swarm intelligence in robotics

Swarm Intelligence in Robotics

Dr. Alaa KhamisPattern Analysis and Machine Intelligence

University of Waterloo

MUSES_SECRET: ORF-RE Project - © PAMI Research Group – University of Waterloo 1/221ECE493T8:2008-2009 - © PAMI Research Group – University of Waterloo

[email protected]

Outline

MUSES_SECRET: ORF-RE Project - © PAMI Research Group – University of Waterloo

• Introduction

• Body/Brain Evolution

• Traditional Robotics

• Swarm Robotics• Swarm Robotics

• Swarm Intelligence (SI)

• SI in Traditional Robotics

• SI in Swarm Robotics

• Concluding Remarks


Outline


• Introduction









Introduction

S h di L b

• PAMI Research Group

CIM L bSynchromedia Lab CIM Lab

Intelligent Multi-craneCRS F3 and CRS T265

Mobile Robotics Lab

Magellan Pro

Pattern Analysis LabSpeech

Understanding

ATRV-miniSoccer-playing Robots

Data Mining Services Catalog

Computer visionPattern

Analysis


Introduction• Swarm Intelligence in Robotics

The objective of this talk is to highlight the different applications j g g pp

of the rapidly emerging field of swarm intelligence in solving

complex problems of traditional and swarm roboticscomplex problems of traditional and swarm robotics.


Outline


• Introduction









Body/Brain Evolution

Brains

SI Cognitive RoboticsSwarm

Robotics

100s

g Robotics

DAI MultiagentDistributed

Robot System10s

y

1AI Robotics Centralized Control

Multiple MachinesMachine MEMS-based Multiple Machines


Bodies10s

p

1 100s

p

Outline


• Introduction









Traditional Robotics

The Evolutionary Stages

IndustrialRobotics

S i

Service Robots for Professional Use

S i R b t fServiceRobotics

Personal

Service Robots forPersonal Use

PersonalRoboticsEvolution


Traditional Robotics• Traditional Problems

Environment Perception

SLAM

Path Planningg

Navigation

Autonomy Autonomy

Human Interaction

L i Learning


Outline


• Introduction









Swarm Robotics• Definition

Swarm robotics is the study of how large number of relatively simple h i ll b di d t b d i d h th t d i dphysically embodied agents can be designed such that a desired

collective behavior emerges from the local interactions among agents and between the agents and the environment. g

Resolving complexity.

I i fIncreasing performance.

Simplicity in design.

Box Pushing

Reliable.


Swarm Robotics• Typical Problem Domains

Box-pushing

Foraging

Aggregation and Segregationgg g g g

Formation Control

Cooperative Mapping Cooperative Mapping

Soccer Tournaments

Sit P ti Site Preparation

Sortinghttp://www.robocup.org/


Collective Constructionhttp://www.fira.net/

Swarm Robotics

Autonomous inspection of complex engineered structures.• Applications of Swarm Robotics

Distributed sensing tasks in micromachinery or the human body. Killing Cancer Tumors in Human Body Mining Agricultural Foraging i ki

Spy robots

Cooperative Tracking Interactive Art S b d C i

UAV drones

Space-based Construction Rescue Operations H it i D i i


Humanitarian Demining Surveillance, Reconnaissance and Intelligence. Mobile Trackers

Swarm Roboticshttp://www.swarm-bots.org/• Projects

The SWARM-BOT project aims to d l b istudy a novel swarm robotics system.

It is directly inspired by the collecti e beha ior of socialcollective behavior of social insects and other animal societies.

It focuses on self-organizationand self-assembling of autonomous agentsautonomous agents.

Its main scientific challenge lays in the development of a


Swarm-bots, Marco Dorigo, 2005

novel hardware and of innovative control solutions.

Swarm Robotics

http://www.ai.sri.com/centibots/index.html• Projects

The Centibots project:

The Centibots are a team of 100 autonomous robots (97 ActivMediaautonomous robots (97 ActivMedia Amigobot and 6 ActivMedia Pioneer 2 AT) The goal of the project is to2 AT). The goal of the project is to demonstrate 100 robots mapping, tracking guarding in a coherenttracking, guarding in a coherent fashion during a period of 24 hours.


