Richard Patrick Samples

pillowfistsAI and Robotics

Nov 13, 2013 (3 years and 8 months ago)

78 views

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
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.


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

Graduate Student, ECE Department

29