Transcript Oral Qualifying Exam - University of Alabama

Richard Patrick Samples
Ph.D. Student, ECE Department
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Introduction
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Introduction
Background
Problem Statement
Previous Research
Approach to Problem
Research Plan
Publication of Results
Preliminary Results
Conclusion
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Background
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Systems of Mobile Robots.
 Multi-Agent Systems
 Multi-Robotic Systems
 (Robot) Swarms.
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Images Courtesy of
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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
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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.
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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
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Combine
 Concept of the social potential function
 Lyapunov analysis
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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.
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Problem Statement
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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.
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Realistic Kinematics:
 Differential-Drive Mobile Robot
 Nonholonomic Constraint: No sideways motion
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Such robots are very nonlinear, but several effective
tracking controllers exist for them.
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Problem Statement
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Stabilization problem (on the macroscopic
level)
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Tracking problem (on the microscopic
level)
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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
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Latombe: motion planning
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Arkin and Murphy: AI Robotics
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Gazi, Passino, Liu, and Polycarpou: the
use of a specific class of continuous social
potential functions in multiagent systems
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Samples: M.S. Thesis
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Previous Research
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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
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Freedom of Motion for the Robots
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The methods developed by V. Gazi and K.
Passino do not allow the robots to move freely.
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Method 1W allows the robots to move freely
when they are within a specified range from
the center of the swarm
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Thus, they can engage in productive tasks
such as foraging, searching, moving objects,
etc.
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Approach to Problem
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Divide the problem into two sub-problems
 Macroscopic problem: Proper swarming
 Microscopic problem: Proper tracking
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Use Lyapunov techniques to achieve and
demonstrate convergence
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Use traditional control techniques to verify
proper tracking by each robot
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Approach to Problem
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Lyapunov’s Direct Method
 Generalization of the Concept of the Energy
of the System
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Lyapunov Function:
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Derivative of the Lyapunov Function
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Demonstrate Stability of a System
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Approach to Problem
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Macroscopic Level: social potential function
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Microscopic Level: tracking controller
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Implementation of social potential function
 Coordination strategy determines desired
position
 Tracking controller drives robot to that desired
position
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Approach to Problem
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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
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Basis Behaviors
 Convergence (Attraction/Repulsion)
 Collision Avoidance (Repulsion)
 Free Action
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Convergence Proofs
 Use Lyapunov’s Direct Method
 Lyapunov Function
 LaSalle’s Invariant Set Theorems
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Research Plan
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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.
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2) Review the literature on switched
system theory.
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3) Review the literature on AI robotics.
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Research Plan
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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
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5) Determine a tracking controller for the
individual robot that is
 Flexible
 Robust
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Controller
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Lee, Cho, Hwang-Bo, You, and Oh
Tracking coordinates (r, Ф)
Nonlinear
Good tracking under all conditions
Variable robot velocity
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Research Plan
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6) Matlab Simulation
 Kinematic model
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7) Experiments (?)
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8) PhD dissertation
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9) Three (3) research papers
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Publication of Results
Ph.D. dissertation
 Three (3) research papers
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 IEEE Transactions on Control Systems
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Technology
American Control Conference (September
2008)
IEEE Transactions on Automatic Control
IEEE Transactions on Robotics
IEEE Transactions on Systems, Man, and
Cybernetics
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Preliminary Results
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M.S. Thesis
 Proof of concept
 Sliding mode theory
 Simple two-robot swarm
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Lyapunov Convergence Proof
 Method 1W Point Convergence Proof
 Method 1W Zone Convergence Proof
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Simulation of Method 1W
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Collision Avoidance Strategy (In Progress)
 Improve Method 1W By Adding a Collision Avoidance Strategy
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Conclusion
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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.
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Sources:
 Siegwart & Nourbaksh, Introduction to Autonomous
Mobile Robots, Chapter 6.
 Latombe, Robot Motion Planning, Chapters 7 and 8.
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Conclusion
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Lyapunov analysis and simulation results demonstrate
that Method 1W is effective at achieving swarm
convergence and the desired flocking behavior.
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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.
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Further Research: Adapt Method 1W to deal with sensor
noise and error, localization errors, environmental
variation, modeling errors, and other similar factors.
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Questions?
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Richard Patrick Samples
Graduate Student, ECE Department
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