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

Introduction  Introduction  Background  Problem Statement  Previous Research  Approach to Problem  Research Plan  Publication of Results  Preliminary Results  Conclusion 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

Background  The multi-robotic system must have a good control system that will coordinate the actions of the individual robots so that they can accomplish a task.  Promising strategy: social potential functions. Artificial potential (popular in robotics) Robot’s motion is controlled by the artificial potential field in the same way that a mass or electric charge is controlled by a gravitational or electrical potential field. Social potential is an artificial potential that controls the robot’s swarming behavior. 5

Background  Combine Concept of the social potential function Lyapunov analysis  To get a powerful set of tools for analyzing the multi-robotic system and for designing control laws for it that maintain cohesion, prevent collisions, and allow freedom of motion. 6

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. 7

Problem Statement  Stabilization problem (on the macroscopic level)  Tracking problem (on the microscopic level)  Optimization: Optimize the social potential function for the system and the tracking controller for the individual robots to maximize overall system performance. 8

Previous Research  Latombe: motion planning  Arkin and Murphy: AI Robotics  Gazi, Passino, Liu, and Polycarpou: the use of a specific class of continuous social potential functions in multiagent systems  Samples: M.S. Thesis 9

Previous Research  Tracking Controllers Lee, Cho, Hwang-Bo, You, and Oh: Nonlinear controller (Lyapunov method) Yang and Kim: Nonlinear controller (sliding mode) Siegwart and Nourbaksh: Linear controller (constant velocity) 10

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.  Method 1W allows the robots to move freely when they are within a specified range from the center of the swarm  Thus, they can engage in productive tasks such as foraging, searching, moving objects, etc. 11

Approach to Problem  Divide the problem into two sub-problems Macroscopic problem: Proper swarming Microscopic problem: Proper tracking  Use Lyapunov techniques to achieve and demonstrate convergence  Use traditional control techniques to verify proper tracking by each robot 12

Approach to Problem  Lyapunov’s Direct Method Generalization of the Concept of the Energy of the System  Lyapunov Function:  Derivative of the Lyapunov Function  Demonstrate Stability of a System 13

Approach to Problem  Macroscopic Level: social potential function  Microscopic Level: tracking controller  Implementation of social potential function Coordination strategy determines desired position Tracking controller drives robot to that desired position 14

Approach to Problem  Coordination Method 1W: Robots adjust their position relative to the center of the swarm. If a robot is too far away from the center of the swarm, then that robot moves closer to the center (attracts) If a robot is too close to the center of the swarm, then that robot movers further away from the center (repels) If a robot is within a specified range, then it moves freely (free action) Mainly a method to get all the robots within a certain distance from each other (i.e., convergence within a hyperball). 15

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Approach to Problem  Basis Behaviors Convergence (Attraction/Repulsion) Collision Avoidance (Repulsion) Free Action  Convergence Proofs Use Lyapunov’s Direct Method Lyapunov Function LaSalle’s Invariant Set Theorems 17

Research Plan  1) Review the literature on potential function methods and swarms. This will include a review of the previous work done by Veysel Gazi and Kevin Passino.  2) Review the literature on switched system theory.  3) Review the literature on AI robotics. 18

Research Plan  4) Develop the control theory for the coordination method. ○ Full description of each method ○ Kinematics ○ Control strategy ○ Convergence theorems ○ Concise set of definitions and theorems 19

Research Plan  5) Determine a tracking controller for the individual robot that is Flexible Robust  Controller Lee, Cho, Hwang-Bo, You, and Oh Tracking coordinates (r, Ф) Nonlinear Good tracking under all conditions Variable robot velocity 20

Research Plan  6) Matlab Simulation Kinematic model  7) Experiments (?)  8) PhD dissertation  9) Three (3) research papers 21

Publication of Results  Ph.D. dissertation  Three (3) research papers IEEE Transactions on Control Systems Technology American Control Conference (September 2008) IEEE Transactions on Automatic Control IEEE Transactions on Robotics IEEE Transactions on Systems, Man, and Cybernetics 22

Preliminary Results  M.S. Thesis Proof of concept Sliding mode theory Simple two-robot swarm  Lyapunov Convergence Proof Method 1W Point Convergence Proof Method 1W Zone Convergence Proof  Simulation of Method 1W  Collision Avoidance Strategy (In Progress) Improve Method 1W By Adding a Collision Avoidance Strategy 23

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Conclusion  Reformulate convergence problem as a more conventional path planning problem with other robots modeled as moving obstacles. This is a very complex problem that may require graph searching techniques in addition to potential fields A modified Method 1W with a moving obstacle avoidance component is my current research focus.  Sources: Siegwart & Nourbaksh, Introduction to Autonomous Mobile Robots, Chapter 6. Latombe, Robot Motion Planning, Chapters 7 and 8. 27

Conclusion  Lyapunov analysis and simulation results demonstrate that Method 1W is effective at achieving swarm convergence and the desired flocking behavior.  But, Method 1W provides only very limited collision avoidance, which means that it needs to be improved by the addition of a collision avoidance sub-strategy.  Further Research: Adapt Method 1W to deal with sensor noise and error, localization errors, environmental variation, modeling errors, and other similar factors.  Questions? 28

Richard Patrick Samples Graduate Student, ECE Department 29