Development of Control Algorithm and a Simulation Tool for Self-Assembly of Microsystems Based on Swarm Technology

Rochester Institute of Technology

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2005

Development of Control Algorithm and a

Simulation Tool for Self-Assembly of Microsystems

Based on Swarm Technology

Siddharth Mestry

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DEVELOPMENT OFCONTROL ALGORITHMAND A SIMULATION TOOL FOR

SELF-ASSEMBLYOF MICROSYSTEMS BASED ON SWARMTECHNOLOGY

A Thesis

Submittedinpartialfulfillmentofthe

Requirements forthedegreeof

MasterofScience in Industrial_Engineering

inthe

DepartmentofIndustrial & SystemsEngineering

Rochester Instituteof_Technology

by

Siddharth_Mestry

DEP ARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING

KATE GLEASON COLLEGE OF ENGINEERING

ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

CERTIFICATE OF APPROVAL

M.S. DEGREE THESIS

The M.S. Degree Thesis of Siddharth Mestry

has been examined and approved by the

thesis committee as satisfactory for the

thesis requirement for the

Master of Science degree

Approved by:

James B. Taylor

Dr. James B. Taylor, Thesis Advisor

Title of thesis or dissertation:

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I understand that I must submit a print copy of my thesis or dissertation to the RIT Archives, per current RIT guidelines for the completion of my degree. I hereby grant to the Rochester Institute of Technology and its agents the non-exclusive license to archive and make accessible my thesis or dissertation in whole or in part in all forms of media in perpetuity. I retain all other ownership rights to the copyright of the thesis or dissertation. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.

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-ABSTRACT

"Chunxel"

Technologyis anovel conceptof_{constructing 3-dimensional}structures _using a

group of intelligent, _autonomous, and _cooperating micro robots. Chunxels are small robotic_modules, cubicalin_shape, which areimmersedin atank_containing a viscousfluid.

The chunxels arepropelled_bythe electromagnetic forces created_bypassing directcurrent

throughasetoflarge coils placedoneachface ofthe tankand small coils embeddedinthe

micro device. The chunxels follow a set of rules which mimic a swarmbehavior and

self-assemble inthe liquidtoform a3-D structure. Swarmbehavior is adynamicproblem and

in order to ensure the completion of the task in reasonable time _by the swarm it is

necessary to have a robust control algorithm and a navigation strategy. The objective of

this research was to _develop such a control algorithm which when followedwould assure

the successful completion ofthe taskgivento thechunxels.Also inordertounderstandthe dynamics ofthe swarm and _verify the control _{strategy it} was important to simulate this

I thankDr. James B. _{Taylor, my}thesis _advisor, for his immensesupport _duringthe course

ofthisresearch. Itwas a great experience _workingunderhim. He hasbeen a great_mentor,

and aperson I will always look_upto forthe rest of_my life. Thank youforyourpatience

andfor yourguidance not _onlyrelatedto thisresearchbut alsoforthe smallbutimportant

thingsyouhavetaughtmeabout life.

Iwould _especiallyliketo thankProf. Paul H. Stiebitzfor_giving me an_opportunitytowork

onthe chunxel project.His enthusiasm and his _timelyadvice helped me tomake progress

inthis_thesis, at crucial moments.

Thanks to Dr. Andres Carrano for_keeping immense faith in me atthe start of_{my Masters}

Degree.

ThankstoDr. Alejandro Engel for his_{help during}the initialstage ofthis thesis.

