Richard Patrick Samples

Ph.D. Student, ECE Department

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

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Background Systems of Mobile Robots.

Multi-Agent Systems

Multi-Robotic Systems

(Robot) Swarms.

Images Courtesy of www.swarm-bots.com http://www.scholarpedia.org/wiki/images/

8/8a/RobotSwarm.jpg

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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.

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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.

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Background

Combine Concept of the social potential functionLyapunov analysis

To get a powerful set of tools for analyzing the multi-robotic systemand for designing control laws for it that

maintain cohesion, prevent collisions, and allow freedom of motion.

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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 RobotNonholonomic Constraint: No sideways motion

Such robots are very nonlinear, but several effective tracking controllers exist for them.

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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.

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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

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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)

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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.

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Approach to Problem Divide the problem into two sub-problems

Macroscopic problem: Proper swarmingMicroscopic problem: Proper tracking

Use Lyapunov techniques to achieve and demonstrate convergence

Use traditional control techniques to verify proper tracking by each robot

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Approach to Problem

Lyapunov’s Direct MethodGeneralization of the Concept of the Energy

of the System

Lyapunov Function:

Derivative of the Lyapunov Function

Demonstrate Stability of a System

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Approach to Problem Macroscopic Level: social potential function

Microscopic Level: tracking controller

Implementation of social potential functionCoordination strategy determines desired

positionTracking controller drives robot to that desired

position

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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).

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Approach to Problem

Basis BehaviorsConvergence (Attraction/Repulsion)Collision Avoidance (Repulsion)Free Action

Convergence ProofsUse Lyapunov’s Direct MethodLyapunov FunctionLaSalle’s Invariant Set Theorems

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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.

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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

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Research Plan 5) Determine a tracking controller for the

individual robot that is Flexible Robust

ControllerLee, Cho, Hwang-Bo, You, and Oh Tracking coordinates (r, Ф)NonlinearGood tracking under all conditionsVariable robot velocity

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Research Plan

6) Matlab SimulationKinematic model

7) Experiments (?)

8) PhD dissertation

9) Three (3) research papers

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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 ControlIEEE Transactions on RoboticsIEEE Transactions on Systems, Man, and

Cybernetics

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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

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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.

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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?

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Richard Patrick Samples

Graduate Student, ECE Department

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