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

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

A Methodology to Enhance Quantitative Technology Evaluation Through Exploration of Employment Concepts in Engagement Analysis

The process of designing a new system has often been treated as a purely technological problem, where the infusion or synthesis of new technologies forms the basis of progress. However, recent trends in design and analysis methodologies have tried to shift away from the narrow scope of technology-centric approaches. One such trend is the increase in analysis scope from the level of an isolated system to that of multiple interacting systems. Analysis under this broader scope allows for the exploration of non-materiel solutions to existing or future problems. Solutions of this type can reduce the cost of closing capability gaps by mitigating the need to procure new systems to achieve desired levels of performance. In particular, innovations in the employment concepts can enhance existing, evolutionary, or revolutionary materiel solutions. The task of experimenting with non-materiel solutions often falls to operators after the system has been designed and produced. This begs the question as to whether the chosen design adequately accounted for the possibility of innovative employment concepts which operators might discover. Attempts can be made to bring the empirical knowledge possessed by skilled operators upstream in the design process. However, care must be taken to ensure such attempts do not introduce unwanted bias, and there can be significant difficulty in translating human intuition into an appropriate modeling paradigm for analysis. Furthermore, the capacity for human operators to capitalize on the potential benefits of a given technology may be limited or otherwise infeasible in design space explorations where the number of alternatives becomes very large. This is especially relevant to revolutionary concepts to which prior knowledge may not be applicable. Each of these complicating factors is exacerbated by interactions between systems, where changes in the decision-making processes of individual entities can greatly influence outcomes. This necessitates exploration and analysis of employment concepts for all relevant entities, not only that or those to which the technology applies. This research sought to address the issues of exploring employment concepts in the early phases of the system design process. A characterization of the problem identified several gaps in existing methodologies, particularly with respect to the representation, generation, and evaluation of alternative employment concepts. Relevant theories, including behavioral psychology, control theory, and game theory were identified to facilitate closure of these gaps. However, these theories also introduced technical challenges which had to be overcome. These challenges stemmed from systematic problems such as the curse of dimensionality, temporal credit assignment, and the complexities of entity interactions. A candidate approach was identified through thorough review of available literature: Multi-agent reinforcement learning. Experiments show the proposed approach can be used to generate highly effective models of behavior which could out-perform existing models on a representative problem. It was further shown that models produced by this new method can achieve consistently high levels of performance in competitive scenarios. Additional experimentation demonstrated how incorporation of design variables into the state space allowed models to learn policies which were effective across a continuous design space and outperformed their respective baselines. All of these results were obtained without reliance on prior knowledge, mitigating risks in and enhancing the capabilities of the analysis process. Lastly, the completed methodology was applied to the design of a fighter aircraft for one-on-one, gun-only air combat engagements to demonstrate its efficacy on and applicability to more complex problems.Ph.D

Toward a Framework for Systematically Categorizing Future UAS Threat Space

Title from PDF of title page, viewed September 21, 2022Dissertation advisor: Travis FieldsVitaIncludes bibliographical references (pages 241-270)Dissertation (Ph.D.)--Department of Civil and Mechanical Engineering, Department of Electrical and Computer Engineering. University of Missouri--Kansas City, 2021The development of unmanned aerial vehicles (UAVs) is occurring as fast or faster than any other innovation throughout the course of human history. Building an effective means of defending against threats posed by malicious applications of novel technology is imperative in the current global landscape. Gone are the days where the enemy and the threat it poses are well defined and understood. Defensive technologies have to be modular and able to adapt to a threat technology space which is likely to recycle several times over during the course of a single defense system acquisition cycle. This manuscript wrestles with understanding the unique threat posed by UAVs and related technologies. A thorough taxonomy of the problem is given including projections for how the defining characteristics of the problem are likely to change and grow in the near future. Next, a discussion of the importance of tactics related to the problem of a rapidly changing threat space is provided. A discussion of case studies related to lessons learned from military acquisition programs and pivotal technological innovations in the course of history are given. Multiple measures of success are proposed which are designed to allow for meaningful comparisons and honest evaluations of capabilities. These measures are designed to facilitate discussions by providing a common, and comprehensible language that accounts for the vast complexity of the problem space without getting bogged down by the details. Lastly, predictions for the future threat space comprising UAVs is given. The contributions of this work are thus threefold. Firstly, an analytic framework is presented including a detailed parameterization of the problem as well as various solution techniques borrowed from a variety of fields. Secondly, measures of success are presented which attempt to compare the effectiveness of various systems by converting to expected values in terms of effective range, or extending the popular concept of kill chain and collapsing effectiveness into units of time. A novel technique for measuring effectiveness is presented whereby effectiveness is composed of various individual probabilities. Probabilities and associated distributions can be combined according to the rules of joint probabilities and distributions and allows performance against a probabilistic threat to be measured succinctly and effectively. The third contribution concerns predictions made with respect to the UAS threat space in the future. These predictions are designed to allow for defensive systems to be developed with a high expected effectiveness against current and future threats. Essentially this work comprises a first attempt toward developing a complete framework related to engagement and mission level modeling of a generic defensive system (or combination of systems) in the face of current and future threats presented by UAS.Introduction -- Literature review -- War gaming -- Measures of success -- Conclusion

Extracting surveillance graphs from robot maps

Abstract — GRAPH-CLEAR is a recently introduced theo-retical framework to model surveillance tasks accomplished by multiple robots patrolling complex indoor environments. In this paper we provide a first step to close the loop between its graph-based theoretical formulation and practical scenarios. We show how it is possible to algorithmically extract suitable so-called surveillance graphs from occupancy grid maps. We also identify local graph modification operators, called contractions, that alter the graph being extracted so that the original surveillance problem can be solved using less robots. The algorithm we present is based on the Generalized Voronoi Diagram, a structure that can be simply computed using watershed like algorithms. Our algorithm is evaluated by processing maps produced by mobile robots exploring indoor environments. It turns out that the proposed algorithm is fast, robust to noise, and opportunistically modifies the graph so that less expensive strategies can be computed. I