FinallyI wantto thank to_mywife, and _myparentsfortheirencouragement and supportin

CONTENTS

1. INTRODUCTION 1

2. BACKGROUND ₃

3. TECHNICAL DETAILS OF THE CHUNXEL DEVICE 6

3.1. Externalcoils_driving sequence 7

3.2. _{Robot assembly} andconstruction 8

3.3. Results ofInitial Trial ₉

4. STATEMENT OF PROBLEM 10

5. LITERATURE REVIEW 13

6. METHODOLOGY 18

6.1. Phase 1: Developmentof aTwo Dimensional Simulation Tool 20

6.1.1. Javaand2D Simulation Tool 20

6.1.2. Javacoordinate system&directionalconventions 21

6.1.3. Basic Control Algorithm 22

6.1.4. Collision Detection 25

6.1.5. Proportional Motion 28

6.2. Phase2: Demonstration ofSynergistic behavior using 2-D Simulation Tool 31

6.2. 1. Synergistic behavioralgorithm 3 1

6.2.2. Searchpath algorithm 34

6.2.3. Shortcomingsofthe search path algorithm 37

6.3. Phase 3: Developmentof aControl Algorithm and a3-D Simulation Tool ₃₈

6.3.1. Introductionto Java3D 39

6.3.2. Forceequations 39

6.3.3. Animationanddisplacementofthechunxel ₄₅

6.3.4. Proportional FeedbackMotion 47

6.3.5. _Coasting 48

6.3.6. User interface 49

6.4. Phase 4: Verification of3-D Simulation Tool 51

6.4.4.

Coasting

Test ₅₆

6.4.5. Cos-Factor Test ₅₇

6.4.6. Proportional Test ₅₈

6.5. Phase 5:Experimentation and_Optimization

usingthe3-D Simulation Tool 62

6.5.1. Designof_{Experiments: Experiment 1 63}

6.5.2. Analysis I 64

6.5.3. Designof_{Experiments: Experiment2 66}

6.5.4. AnalysisII ₆₆

7. CONCLUSIONS & FUTURE RESEARCH 69

7.1. Results & Conclusion 69

7.2. Future Research & Recommendations 70

REFERENCES 72

APPENDICES 76

Appendix A: 2D Simulation Flowchart 76

Appendix B: Screenshotof3D Simulation Tool 81

AppendixC: DateofForce Test 82

Appendix D: Screenshots ofCos Factor Test 92

Appendix E: DataofProportional Feedback Motion Test 93

Appendix F: Experiment 1 Data & Results 118

List_ofTables

Table 1: 2DArrayfor storing _{Chunxel InformationinJava 24}

Table2: Rules for Search PathAlgorithm 37

Table3: FactorsandLevels for Experiment _{I 63}

Table 4: FactorsandLevels forExperiment2 66

Table5: Optimum Values_oftheFactors from Response Optimizer 67

Table 6: Predicted Values for Response Variables 67

Table 7: 7l

RunConfiguration 67

Table8: Optimum Configuration 70

Table 9: Force Testdata 82

Table 10: Proportional Feedback Motion Test Data (without_PFM) 93

Table 11: Proportional Feedback Motion Test Data (with_PFM) 102

Table 12: 4 Factor-3 level, Full Factorial Design-Experiment 1 118

Figure 1: Chunxel Device

(Prototype)

4

Figure2: CurrentGeneration Chunxels 5

Figure3: Control_DrivingSequence 7

Figure4: _{Timing Delay} 8

Figure 5: Schematic Diagram_ofthe Chunxel 8

Figure 6: Javacoordinate system & ChunxelDimensions inJava 2D 22

Figure 7:_BoundingBoxCollision Detection 27

Figure 8: Proportional Feedback Motionin2DSimulation Tool 29

Figure9: Block Diagramfor General_{flow of2D}SimulationProgram 30

Figure 10: Figure 11 Figure 12: Figure 13: Figure 14: Figure 15: Figure 16:

Figure 1 7.

