Richard Patrick Samples Ph.D. Candidate, ECE Department 1

Introduction/Overview  Introduction/Overview  Background  Article 1 Results  Article 2 Results  Article 3 Results  Conclusion  Questions/Answer Period 2

Background  Systems of Mobile Robots. Multi-Agent Systems Multi-Robotic Systems (Robot) Swarms.  Images Courtesy of 8a/RobotSwarm.jpg 3

Background Multi-robotic systems are one kind of multi- agent system or swarm (there are others). They have great potential for both peaceful and military use. Examples: ○ Search and rescue operations in collapsed buildings or mines. ○ Minesweeping operations in combat zones. 4

Problem Statement  Design a control strategy for a multi-robotic system that will maintain the cohesion of the group, prevent collision between individual robots, and allow each robot enough freedom of action so that it can accomplish a useful task.  Realistic Kinematics: Differential-Drive Mobile Robot Nonholonomic Constraint: No sideways motion  Such robots are very nonlinear, but several effective tracking controllers exist for them. 5

Previous Research  Stability Analysis of Swarms  Continuous Social Potential Function (SPF)  “Particle Physics”-style Approach  V. Gazi and K.M. Passino: “The Template”  Robot Motion Planning  Artificial Potential Functions  Reactive Paradigm (Behaviors, Subsumption)  R. P. Samples  M.S. Thesis: “Particle Physics”  Ph.D. Dissertation: (AI) Mobile Robotics 6

Previous Research  Tracking Controller Lee, Cho, Hwang-Bo, You, and Oh: Nonlinear controller (Lyapunov method) 7

Extension of Previous Research  Freedom of Motion for the Robots  The methods developed by V. Gazi and K. Passino do not allow the robots to move freely.  My Method (“2C”) allows the robots to move freely.  Thus, they can engage in productive tasks such as foraging, searching, moving objects, etc. 8

Article 1: Overview  Investigation of Flocking in a Two-Robot Swarm of Wheeled Mobile Robots Two-Robot Swarm Flocking Behavior: Cohesiveness, Collision Avoidance, Freedom of Action Analysis Simulations Behavioral State Residency Time (BSRT) 9

Article 1  Tracking Coordinates 10

Article 1 11

Article 1  Relative Coordinates 12

Article 1. 13

Article 1  Social Potential Function 14

Article 1  Kinematics  Tracking Kinematics 15

Article 1  Position Tracking Controller 16

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Article 1  Freedom of Action: In Free Action Zone, the robot is free to move on its own. There is no “force” placed on it by the social potential function. Also, the swarm as a whole has freedom of action. 20

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Article 1: Conclusion  Successful... ... But Limited: Good for a Two-Robot Swarm But Won’t Work Well With Larger Swarms 25

Article 2: Overview  Implementation of Artificial Potential Functions Using A Position Tracking Controller  Implement artificial potential functions (APFs) Quadratic Attractive APF Repulsive APF  Using a Position Tracking Controller Usually, APF methods assign a velocity to the robot directly. 26

Article 2  Attractive Behavior Move Closer to a Reference Position k  Repulsive Behavior Move Further Away from a Reference Position k 27

Article 2  Quadratic Attractive APF 28

Article 2  Desired Velocity (per Gradient Descent) 29

Article 2  Use Position Tracking Controller Define Reference Position k as the Desired Position 30

Article 2 31

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Article 2  Repulsive APF 33

Article 2  Desired Velocity (per Gradient Descent) 34

Article 2  Desired Position Formula for Repulsive APF 35

Article 2 36

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Article 2: Conclusion  The Method is Successful.  Good Tracking of Ideal Trajectories for both attractive and repulsive AFPs.  Limitation: No method to handle additive methods that sum up multiple APFs. 38

Article 3: Overview  Analysis of Flocking in a Swarm of Wheeled Mobile Robots  Extend Method of Article 1 to a Large (M-member) Swarm Using Techniques from Article 2.  Coordination Method “2C” 39

Article 3  Define Two (2) Subswarms  Attractive Subswarm:  Robot i  Other Robots Outside Its Attraction Range  Repulsive Subwarm:  Robot i  Other Robots Inside Its Repulsion Range 40

Article 3  Additive Attraction: Drive Robot i Toward the Center of the Attractive Subswarm  Additive Repulsion: Drive Robot i Away From the Center of the Repulsive Subswarm  Free Action: Command Robot i to Move Randomly  Overall Emergent Behavior: Flocking 41

Article 3  Social Potential Function 42

Article 3  Attractive and Repulsive Components Sum up the contributions of multiple attractive or repulsive APFs. Use Gradient Descent Method. 43

Article 3  Full Kinematic Model (and SPF) 44

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Article 3  Control Strategy Additive Attractive Behavior ○ Define the desired position as the center of the attractive subswarm Additive Repulsive Behavior ○ Define the reference position as the center of the repulsive subswarm ○ Use Desired Position Formula 47

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Article 3  Ideal Case: Free Action Region Exists We will get convergence – and free action. 50

Article  Radius of Convergence 51

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Conclusion  Method “2C” is a Success  Analysis and simulation results demonstrate that the method (“2C”) is successful at producing flocking behavior. 58

Further Research  Adapt Method “2C” to deal with sensor noise and error, localization errors, environmental variation, modeling errors, and other similar factors.  Beyond 2-D: Aerial Vehicles and Undersea Vehicles are 3-D !  Have Robots Perform Task (Foraging, Search, etc.)  Target Evasion Controller for Implementing the Repulsive APF  Gain-Scheduling for Constants of APFs  More Advanced Additive Method(s) 59

Publication of Results  Ph.D. dissertation  Article-style Dissertation  Three (3) Papers  Electronic Submission (ETD)  IEEE Transactions on Robotics  Additional Article(s) ? 60

Richard Patrick Samples PhD Candidate, ECE Department 61

Richard Patrick Samples PhD Candidate, ECE Department 62