Swarm RoboticsPAMI Lab• Projects

http://horizon.uwaterloo.ca/multirobot/

Leaderless Distributed (LD) Flocking AlgorithmFlocking in Embedded Robotic Systems Flocking in Embedded Robotic Systems

CORO - Caltech


Swarm Robotics• Team Size and Composition

Team Size

Alone Pair Limited Infinite

Team Composition

H H tAlone Pair LimitedGroup

InfiniteGroup

Homogenous Heterogeneous


Swarm Robotics• Team Reconfigurability

Team Reconfigurability

Static Coordinated Dynamicy


Swarm Robotics• Communication Pattern

Explicit Communication

Add B d t G h

Implicit Communication

I t ti i I t tiAddress or DirectedMessages

Broadcast Graph Interaction via Environment (Stigmergy)

Interaction via Sensing

nn

onA

ctio

n

Perc

eptio

n

EnvironmentVirtual

Pheromone Perc

eptio

n

Act

io

Perc

eptio

n


Swarm Robotics• Communication Range and Bandwidth

Communication Range

None N Infinite

Communication Bandwidth

High Moderate zeroLowNone Near Infinite High Moderate zeroLow


Swarm Robotics• Organizational Paradigm

Hierarchical Organization Holarchical Organization



Coalition-based Organization Team-based Organization



Congregations Organization Societies Organization

Congregation

Social laws, norms or

conventions

Socialization process



Federations Organization Market-based OrganizationRegional province

or federate

Federal Level

Delegate or facilitator

B ing agentsBuying agents

Selling agents or auctioneers



Matrix Organization Compound OrganizationManger

Worker



Paradigm Key Characteristic

Benefits Drawbacks

Hierarchy Decomposition Maps to many common domains; handles scale well

Potentially brittle; can lead to bottlenecks or delays

Holarchy Decomposition withautonomy

Exploit autonomy of functional units Must organize holons;lack of predictable performance

Coalition Dynamic, goal- Exploit strength in numbers Short term benefits may not outweigh Coalition Dynamic, goaldirected

Exploit strength in numbers Short term benefits may not outweigh organization

construction costs

Team Group level cohesion Address larger grained problems; task-centric Increased communication

Congregation Long-lived, utility-directed

Facilitates agent discovery Sets may be overly restrictivedirected

Society Open system Public services; well defined conventions Potentially complex, agents may require additional

society-related capabilities

Federation Middle-agents Matchmaking, brokering, translation services; facilitates dynamic agent pool

Intermediaries become bottlenecksdynamic agent pool

Market Competition through pricing

Good at allocation; increased utility through centralization; increased fairness through bidding

Potential for collusion, malicious behavior; allocation decision complexity can be high

Matrix Multiple managers Resource sharing; multiply-influenced agents Potential for conflicts; need for increased agentsophistication


Compound Concurrent organizations

Exploit benefits of several organizational styles Increased sophistication; drawbacks of severalorganizational styles

Source: B. Horling and V. Lesser, "A Survey of Multi-Agent Organizational Paradigms, The Knowledge Engineering Review, Vol: 19, Num: 4, pp. 281 - 316, Cambridge University Press, 2005.

Swarm Robotics• Challenging Problems

Coordination

Algorithm Design

I l i d T Implementation and Test

Analysis and Modelling


Swarm Robotics• Challenging Problems: Coordination

Coordination

Cooperation Collaboration Competition

Planning Negotiation

Resource Allocation

Coordinated Motion Planning


Coordinated Motion Planning

Swarm Robotics

Swarm roboticists face the problem of designing both the

• Challenging Problems: Algorithm Design

physical morphology and behaviours of the individual robots such that when those robots interact with each other and their environment, the desired overall collective behaviours will emerge. At present there are no principled approaches to the design of low-level behaviours for a given desired collective behaviour [1].

“collective behavior is not simply the sum of each participant’s b h i th t th i t l l” [ ]


behavior, as others emerge at the society level” [2].

