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 Article 1 17 Article 1 18 Article 1 19 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 Article 1 21 Article 1 22 Article 1 23 Article 1 24 Article 1: Conclusion Successful... ... But Limited: Good for a Two-Robot Swarm But Wont 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 Article 2 32 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 Article 2 37 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 Article 3 45 Article 3 46 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 Article 3 48 Article 3 49 Article 3 Ideal Case: Free Action Region Exists We will get convergence and free action. 50 Article Radius of Convergence 51 Article 3 52 Article 3 53 Article 3 54 Article 3 55 Article 3 56 Article 3 57 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