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Control of Self-Organizing andGeometric Formations of
Autonomous Mobile Robots
Elisha Pruner
January 11, 2013
Supervisor: Dr. Dan Necsulescu
In cooperation with Defense
Research and Development Canada
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INTRODUCTION
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Demand for Unmanned VehicleSystems in Military Applications
In 2001, the US congress was sufficiently persuaded by the militarypotential of these systems that it directed its Department of Defense
that:
One third of all operational deep strike force aircraft must be unmanned by 2010 One third of its operational ground combat vehicles must be unmanned by 2015
Although fully autonomous UVS is still a long way away, the deadlineshave applied considerable pressure of the US military to introduce
large numbers of tele-operated or semi-autonomous UVS intocapability
Advantages of UVS Reduce risk to war-fighting personnel Reduce cost of acquisition and operations Revolutionary impact on military operations, and how we fight wars
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Unmanned Ground Vehicles
Remote control and teleoperation- a human operator controls a robotic vehicle
from a distance
- the human performs all the cognitive
processes
- the onboard sensors and communications
enable the operator to visualize the location
and movement of the platform within itsenvironment
Semi-autonomous- these systems have advanced navigation,
obstacle avoidance, and data fusion
capabilities that minimize the need for operator
interaction
- they have sufficient on-board processing to
adapt to simple changes in objective
designated by an operator
Platform-centric autonomous- a fully autonomous UVS can undertake
complex task/missions, acquiring information
from other sources as required
- it can respond to additional commands from
a controller without the need for further
guidance
Network-centric autonomous- these systems have sufficient autonomy to
operate as independent nodes
- they should be capable of receiving
information from the network, incorporating it
in their mission planning and execution, and
responding to other information requests,
including resolution of conflicting commands
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Navigating in DynamicEnvironments
military environments are inherently dynamic and vehiclesmust be able to adapt to changing terrain
they need to know what is going to happen next and whatthe best decision is now
PlanningControl
ExplicitMethods
Continuous
Optimalcontrol
Recedinghorizon control
Discrete
Celldecomposition
Probabilisticroadmap
ImplicitMethods
Reactive AI
Behaviorbased control
Learning
Potential Fields
Navigationfunctions
Harmonicpotential functions
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Collision Avoidance DiscreteMethods
Graphing methods such as celldecomposition and probabilistic roadmaps
are popular methods of determining optimalpath planning routes for robot motion
Cell decomposition method is a grid basedsearch
Algorithms determine the shortest pathacross the cells
Probabilistic roadmaps method places nodesat the start and goal position, and at thevertices of the obstacles
The task of the path planner is to findthe shortest path from the available road
ways to the goal position
http://imlab.postech.ac.kr/research/subjects/path_plan/Path-Planning.html
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Collision Avoidance ReactiveArtificial Intelligence
Intelligent agents Each agent has its own set of rules and commands Onboard processors determine the best logical
course of action depending on constraints
Planning algorithms, searching algorithms, swarmingalgorithms
Learning algorithms Evolutionary algorithms
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Collision Avoidance ArtificialPotential Fields
The artificial potential field method Obstacles are assigned a repulsive potential and the goal is
described by an attractive potential
The path of motion is calculated using the gradient of totalartificial potential
The main drawback of potential field technique is the localminimum problem
Solutions exist to alleviate the local minimum problem Escape mechanisms from local minima Harmonic potential functions
GOAL
Fattractive
Frepulsive
Fnet= 0
obstacle
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Advantages of Multi-VehicleSystems
In certain applications, such as search and rescue,reconnaissance, and surveillance
Many small inexpensive robots working as a teamcan achieve more than one sophisticated vehicle
working on its own The success of robot teams in accomplishing a mission
depends on their ability to work together through anappropriate coordination strategy
Multi-vehiclerobotic systems
Perform tasks withgreater efficiency
Inexpensivesolution
Offer a morerobust solution
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Coordinating Groups ofAutonomous Mobile Vehicles
Coordination in multi-vehicle systems Centralized models: centralized monitoring system
oversees and controls the group
Decentralized models: no supervisor, relies solely onrelative positions of vehicles to coordinate the robotmovements
In a decentralized approach, formations are often applied toadd order and organization to the group
Types of formation: Self-organizing formations obtain its overall shape from
the motion characteristics of the algorithm
Geometric formations have a predefined geometry whiletravelling through the terrain
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Self-Organizing Formations:Biologically Inspired Formations
Initial work in formation control wasinspired by social characteristics andbehavior-based paradigms ofbiological systems
Researchers developed formationmovement taken from successfulcooperative groupings in naturesuch as:
Flocking (birds) Schooling (fish) Swarming (bees)
http://nacwr.blogspot.ca/2011/07/closer-we-humans-live-by-mother-natures.htmlhttp://en.wikipedia.org/wiki/Shoaling_and_schooling
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Self-Organizing Formations:Behavior Based Formations
In behavioral based approaches to formation control, anumber of basic behaviors are prescribed
Ex. Obstacle avoidance, formation keeping, goalseeking
The overall control action is a weighted average of thecontrol actions for each basic behavior
http://photography.nationalgeographic.com/staticfiles/NGS/Shared/StaticFiles/Photography/Images/POD/s/swarm-bots
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Geometric Formations:Virtual Structures
When working with groups ofmobile robots, the pathplanner must find a collision-free path for the entire groupto reach the goal position
A virtual structure considersthe entire formation as a rigidbody
Once the desired dynamics ofthe virtual structure are
defined, then the desiredmotion for each agent isderived
Ge , Shuzhi Sam , and Frank L. Lewis .Autonomous Mobile Robots. Boca Raton, FL: Taylor & Francis Group , 2006.