Swarm Robotics• Challenging Problems: Algorithm Design

Main decisional abilities:

- Mission planning,

- Task allocation and

- Coordinated task achievement

Management the task allocation,SchedulingScheduling,Cooperation/collaboration between the entities,Conflict avoidance, etc.


Conflict avoidance, etc.

Swarm Robotics

To build and rigorously test a swarm of robots in the laboratory

• Challenging Problems: Implementation and Test

requires a considerable experimental infrastructure. Real-robot experiments thus typically proceed hand-in-hand with simulation and good tools are essential [1].


Swarm Robotics• Challenging Problems: Implementation and Test

Advanced Robotics Interface for Applications (ARIA):Robotic Sensing and Control Libraries.

Open Robot Control Software (OROCOS): open-source p f preal time control architecture for different machines.

Microsoft Robotics Studio: is a Windows-based

Pl /St /G b PSG i ft th t d

Microsoft Robotics Studio: is a Windows based environment for robot control and simulation.

Player/Stage/Gazebo: PSG is open source software that used and developed by an international community of researchers from over 30 universities/companies.


3 / p

Swarm Robotics

Stage 3.0 [3]

• Challenging Problems: Implementation and Test


2,000 minibots 100 Pioneer Robots

Swarm Robotics

A robotic swarm is typically a stochastic, non-linear system and

• Challenging Problems: Analysis and Modelling

constructing mathematical models for both validation and parameter optimization is challenging. Such models would surely be an essential part of constructing a safety argument for real-world applications [1].


Outline


• Introduction









Swarm Intelligence

DNA Cellular Automata

Brain Neural Networks

Immune System Protection of computers and networks

Evolution Genetic Algorithms

and networks

Evolution Genetic Algorithms

Social Insects Swarm Intelligence


Social Insects Swarm Intelligence

Swarm Intelligence

Nature Unmanned Aerial/Ground VehiclesAnalogies

Ants/UAVs

Prey/Target

Predators/Threats

Environment/Battlefield


Swarm Intelligence• Definition

Swarm intelligence (SI) refers to the phenomenon of a system of spatially distributed individuals coordinating their actions in a decentralized and self-organized manner so as to exhibit complex collective behavior.

“SI is the property of a system whereby the collective behaviors of (unsophisticated) agents interacting locally with their environment cause coherent functional global patterns to emerge.”


Swarm intelligence solves optimization problems.

Swarm Intelligence• Key Elements A large number of “simple” processing elements;

Neighborhood communication;

Though convergence in guaranteed, time to convergence is

uncertain.

Most of the research are experimental:Most of the research are experimental:

ModelObservation Create MetaheuristicExtract

Build

Simulation

Test

Refine


AlgorithmSimulation

Swarm Intelligence

Initialize parameters

• SI-based Approaches

Initialize parameters

Initialize population

While (end condition not satisfied ) loop over all individuals

Find best so farFind best so far

Find best neighbor

Update individual


Swarm Intelligence• SI-based Approaches

Ant Colony Optimization (ACO)

Particle Swarm Optimization (PSO)

Stochastic Diffusion Search (SDS) Stochastic Diffusion Search (SDS)


Outline


• Introduction









SI in Traditional Robotics• ACO-based Motion Planning [4]

• PSO-based Motion Planning [5]g [5]

• Wall-following autonomous robot (WFAR) navigation [6]

• Gait Optimization [7]

• Kinematics and Dynamics of Robot Manipulators [8,9]

• Learning [10]


SI in Traditional Robotics• Motion Planning

Path planning is a process to compute a collision-free path for a robot from a start position to a given goal position, amidst a collection of obstacles.

T


S

SI in Traditional Robotics• ACO-based Motion Planning [4]

Proposed Method

Step 1: MAKLINK graph theory to establish the free space

model of the mobile robot;;

Step 2: utilizing the Dijkstra algorithm to find a sub-

optimal collision-free path;optimal collision-free path;

Step 3: utilizing the ACS algorithm to optimize the location

f h b i l h h l b ll of the sub-optimal path so as to generate the globally

optimal path.