Figure 18. Figure 19: Figure 20: Figure 21: Figure 22: Figure 23: Figure 24: Figure 25: Figure 26. Figure 27. Figure 28: Figure 29:

2DSimulation ToolScreenshots 32

Dead Chunxel Retrievalfrom nearthe Tank Walls 33

Dead Chunxel Retrievalfromnearthe_{Base of}the Tank 33

MovingChunxel Trappedin One Direction 34

MovingChunxel Trappedin Two Directions 34

Sub-routineto Circumventan Obstaclein Y-axis_{(Step 1)} 35

Sub-routineto Circumventan Obstaclein Y-axis_{(Step 2)} 35

Sub-routineto Circumventan Obstacle in X-axis(Step 1) 36

Sub-routine to Circumventan ObstacleinX-axis _{(Step 2)} 36

Java 3D Co-ordinate System 39

Calculation ofMagnetic Force ofAttraction 41

Calculation of Cosfactor 41

Forces actingona_{Body Completely}Submerged inaLiquid 44

Relationshipof Time ON ofInternal CoilversusDistancefromthe Target 48 Block Diagram_showingthe_Start-upOptionsfor3D Simulation Tool 50

Propulsion Forcev/sDistance fromtheCoil 54

Velocityv/sDistance from thecoil 55

Distance fromthe Coilv/sTime 56

Distance fromthe Coilv/sTime (withinfluence_ofCoasting) 57

Time ONfortheInternal CoilwithoutProportionalFeedbackMotion 60

Figure 31: Oscillations_oftheChunxelwith_{ProportionalFeedbackMotion OFF} 61 Figure 32: Oscillations_ofthe ChunxelwithProportionalFeedback Motion ON 61

Figure 33: MainEffects Plotfor Response Time 64

Figure34: MainEffectsPlotfor Std. Deviation_{(Oscillations)} 65

Figure35: 3DSimulation ToolScreenshot 81

Figure36:Screenshots _ofthe Visual Observation Testfor Cos Factor Effect 92

Equation 1: Magnetic ForceofAttraction 40

Equation2: Cos Factor Equation 42

Equation3: _DragForce 42

Equation4: Effective Propulsion Force 43

Equation5: BuoyantForce 44

Equation6:Net Forceon aSubmerged_Body 44

Equation 7: Net Force on aSubmerged_{Bodymoving in}theDownward Direction 45

Equation8: NetForce on aSubmerged_{Body Moving}inthe Upward Direction 45

Equation 9: _{Force acting}on a_bodyinmotion 45

Equation 10:_{Acceleration of}the Chunxel 45

Equation 11: _Velocityofthe Chunxel 46

1. INTRODUCTION

Theneedto_quicklyconstruct_{three-dimensional}colordisplays and objectsfrom computer-generated designs is extensive. Designers _using personal computers or workstations

commonly emulate three-dimensional objects _{by using} computer graphics software to

create sophisticated _shading and_coloring schemes. Rapid_Prototyping technologies canbe employed to construct permanent three-dimensional objects _{by building} shapes from specialized materials. _{Alternatively,} specialized _imaging techniques can _quickly produce color stereoscopic images that are quite _realistic, but these have no solid substance and often require a special _viewingapparatus. The combination oftwo _emerging technologies, swarms _technology and Microsystems _technology, offers a unique _{opportunity to quickly} create color three-dimensional objects and displays. "Construction of three dimensional objects and displays _using swarms of intelligent microsystems"

is a concept for a new

device based on_emerging swarm and micro-systemtechnologies. This concept is referred

asthe"Chunxel Technology".

Swarm _{technology, following} the social insect metaphor is concerned with the collective behavior of large number of intelligent autonomous agents, with limited capability to perceive, reason and act, that are capable of_performing sophisticated _tasks, such as food harvesting and nest _building (Stiebitz P.H., Carrano A.L., Alejandro B.E., 2002). Swarm

research attempts to understand and mimic thisbehaviorof social insectsto come _upwith alternative robotic solutions. Swarm engineering requires generation of swarm conditions and fabrication of a set ofbehaviors that satisfy the given swarm condition. This swarm

condition, when_satisfied, will guidethe generationof a swarm ofagents,which is capable of_carrying outthe desiredactions. No specific method is formulated for the generation of swarm condition anditis largelyproblemdependent.

Microsystems technologies are those focused on the development of_highly integrated

mechanical, electrical, optical, chemical, biological and _computing systems whose

2002).

