# Richard Patrick Samples

Τεχνίτη Νοημοσύνη και Ρομποτική

13 Νοε 2013 (πριν από 7 χρόνια και 8 μήνες)

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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

www.swarm
-
bots.com

http://www.scholarpedia.org/wiki/images/8/
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

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

16

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

24

25

26

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