SI in Traditional Robotics

Step 1: MAKLINK-based Free Space Model

• ACO-based Motion Planning [4]

1. The heights of the environment and obstacles can be

ignored;

2. There exist some known obstacles distributed in the

environment both the environment and the obstacles have environment, both the environment and the obstacles have

a polygonal shape;

I d t id i th t l t th b t l 3. In order to avoid a moving path too close to the obstacles,

the boundaries of every obstacle can be expanded.





RealOb t l

F MAKLINK li

Obstacle

Grown Obstacle

Free MAKLINK line:

1) Either its two end points are two vertices on two different grown obstacles or one point is a vertex of different grown obstacles or one point is a vertex of a grown obstacle and the other is located on a boundary of the environment;


2) Every free MAKLINK line cannot intersect any of the grown obstacles. boundary


Step 1: MAKLINK-based Free Space Model [11,5]


1. Find all the lines that connect one of the corners that belong to a

◊ Constructing MAKLINK graph

polygonal obstacle, with all the other obstacles’ corners including the corners of the current obstacle;

S


T




2. Delete the redundant free links to make every free space, of which the


edges are free links, obstacle edges and boundary walls, be a convex polygon and its area be largest;

S


T




3. Find the midpoint of the remained free links and take them as the


path nodes, labeling orderly as 1, 2,…, n. The connections among the midpoints that belong to the same convex area compose a network.

S


T




v1, v2, . . . , vl are the middle points of these f MAKLINK lifree MAKLINK lines;

l is total number of the f li free MAKLINK lines on a MAKLINK graph.

l=26

v0 is S


vl+1 is TNetwork graph for free motion of robot


Step 2: Dijkstra Algorithm


vvvvvvS 1312111021

Sub-optimal path

Path length= 507 692 m

Tvvv 241716

30

Path length= 507.692 m.

This path is just a sub-optimal path because it passes only through the middle points of th f MAKLINK li


Sub-optimal path generated by Dijkstra

those free MAKLINK lines


Step 3: ACS Algorithm


1210 ... dPPPPAssume sub-optimal path generated by the Dijkstra algorithm is

1210 d

These path nodes lie on the middle points of the relevant free MAKLINK lines Now we need to adjust and optimize their MAKLINK lines. Now, we need to adjust and optimize their locations on their corresponding free MAKLINK lines.

dihhPPPP iiiiii ,...,2,1 ],1,0[ ,)( 121

midpoint502/)( 0 1

iii

hPPPhPP


Path Coding Method 1

midpoint 5.0 2/)(

2

21

iii

iiii

hPPhPPP




)}()({d

hPhPlengthL

The objective function of the optimization problem will be:

)}(),({ 110

iii

ii hPhPlengthL

ACS algorithm is used to find the optimal parameter set

}{ *** hhhsuch that L has the minimum value.

},...,,{ 21 dhhh





Grid graph on which there are dx11 nodes in total.

nij is node j on line hi.

The path of an ant depart The path of an ant depart from the starting point S is

S

Tn

nnS

dj

jj

...21


Generating of nodes and moving paths




Assume that at initial time t =0

◊ Pheromone Concentration

Assume that at initial time t 0

All the nodes have the same pheromone concentration 0:

)10,...,2,1,0 ;,...,2,1()0( jdioij





◊ Transition Rule

Assume the number of ants is m.

In moving process, for an ant k, when it locates on line hi-1, it will choose a node j from the eleven nodes of the next line hi

Assume the number of ants is m.

will choose a node j from the eleven nodes of the next line hi

to move to according to the following rule:

, },])].[({[max arg

o

oiuiuAu

qqifJqqift

j





◊ Transition Rule

}])] [({[maxarg qqift

, },])].[({[max arg

o

oiuiuAu

qqifJqqift

j

where

A represents the set: {0, 1, 2, . . . , 10};

iu(t) is the pheromone concentration of node niu;





◊ Transition Rule


, },])].[({[max arg

o

oiuiuAu

qqifJqqift

j

iu represents the visibility of node niu and is computed by the following equation: 1.1 *

ijij yy

1.1j

ij

yij is the y-coordinate of node nij and y*ij are values that are

d h h d h l b h


corresponding to the path nodes on the optimal robot pathgenerated by the ACS algorithm in the previous iteration.




