University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 3-3-2008 A Potential Field Based Formation Control Methodology for Robot Swarms Laura E. Barnes University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Barnes, Laura E., "A Potential Field Based Formation Control Methodology for Robot Swarms" (2008). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/131 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. A Potential Field Based Formation Control Methodology for Robot Swarms by Laura E. Barnes A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Computer Science and Engineering College of Engineering University of South Florida Major Professor: Kimon Valavanis, Ph.D. Lawrence Hall, Ph.D. Rangachar Kasturi, Ph.D. Rafael Perez, Ph.D. Stephen Wilkerson, Ph.D. Maryanne Fields, Ph.D. Date of Approval: March 3, 2008 Keywords: swarm formation, mobile robots, robot control, multirobot systems, intelligent systems © Copyright 2008, Laura E. Barnes Note to Reader The original of this document contains color that is necessary for understanding the data. The original dissertation is on file with the USF library in Tampa, Florida. Dedication This work is dedicated to my family and friends without whom this work would not have been possible. I would like to specifically thank my parents for their ongoing support. I would also like to thank Richard Garcia for his constant friendship and technical assistance throughout our journey the past years. Last but not least, I would like to thank Sakis for his love and encouragement. Acknowledgments This research was supported in part by an appointment to Student Research Participation Program at U.S. Army Research Laboratory administered by the Oak Ridge Institute for Science and Education through interagency agreement between the U.S. Department of Energy and US ARL. This work was also supported partially by two grants ARO W911NF-06-1-0069 and SPAWAR N00039-06-C-0062. I would specifically like to thank Dr. MaryAnne Fields from the Army Research Lab for all her time and help. Table of Contents List of Tables v List of Figures vi Abstract x Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Problem Statement 2 1.3 Method of Approach 2 1.4 Research Contributions 2 1.5 Summary of Results 3 1.6 Thesis Outline 4 Chapter 2 Background Information 5 2.1 Mobile Robot Systems 5 2.2 Multirobot Systems 7 2.3 Multirobot Architectures 8 2.4 Robot Swarms 10 2.5 Swarm Formation Control 12 Chapter 3 Literature Review 14 3.1 Formation Control Methods 14 3.1.1 Behavior-Based and Potential Field Formation Control Strategies 17 3.1.2 Leader-Follower and Graph Theoretic Formation Control Strategies 19 3.1.3 Virtual Structure Formation Control Strategies 22 3.1.4 Other Control Strategies in Formation Control 22 3.2 Foundation of the Proposed Approach 24 3.3 Summary 25 Chapter 4 Proposed Formation Control Approach 27 4.1 Swarm Surface 27 4.2 Formation Problem 28 i 4.3 Generation of Vectors and Vector Field 31 4.3.1 Description of Vector Fields 31 4.3.2 Description of Limiting Functions 33 4.3.2.1 Sin and Sout Sigmoid Limiting Functions 33 4.3.2.1.1 Mathematical Solution for αin-Control Variable 37 4.3.2.1.2 Mathematical Solution for αout-Control Variable 38 4.3.2.1.3 Mathematical Proof for Convergence of Sin and Sout Limiting Functions 40 4.3.2.2 N⊥ Normal Limiting Function 42 4.3.3 Controlling Swarm Member Dispersion within Bands 45 4.4 Parameter Selection 47 4.4.1 Logical and Static Parameter Selection for R-Parameters 47 4.4.1.1 Ellipse Formation 47 4.4.1.2 Arc Formation 48 4.4.1.3 Line Formation 48 4.4.1.3.1 Line Formation with Skinny Ellipse 48 4.4.1.3.2 Leader-Follower Line Formation 49 4.4.2 Fuzzy Speed Control and Parameter Selection 49 4.4.2.1 Fuzzy Speed Control 50 4.4.2.2 Fuzzy Parameter Selection of ΔRavoid 53 Chapter 5 Simulation Software 55 5.1 Matlab Simulink Model 55 5.1.1 Vector Generator Block 57 5.1.2 Vehicle Model Block 57 5.1.2.1 Particle Model 57 5.1.2.2 Robot Model 58 5.1.2.2.1 Forward Body Reference Dynamics 58 5.1.2.2.2 Motor Model 59 5.1.2.2.3 Kinematic Calculations 60 Chapter 6 Hardware Architecture and Platform 63 6.1 Radio-Controlled Vehicles 64 6.1.1 Radio-Controlled Ground Vehicles 64 ii 6.1.2 Radio-Controlled Helicopter 65 6.2 Sensors 66 6.3 Computer System 67 Chapter 7 