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Geometric Formations:Leader-Follower Method
In the Leader-Follower method, one vehicle acts as aLeader and generates the reference trajectory for theteam of Followers
The behavior of the group is defined by the Leader Follower vehicles traverse its environment by following
a trail of makers, or breadcrumbs, left by the leader
Leader can be a dismounted human, a manned vehicle,or an autonomous vehicle
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RESEARCH OBJECTIVES
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Challenges
Important Factors for our Algorithm
Efficiently reaching the goal position
Avoiding collisions with the environment
Avoiding collisions with other robots
Fully decentralized command
No pre-planned trajectory
Efficient Algorithms for fast processing and reaction time
Multi-robot teams perform tasks with greater efficiency,less cost, and offer a more robust solution
The challenge in working with multi-robot systems isdeveloping a coordination strategy for their motion
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Research Objectives
In our research we are looking into navigationalgorithms for teams of mobile robots
The objective is to develop formation controllers thatallow the team to move as a group
Research efforts will focus on two important types offormations:
Military style geometric formations Self-organizing formation, that arise from the motionalgorithm with no fixed geometry
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RESEARCH TOOLS
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MATLAB Simulation Software
Simulations were created inthe MATLAB Editor using theMATLAB programminglanguage
Simulations were executedin the form of animations To quickly display robot
movement and collisionavoidance characteristicsof the navigation
algorithms
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X80 Wireless Robots
The X80 mobile robot is equippedwith passive and active sensors
including:
Ultrasonic, infrared, temperature,camera, and microphone
Two 12V DC motors power thewheels of the differential drive robot
Quadrature encoders on the wheelsprovide measurement and position
estimation
The navigation controller will be sentdirectly from the computer to the
robot through a Wi-Fi connection
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Player/Stage Robot DevelopmentEnvironment
Player/Stage is a robot developmentenvironment that provides a
hardware abstraction layer tosimplify the work of programming
robots
In Stage, you can create simulationsthat take into account the exact
geometry of the robot, along with
sensor locations, sensor limits, andactuator variables
Experiments with the robots are thenexecuted with Player
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COLLISION AVOIDANCE
USING THE VELOCITYPOTENTIAL APPROACH
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Control Inspiration Fluid Mechanics
Goal: to design a navigation controllerthat would have a more fluid movement
In the Velocity Potential approach wewill work with velocities and velocityflow fields
Vehicle will be attracted to the goal viathe attractive flow (u)
Vehicles travel safely around obstaclesdue to torsional velocities, similar to avortex around the obstacle
Fox, Robert W. Introduction to Fluid Mechanics. New York, NY: John Wiley & Sons Inc., 2004.