◊ Transition Rule


, },])].[({[max arg

o

oiuiuAu

qqifJqqift

j

is an adjustable parameter which controls the relative importance of visibility iu versus pheromone concentration

( ) iu(t);

q is a random variable uniformly distributed over [0, 1]; q0 is a


tunable parameter (0q0 1);




◊ Transition Rule


, },])].[({[max arg

o

oiuiuAu

qqifJqqift

j

J is a node which is selected according to the following probability formula and “Roulette Wheel Selection Method”

10

])] [([

])].[([)(

iJiJkiJ

t

ttP


0

])].[([

iwiw t




◊ Pheromone Update: After Each Iteration

)()()1()( ttt )(.)().1()( ttt ijijij

10

L

tij1)(L

where L+ is the length of robot path corresponding to the best ant tour.


b




◊ Pheromone Update: After passing through a node nij

tt )()1()( oijij tt .)().1()(

When a node is visited several times by ants, repeatedly applying the local updating rule will make the pheromone level of this node diminish.

This has the effect of making the visited nodes less and less attractive to the ants, which indirectly favors the exploration of not yet visited nodes


exploration of not yet visited nodes.


Results


ACS Algorithm

Real-coded GA

Average CPU 0 00059 0 00067Average CPU time per

iteration (sec.)

0. 00059 0. 00067

Average number 175 912of iterations needed for

convergence

Average CPU 0.1033 0.6110Average CPU time needed for

obtaining optimal solution

(sec.)

0.1033 0.6110


(sec.)

SI in Traditional Robotics• PSO-based Motion Planning [5]

Sub-optimal path from Dijkstra algorithm is

1210 ... dPPPP

Th h d li h iddl i f h l f These path nodes lie on the middle points of the relevant free MAKLINK lines. Location adjustment:

dihhPPPP iiiiii ,...,2,1 ],1,0[ ,)( 121

0 hPP

1 midpoint 5.0 2/)(

0

2

21

1

iii

iiii

iii

hPPhPPP

hPP


Path Coding Method2 iii


Each particle Xi is constructed as:

• PSO-based Motion Planning [5]

i

),...,( 21 di hhhX )( ii hP

The fitness value of each particle is:

d

Euclidian Distance

)}(),({)( 110

iii

iii hPhPlengthXf)( 11 ii hP

The smaller the fitness value is, the better the solution is.



1. Initialize particles at random, and set pBest= Xi;


i

2. Calculate each particle’s fitness value according to equation

d

)}(),({)( 110

ii

d

iiii hPhPlengthXf

and label the particle with the minimum fitness value as gBest;



3. For k1=1 to k1max do {


4. For each particle Xi do {

5 Update v and x according to the following equations:5. Update vi and xi according to the following equations:

)]()([() )]()([())()1(

2

1

kxkgBestrandckxkpBestrandckvkv

i

iiii

6. Calculate the fitness according to equation

,1 ),1()()1( nikvkxkx iii

7 Update gBest and pBest ;

)}(),({)( 110

ii

d

iiii hPhPlengthXf


7. Update gBest and pBesti ;

8. If ||v|| , terminate ;}

SI in Traditional Robotics• PSO-based Motion Planning [5]


Outline


• Introduction









SI in Swarm Robotics• Multirobot Control [12]

• Collective Robotic Search (CRS) [13]( ) [ 3]

• Odor-source Localization [14,15]

• Mobile Sensor Deployment [16]

• Learning [17]

• Communication Relay [18]

• Group Behavior [19]



Unintelligent carts are commonly found in large airports. Travelers pick up carts at designated points and leave them in arbitrary places. It is a considerable task to re-collect them.

It is, therefore, desirable that intelligent carts (intelligent robots) , , g ( g )draw themselves together automatically.



Objectives

Using mobile software agents to locate robots scattered in a field, e.g. an airport, and make them autonomously determine their moving behaviors by using an ACO-based clustering algorithm.



Assumptions

- Each robot has a function for collision avoidance;

- Each robot has a function to sense RFID embedded in the floor carpet to detect its precise coordinate in the field.


A team of mobile robots work under control of mobile agents RFID under a carpet tile


Quasi Optimal Robots Collection

Step 1:

One mobile agent issued from the host computer visits scattered robots one by one and collects the positions of them.

