche Bewegung. Abhängig vom angenommenen Verhalten eines Eindringlings, von aktiv ausweichend bis zu ignorant, werden verschiedene Klassen von menschlichem Verhalten unterschieden. Für zwei dieser Klassen stellen wir Modelle auf: Für den Fall einer intelligenten und aktiv ausweichenden Person, generieren wir ein Modell basierend auf dem Konzept von Kontamination. Das zweite Modell entspricht einem Eindringling, der sich der Suche nach ihm nicht bewusst ist. Wir zeigen, dass einfache Markov-Modelle, wie sie in der Vergangenheit oft vorgeschlagen worden sind, ungeeignet sind, um realistische Bewegung zu abzubilden und entwickeln entsprechend erweiterte Markov-Modelle für eine realistischere Modellierung. Der zweite Teil der Arbeit beschäftigt sich mit der Frage, wie man einen intelligente und aktiv ausweichenden Eindringling aufspüren kann. Die vorgestellte Lösung basiert auf der Projektion des Problems auf einen Graphen, der anschließend von einem hoch optimierten A*-Planungsalgorithmus durchsucht werden kann. Diese Lösung kann anschließend auf den ursprünglichen Raum rückprojeziert werden und kann als direkter Plan von den verfolgenden Robotern ausgeführt werden. Mittels der Modelle aus dem ersten Teil wird die Korrektheit und Effizienz der Lösung gezeigt. Der letzte Teil befasst sich mit der Frage, wie ein Eindringling gefunden werden kann, der sich neutral zur Suche verhält. Basierend auf den erweiterten Markov-Modellen aus dem ersten Teil, wird eine Lösung durch gierige Suche präsentiert, die die Wahrscheinlichkeit eine Person im nächsten Zeitschritt aufzuspüren, maximiert. Wie im zweiten Teil werden Experimente diskutiert und diese mit der Proformanz simplerer Methoden verglichen

3D Particle Tracking Velocimetry Method: Advances and Error Analysis

A full three-dimensional particle tracking system was developed and tested. By using three separate CCDs placed at the vertices of an equilateral triangle, the threedimensional location of particles can be determined. Particle locations measured at two different times can then be used to create a three-component, three-dimensional velocity field. Key developments are: the ability to accurately process overlapping particle images, offset CCDs to significantly improve effective resolution, allowance for dim particle images, and a hybrid particle tracking technique ideal for three-dimensional flows when only two sets of images exist. An in-depth theoretical error analysis was performed which gives the important sources of error and their effect on the overall system. This error analysis was verified through a series of experiments, which utilized a test target with 100 small dots per square inch. For displacements of 2.54mm the mean errors were less than 2% and the 90% confidence limits were less than 5.2 μm in the plane perpendicular to the camera axis, and 66 μm in the direction of the camera axis. The system was used for flow measurements around a delta wing at an angle of attack. These measurements show the successful implementation of the system for three-dimensional flow velocimetry

The non-equilibrium statistical physics of stochastic search, foraging and clustering

This dissertation explores two themes central to the field of non-equilibrium statistical physics. The first is centered around the use of random walks, first-passage processes, and Brownian motion to model basic stochastic search processes found in biology and ecological systems. The second is centered around clustered networks: how clustering modifies the nature of transition in the appearance of various graph motifs and their use in modeling social networks. In the first part of this dissertation, we start by investigating properties of intermediate crossings of Brownian paths. We develop simple analytical tools to obtain probability distributions of intermediate crossing positions and intermediate crossing times of Brownian paths. We find that the distribution of intermediate crossing times can be unimodal or bimodal. Next, we develop analytical and numerical methods to solve a system of diffusive searchers which are reset to the origin at stochastic or periodic intervals. We obtain the optimal criteria to search for a fixed target in one, two and three dimensions. For these two systems, we also develop efficient ways to simulate Brownian paths, where the simulation kernel makes maximal use of first-passage ideas. Finally we develop a model to understand foraging in a resource-rich environment. Specifically, we investigate the role of greed on the lifetime of a diffusive forager. This lifetime shows non-monotonic dependence on greed in one and two dimensions, and surprisingly, a peak for negative greed in 1d. In the second part of this dissertation, we develop simple models to capture the non-tree-like (clustering) aspects of random networks that arise in the real world. By 'clustered networks', we specifically mean networks where the probability of links between neighbors of a node (i.e., 'friends of friends') is positive. We discuss three simple and related models. We find a series of transitions in the density of graph motifs such as triangles (3-cliques), 4-cliques etc as a function of the clustering probability. We also find that giant 3-cores emerge through first- or second-order, or even mixed transitions in clustered networks

Distributed Systems and Mobile Computing

The book is about Distributed Systems and Mobile Computing. This is a branch of Computer Science devoted to the study of systems whose components are in different physical locations and have limited communication capabilities. Such components may be static, often organized in a network, or may be able to move in a discrete or continuous environment. The theoretical study of such systems has applications ranging from swarms of mobile robots (e.g., drones) to sensor networks, autonomous intelligent vehicles, the Internet of Things, and crawlers on the Web. The book includes five articles. Two of them are about networks: the first one studies the formation of networks by agents that interact randomly and have the ability to form connections; the second one is a study of clustering models and algorithms. The three remaining articles are concerned with autonomous mobile robots operating in continuous space. One article studies the classical gathering problem, where all robots have to reach a common location, and proposes a fast algorithm for robots that are endowed with a compass but have limited visibility. The last two articles deal with the evacuations problem, where two robots have to locate an exit point and evacuate a region in the shortest possible time