Software System Architecture 68 7.1 Operating System 68 7.2 Software Architecture 69 7.2.1 Sensor Suite 72 7.2.1.1 GPS Sensor 72 7.2.1.2 IMU Sensor 73 7.2.2 Navigation and Obstacle Avoidance 74 7.2.2.1 Swarm Formation Controller 75 7.2.2.2 Robot Motion Controller 75 7.2.3 Communication Server / Client Model 76 Chapter 8 Simulation Results 77 8.1 Simulations with Robot Model 77 8.1.1 Ten Heterogeneous Robots Circling a Point 77 8.1.2 Ten Homogeneous Robots Following a Straight Trajectory without Limiting Functions 79 8.1.3 Ten Heterogeneous Robots in a Line Formation 81 8.1.4 Ten Heterogeneous Robots in an Ellipse Formation 82 8.2 Simulations with Particle Model 84 8.2.1 Simulations with Particle Model and Static Variable Selection 84 8.2.1.1 Four Particles in Arc and Circle Formations 84 8.2.1.2 Ten Particles in Circle and Ellipse Formations 86 8.2.2 Simulations with Particle Model and Fuzzy Variable Selection 88 8.2.2.1 Four Particles in Arc / Wedge Formation 88 8.2.2.2 Four Particles in Circle / Square Formation 90 8.2.2.3 Four Particles in Ellipse / Rectangle Formation 92 Chapter 9 Field Experiments 94 9.1 Experiment 1: Four Robots in an Ellipse Formation with a Virtual Center 94 9.2 Experiment 2: Three Robots in an Ellipse Formation with a Virtual Center 98 9.3 Experiment 3: Three Robots in an Ellipse Formation with a Robot Center 101 9.4 Experiment 4: Three Robots in a Line Formation 104 iii 9.5 Experiment 5: Three Robots in an Ellipse Formation with a Failure 106 9.6 Experiment 6: UAV-UGV Swarm Coordination 109 Chapter 10 Future Approach Utilizing Deformable Ellipses 113 10.1 Technical Approach 113 10.2 Improving Static Formations 113 10.3 Bending the Ellipsoid 116 10.4 Translating and Rotating the Ellipsoid 119 Chapter 11 Conclusions and Future Work 125 11.1 Conclusions 125 11.2 Future Work 125 References 127 Appendices 137 Appendix A Nomenclature for Mathematical Variables 138 About the Author End Page iv List of Tables Table 3.1. Formations with implicit robotic control. 16 Table 3.2. Formations with explicit robotic control utilizing leader-follower reference. 16 Table 3.3. Formations with explicit robotic control utilizing other reference types. 17 Table 5.1. Robot physical parameters. 59 Table 5.2. Motor parameters. 60 Table 7.1. GPS shared memory data structure. 72 Table 7.2. IMU shared memory data structure. 73 Table 8.1. Control variables with ten robots. 78 Table 8.2. Control variables with ten heterogeneous robots. 81 Table 8.3. Control variables with four particles. 84 Table 8.4. Control variables with ten particles. 86 Table 8.5. Control variables for arc formation utilizing fuzzy parameter selection. 88 Table 8.6. Control variables for circle formation utilizing fuzzy parameter selection. 90 Table 8.7. Control variables for ellipse formation utilizing fuzzy parameter selection. 92 Table 9.1. Control variables for experiment 1. 95 Table 9.2. Control variables for experiment 2. 98 Table 9.3. Control variables for experiment 3. 101 Table 9.4. Control variables for experiment 4. 104 Table 9.5. Control variables for experiment 5. 107 Table 9.6. Control variables for experiment 6. 110 Table A.1. Swarm equation variables. 138 v List of Figures Figure 2.1. Examples of robots. 6 Figure 2.2. Multirobot system groups. 7 Figure 2.3. Centralized control model. 8 Figure 2.4. Distributed, decentralized control model. 9 Figure 2.5. Examples of swarms in nature. 11 Figure 3.1. Examples of formation shapes with three robots. 15 Figure 4.1. Convoy description. 28 Figure 4.2. Convoy of vehicles surrounded by concentric ellipses. 29 Figure 4.3. Elliptical attraction band for the swarm robots. 30 Figure 4.4. Vector fields directed away from the center (G-). 32 Figure 4.5. Vector fields directed towards the center (G+). 32 Figure 4.6. Vector fields directed perpendicular to the center (G┴). 33 Figure 4.7. General sigmoid function. 34 Figure 4.8. Combined in (G+) and out (G-) fields. 35 Figure 4.9. The weighting functions Sin and Sout as a function of the weighted distance r defined in (4.17). 36 Figure 4.10. Weighting function W(r) (shown in green) when ΔRin = ΔRout. 41 Figure 4.11. Weighting function W(r) (shown in green) when ΔRout > ΔRin. 42 Figure 4.12. The weighting function N⊥ as a function of the weighted distance r defined in (4.17).