Mobile Agent

AssemblyiPoint Assembly

Point

IntelligentCart

HostComputer


AssemblyPoint



Step 2:

Another agent called the simulation agent, performs ACC algorithm and produces the quasi optimal gathering positions for the mobile robots. The simulation agent is a static agentthat resides in the host computerthat resides in the host computer.

Assemblyi

HostComputer

Point AssemblyPoint

IntelligentCartSimulation

Agent


AssemblyPoint

AgentACO-based Clustering



Step 3:

A number of mobile agents are issued from the host computer. One mobile agent migrates to a designated mobile robot, and drives the robot to the assigned quasi optimal position that is calculated in step 2position that is calculated in step 2.

Assemblyi

Mobile Agents

HostComputer

Point AssemblyPoint

IntelligentCart


AssemblyPoint


ACO-based Clustering

- More objects are clustered in a place where strong pheromone sensed.

- When the artificial ant finds a cluster with certain number of objects, it tends to avoid picking up an object from the cluster. This number can be updated later.

- If the artificial ant cannot find any cluster with certain strength of pheromone, it just continues a random walk.




Start

Have anbj t

yes noobject

Pheromone Random

Picking up or not unlocked object is probabilistically determined using the walk walk

Empty spaced t t d?

objectd t t d?

nono

determined using the formula:

*)( klp detected? detected?

Put object Catch object

yes yes100)(1)( klppf

p: density of pheromone

Satisfiedrequirement?

no

p: density of pheromone=number of adjacent objects.Thus, when an object is


requirement?

End

yescompletely surrounded byother objects, p is the max. value=9



100*)(1)( klppf

k: constant value

Authors selected k= 13 in order to prevent any object surrounded Authors selected k 13 in order to prevent any object surrounded by other eight objects be picked up.

13*)08( (never pick it up).004.004.11100

13*)08(1)(

pf




100*)(1)( klppf

l: constant value to make an object be locked.

l = zero (not locked).

If c=# of clusters & o=# of objects

37and3163 and 32

lpoclpoc

Any objects meet these conditions are locked This


19 37 and 31

lplpoc

conditions are locked. This lock process prevents artificial ants remove objects from growing clusters.

SI in Swarm RoboticsStart

• Multirobot Control [12]


Start

Have anobject

yesobject

Pheromonelk

In “pheromone walk” state, anartificial ant tends probabilistically move toward a place it senses the walk

Empty spacedetected?

no

move toward a place it senses the strongest pheromone. The probability that the artificial ant takes a certain di i i / h i h h detected?

Put object

yesdirection is n/10, where n is the strength of the sensed pheromone of that direction.


no


equ e e t?

End

yes




Start

Have anobject

yesobject

Pheromonelk

An artificial ant carrying an object determines whether to put the carrying object or to continue to carry This walk


no

object or to continue to carry. This decision is made based on the formula:

*)( kppf detected?

Put object

yes100)( ppf

The more it senses strong pheromone, h d h


no

the more it tends to put the carrying object.


equ e e t?

End

yesThe probability f(p)=1 (must put it down).




Start

Have anobject

yesobject

Pheromonelk

Termination Condition:

h b f l d l i walk


no

The number of resulted clusters is less than ten, and

detected?

Put object

yesall the clusters have more or equal to three objects.


no


equ e e t?

End

yes


Results

Airport Ant Colony Clustering Specified Position Clustering

Airport Field (Objects: 400, Ant Agent: 100)

po t field

t Co o y C uste g Spec ed os t o C uste gCost Ave Clust Cost Ave Clust

1 4822 12.05 1 11999 29.99 42 3173 7.93 6 12069 30.17 43 3648 9.12 4 12299 30.74 44 3803 9.51 3 12288 30.72 44 3803 9.51 3 12288 30.72 45 4330 10.82 5 1215 30.31 4


Clust represents the number of clusters, andAve represents the average distance of all the objects moved.

SI in Swarm Robotics• Collective Robotic Search (CRS) [13]

A group of unmanned mobile robots are searching for a specified target in a high risk environment.



