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