control of self-organizing and geometric formations of autonomous mobile robots

7/29/2019 Control of Self-Organizing and Geometric Formations of Autonomous Mobile Robots

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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

control of self-organizing and geometric formations of autonomous mobile robots

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