Assumptions

- A number of robots/particles are randomly dropped into a specified area and flown through the search space with one new position calculated for each particle per iteration;

- The coordinates of the target are known and the robots use a fitness function, in this case the Euclidean distance of the individual robots relative to the target, to analyze the status

f th i t itiof their current position;

- Obstacle’s boundary coordinates are known.



PSO-CRS Algorithm

Step 1:

A population of robots is A population of robots is initialized in the search environment containing a environment containing a target and an obstacle, with random positions, pvelocities, personal best positions (pid), and global


best position (pgd).


PSO-CRS Algorithm

Step 2:

The fitness value, Euclidean distance from the robot to the target, is determined for each robot where T and Teach robot where Tx and Tyare the targets coordinates and Px and Py are the

t di t f th current coordinates of the individual robot.

22 )()( PTPTfitness


)()( yyxx PTPTfitness


PSO-CRS Algorithm

Step 3:

The robot’s fitness is compared with its previous best fitness(pBestid) for every iteration to determine the next possible coordinate position for each robot in the search environment. The next possible velocity and position of each robot are The next possible velocity and position of each robot are determined according to the following equations:

)]()([())()1( 1 kxkpBestrandckvkv idididid

)1()()1()]()([()

)]()([())()1(

2

1

kvkxkxkxkgBestrandc

kxkpBestrandckvkv

idd

idididid


)1()()1( kvkxkx ididid


PSO-CRS Algorithm

Step 4:

If the next possible position xid(k+1) resides within the If the next possible position xid(k+1) resides within the obstacle space, the obstacle avoidance mechanism is employed,

otherwise the robot moves to this new position.



PSO-CRS Algorithm

Obstacle avoidance mechanism:

),,( nextverthoriz )points,,_,_,_,_(

),,(dircenterycenterxstartystartxarc

dir: CW – CCWpoints=4

nearest corner of the obstacle

The new position of the particle is set at the second point in the arc


arc.


PSO-CRS Algorithm

Step 5:

The pBestid with the best fitness for the entire swarm isiddetermined and the global best coordinate location, gBestd, isupdated with this pBestid.

Step 6:

Until convergence is reached, repeat steps.



Simulation Results

Search space: 20 by 20 units.

Vmax = 0.5 units.

# of robots = 10# of robots 10

# of targets = 1

# of obstacles=1



Simulation Results

Robots’ pathways to the target location R b t ’ th t th t t l ti


Robots pathways to the target location. Two robots collide into the obstacle.

Robots’ pathways to the target location with obstacle avoidance mechanism.


Simulation Results

Average Number of Iterations taken by the Swarm with standard deviations over 20 trails

Obstacle Type

PSO Parameters 1-c1=0.5,c2=2, w=0.6

PSO Parameters 2-c1=2,c2=2, w=0.6

Square Average±std 89 43±9 86 105 6±10 68Square Average±std 89.43±9.86 105.6±10.68

Maximum 104 128

Minimum 66 85

Circle Average±std 76.75±8.75 106.1±11.61

Maximum 95 128


Minimum 64 78

Outline


• Introduction









Concluding Remarks• Swarm intelligence techniques such as Ant Colony Optimization

(ACO) and Particle Swarm Optimization (PSO) have shown to be an effective global optimization algorithms in traditional and swam robotics.

• ACO and PSO have been successfully applied in solving problems such as motion planning, gait optimization, group behavior, control, learning, odor-source localization, collective robotic search and mobile sensor deployment, to mention a few.


References[1] E. Sahin and A. Winfield, “Special issue on swarm robotics,” Swarm Intelligence, 2: 69–72, Springer Science, 2008.

[2] Pasteels et al. From Individual to Collective Behavior in Social Insects. Pages 155-175, 1987.

[3] Richard Vaughan, “Massively multi-robot simulation in stage,” Swarm Intelligence 2: 189–208, 2008.3 g , y g , g 9 ,

[4] T. Guan-Zheng, H. Huan and S. Aaron, "Ant Colony System Algorithm for Real-Time Globally Optimal Path Planning of Mobile Robots", Acta Automatica Sinica, 33(3), p. 279-285, March 2007.

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