Oral Qualifying Exam - University of Alabama
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Transcript Oral Qualifying Exam - University of Alabama
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 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.
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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 Robot
Nonholonomic 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 swarming
Microscopic 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 Method
Generalization 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 function
Coordination strategy determines desired
position
Tracking 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 Behaviors
Convergence (Attraction/Repulsion)
Collision Avoidance (Repulsion)
Free Action
Convergence Proofs
Use Lyapunov’s Direct Method
Lyapunov Function
LaSalle’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
Controller
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
6) Matlab Simulation
Kinematic 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 Control
IEEE Transactions on Robotics
IEEE 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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