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A Thesis Entitled a Stochastic, Swarm-Based Control Law For A Thesis entitled A Stochastic, Swarm-Based Control Law for Emergent System-Level Area Coverage by Robots by Adam M. Schroeder Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Masters of Science Degree in Mechanical Engineering ________________________________________ Dr. Manish Kumar, Committee Chair ________________________________________ Dr. Abdollah Afjeh, Committee Member ________________________________________ Dr. Brian Trease, Committee Member ________________________________________ Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May 2016 Copyright 2016, Adam M. Schroeder This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of A Stochastic, Swarm-Based Control Law for Emergent-System-Level Area Coverage by Robots by Adam M. Schroeder Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering The University of Toledo May 2016 This work proposes a stochastic, swarm-based control law for providing system- level area coverage in robots. In the first half of the work, it was investigated how a decentralized, ant-inspired, virtual pheromone-based method of area coverage performed when important parameters like rate of pheromone diffusion, rate of pheromone evaporation, and introduced noise were varied. Although this type of control scheme has been studied in literature, the interdependent sensitivity to these parameters has not been investigated. It was shown that the most influential of these parameters is the introduced noise. Part of this investigation included devising appropriate performance metrics, which were selected to measure the rate, exhaustivity, and frequency of area coverage. After optimal values for diffusion, evaporation, and noise were obtained, these values were used in the second half of this work. The investigation was then expanded to study the effect of using gradient following in combination with Lévy flight, which takes variable path lengths from a power-law distribution. Lévy flight had been shown to be effective in robot search, but had not yet been applied to area coverage. It was shown that this combination of iii gradient following and Lévy flight provides superior area coverage and pop-up threat detection. iv This work is dedicated to Michelle, and Linus, and to learning more quickly than we forget. Acknowledgements I gratefully acknowledge the many contributions of Dr. Manish Kumar to this work. His time and efforts were indispensable, and especially in hindsight, I recognize the wisdom and prudence of his council throughout the research process. I also would like to humbly acknowledge the support and kindness of my lab partners Ali, Reza, Sarim, Jisheng, Yixuan, and Padma who made it a joy to work together. v Table of Contents Abstract .............................................................................................................................. iii Acknowledgements ..............................................................................................................v Table of Contents ............................................................................................................... vi List of Tables .......................................................................................................................x List of Figures .................................................................................................................... xi List of Abbreviations ....................................................................................................... xiii List of Symbols ................................................................................................................ xiv 1 Introduction and Background ..................................................................................1 1.1 Area Coverage ...................................................................................................2 1.1.1 Area Coverage Applications ...............................................................2 1.1.2 Single Agent versus Multi-Agent Systems .........................................4 1.1.3 Area Coverage as a Special Form of Search .......................................4 1.2 Chemotaxis and Random Walks ........................................................................5 1.2.1 Ant Model of Chemotaxis ...................................................................5 1.2.2 E. Coli Chemotaxis and Random Walks.............................................7 1.2.3 Lévy Flight and Brownian Motion .....................................................8 1.2.4 Lévy Foraging Hypothesis ..................................................................9 1.3 Swarm Intelligence ..........................................................................................10 1.3.1 Return to Any Model ........................................................................11 vi 1.3.2 Other Examples of Swarm Intelligence in Nature ............................11 1.3.3 Central vs. Decentral/Distributed Control ........................................12 1.3.4 Advantages of Swarm Intelligence Approach ..................................13 1.4 Combining Area Coverage, Biased Walks, and Swarm Intelligence ..............13 1.5 Literature Review and Research Gaps .............................................................14 1.5.1 Pheromone-Based Research ..............................................................14 1.5.2 Other Swarm Research .....................................................................17 1.5.3 Lévy Flight Swarm Research ............................................................18 1.5.4 Other Multi-Agent Area Coverage Approaches ...............................18 1.6 Objective and Organization of Thesis..............................................................19 2 Problem Formulation .............................................................................................21 2.1 Defining a Mathematical Model ......................................................................21 2.2 Defining Performance Metrics .........................................................................23 2.2.1 Metric 1-Percent Area Coverage Integral .........................................23 2.2.2 Metric 2-Visit Entropy ......................................................................25 2.2.3 Metric 3-Pop-Up Threat Detection ...................................................28 2.2.4 Metric Shortcomings .........................................................................29 3 Implementation ......................................................................................................30 3.1 Summary of Cases ...........................................................................................30 3.2 General Implementation Details ......................................................................31 3.2.1 Biased Walk Implementation Details ...............................................31 3.2.2 Constant and Variable Path Length Implementation Details ............33 3.3 Performance Metric Implementation ...............................................................37 vii 3.4 Implementation Sequence ................................................................................38 3.4.1 Comprehensive Survey of Evaporation, Diffusion, and Noise .........38 3.4.2 Introduction of Lévy Flight and Comparison of Cases .....................39 3.5 Implementation in MATLAB ..........................................................................40 4 Results………. .......................................................................................................41 4.1 Survey of Evaporation, Diffusion, and Noise ..................................................41 4.2 Comparison of Three Cases .............................................................................48 5 Discussion…… ......................................................................................................52 5.1 Survey of Evaporation, Diffusion, and Noise ..................................................52 5.1.1 Impact of Noise .................................................................................52 5.1.2 Impact of Diffusion ...........................................................................53 5.1.3 Impact of Evaporation.......................................................................53 5.1.4 General Survey Results .....................................................................54 5.2 Comparison of Three Cases .............................................................................56 5.2.1 Area Coverage ..................................................................................56 5.2.2 Entropy ..............................................................................................57 5.2.3 Pop-Up Threat Detection ..................................................................60 5.2.4 General Comparison Results.............................................................62 5.2.5 Contrasting Control Law and Lévy Foraging Hypothesis ................63 5.3 Limitations and Open Research Areas .............................................................63 6 Conclusion…… .....................................................................................................67 viii References ..........................................................................................................................72
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