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Attractive Velocity Equations
To find the attractive velocity commands,calculate the distance to the goal and the
attractive angle using robot and goalcoordinates
The velocity command is based on themagnitude u defined by the user and theattractive angle
G=
xGx( )
2
yG
y( )
2
a =
tan1 yG y( )
xG x( )
x,y,( )
xG
,yG
,G( )
x
y
GOAL
ua
v
a
G
ua = ua cosa + jsina( )
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Attractive Velocity Equations (cont)
We would like the vehicle to slow down andstop as it reaches the goal position In order to do so we include a exponential
term that is a function of the distance tothe goal and the goal radius of interest
The final linear velocity command is a functionof the velocity vector and the exponentialterm, multiplied by a gain k
The attractive angular velocity is
f G ,GR( ) = e
GGR
( )
va = kaua 1 f G ,GR( )( )
x,y,( )
xG ,yG ,G( )
x
y
GOAL
ua
v
a
G
a = ka 1 f G ,GR( )( )
t
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MATLAB SimulationOne Robot with
Attractive Velocity Commands
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Normal and Tangent Velocity
To move around obstacles, the robot will useits direct sensor data. The circle around the
robot represents its maximum sensor range,and the dotted lines represent the sensor
angles
The shortest sensor reading is taken as thepoint of interest
Normal and tangent vectors are determined atthe point of interest
The magnitude of the normal and tangentvelocity are a function of the obstacle distance
ut
un
ua
GOAL
O
v
n=
o
t=
n
2
un= u
t=
1
o
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Normal and Tangent VelocityEquations (cont)
The normal and tangent vectors are then calculated as afunction of the magnitude and the angle
An exponential obstacle function is added to slow the vehicledown as it approaches an obstacle
The final velocity and angular velocity commands are
un = un cosn + jsinn( ) ut = ut cost + jsint( )
f O ,OR( ) = e
OOR
( )
v = kaua 1 f G ,GR( )( )+ knun f O ,OR( )+ ktut f O ,OR( )
o= ko f O ,OR( )( )
t
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MATLAB Simulation1 Robot with an Obstacle
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X80 Test Collision Avoidance
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Approaching a Concave
Obstacle The concave obstacle is a
local minimum struggle forthe artificial potential fields
approach
The vehicle must go aroundthe C-shape obstacle toreach the goal position
ut
un
ua
GOAL
O
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MATLAB Simulation1 Robot Concave Obstacle
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X80 Test Concave Obstacle
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GEOMETRIC APPROACHTO GROUP BEHAVIOR
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Formation Controller Setup
Leader-Follower One robot acts as a leader and generates the
reference trajectory for the follower vehicle
The leader can be controlled manually by ajoystick, or it can navigate autonomously
through the environment
Method: Using the x, y, and theta components of both
the leader
and the follower convert to polar coordinates
F
F
vF
(xL, yL, L)
(xF, yF, F) x
y
L
L
vL
!
G=
xL
xF( )
2
yL
yF( )
2
= tan1yL yFxL xF
F
=+F L +
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Determining Follower VelocityValues
Find the derivative of rho, alpha, and psi in terms of theleader and follower velocities
Reduce the matrix to the derivative rho and alpha termsand rearrange the equation to solve for the follower
velocity terms
i
i
i
=
cos 0
sin
1
sin
0
vF
F
+
cos 0
sin
0
sin
1
vL
L
=
cos 0
sin
1
vF
F
+
cos 0
sin
0
vL
L
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Adding a Proportional-Derivative (PD)Controller to the Follower Velocity
Equation
PD controller in generalized coordinates
The follower velocity equation with PD control became
vF
F
=
1
cos0
tan
1
+
cos
cos0
tancos
+sin
0
vL
L
u = kP q qd( ) kD q
vF
F
=
kP
1+ kD( )cos
0
kPtan
kP
1+ kD( )
d
d
+
cos
cos0
1+ kD( )
tancos
+sin
0
vL
L
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Leader-Follower Controllerwith Two Robots
The following simulationshow a leader robot (red)moving in a circle withconstant angular velocity
The follower robot (blue)tracks the leader using theleader-follower controller
The follower is initiallypositioned at the mostdifficult position, at a 180angle from the leader
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MATLAB Simulation:Platoon Formation
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X80 Test - Platoon
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MATLAB Simulation: V - FormationThrough a Narrow Passage
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MATLAB Simulation: V - FormationThrough a Narrow Passage
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X80 Test: V-Formation Through aNarrow Passage
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SELF-ORGANIZINGFORMATIONS
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Self-Organizing Formation:3 Robots using the Velocity
Potential Method
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Self-Organizing Formations:Simulation of 8 Robots using
the Velocity Potential Method
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CONCLUSIONS
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Conclusions
In this research we looked at A reactive collision avoidance strategy using the
velocity potential method
A self-organizing formation controller using thevelocity potential method
A geometric formation controller using the leaderfollower approach
Simulations were carried out in MATLAB and Stage, andexperiments were performed on the X80 mobile robotwith Player
We found that larger groups benefited from the self-organizing approach
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Future Work
Improve the self-organizing algorithm to handle verylarge groups of autonomous robots
Adding GPS and localization algorithms for X80experiments, to accurately define the position of therobots in the terrain
Currently relying on dead reckoning localization To add more intelligence to the followers in the leader-
follower controller
Currently the leader dictates the desiredconfiguration of the followers
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QUESTIONS
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