Integratingtheabove twotechnologiesgives riseto thechunxel _technologythatconsistsof intelligent, autonomous, cooperating micro _robots, known as _chunxels, and a _display housing,whichisacubicaltank_containingaliquidcarrier mediainwhichthechunxels are

neutrally buoyant (Stiebitz P.H., Carrano _A.L., Alejandro _B.E., 2002). The chunxels can self-propel and selfnavigate through a viscous fluid. Within this environment, chunxels will be able to self-assemble to form different pre-defined three-dimensional shapes

(Stiebitz_P.H.,Carrano_A.L.,Alejandro _B.E.,2002).

This _technology has numerous applications in the areas of three-dimensional real-time displays, rapid _prototyping, entertainment special _effects, games and toys. Other uses of the chunxels _technology are in production of three-dimensional maps for military or exhibition purposes and 3D organs for medical _training (Stiebitz _P.H., Carrano _A.L., Alejandro _B.E., 2002).

Variouspossible fields of applicationhave beenmentionedforthisinvention. The chunxel technology has been conceptualized with rapid _{prototyping in} mind. CAD files would be transferred to a control _{station, sending information}tochunxels. The chunxels wouldthen assembleintoa prototype oftheitem described inthe CADfiles.

An as yet unexplored area for chunxel research and application is that chunxels can be usednot _onlyto generate static structuresbut also canbe usedto showdynamic behavior.

This dynamic behavior can be used in animating displays for advertising and also in entertainment industry. Another serious application of dynamic chunxel behavior is

2. BACKGROUND

In August 2001, an _{invention disclosure entitled} "

Construction of three dimensional

objects and displays _using swarms of_intelligent Microsystems" _{was filed} withRochester Institute ofTechnology's office of_Grants, contracts and Intellectual Property. The work for _{this research,} which was referredto as "Chunxel Technology"

was _{already initiated in}

summer of_{2001 utilizing Kate Gleason College ofEngineering (KGCOE) research funds}

granted to the _Laboratory for Autonomous and Cooperative Microsystems (LACOMS). LACOMS is a _{multi-disciplinary} research effort focused on the development and integrationof swarmtechnologieswithMicrosystemstechnologies.

Thewhole chunxel systemwillconsistofthe_followingmajor components:

A system of_{intelligent, mobile, partially}autonomous Microsystems (referredto as Chunxels)thatcan altertheircolor and self assembleintopre-defineddesired

three-dimensional color shapes.

A _{display housing containing} liquid carrier media that provides _buoyancy for the

chunxels.

Softwarethat translates standardCADfilesintochunxel_assemblyinstructions.

Controlsoftwarethatco-ordinatesthe_assemblyof chunxels.

Acommunicationsystemthatallows a computerto send and receiveinformationto

andfromthechunxels.

Ameans to transfer _energyto the chunxels (Stiebitz_P.H., Carrano_A.L., Alejandro

B.E.,2002).

Chunxels are propelled by forces created _by magnetic fields due to a set of large coils placed inthe environment and poweredbydirect current, and small coils embeddedinthe device also powered by direct current. Figure 1 shows the chunxeldevice prototype _along

with a chunxel placed in the center of the tank. The _{display housing} of the current prototype is a 6-inch cubical tank made of acrylic walls and surrounded by six external

[image:16.526.139.397.158.353.2]

proportionalto the _{radius, current,}andnumberofwindings oftheexternal_{coils, the radius,} current and number ofwindings ofthe internal_coil,the distance betweenthe two coils and the_permeabilityoftheliquidmedium.

Figure 1: Chunxel Device_(Prototype)

The development of _working prototypes is envisioned to be in four stages. The first

generation chunxels are 25mm cubes. This chunxel has anovel six-sided shape with three out-dented and three in-dented surfaces that have been developed to promote the self-alignment ofthe groups (Stiebitz P.H. 2002). Eachside ofthe firstgeneration chunxels is manufactured _{by injection molding} such that size identical pieces could be assembled in

any combination ofin-dents and out-dents. Figure 2 shows the current generation 25 mm chunxels. Each chunxel consists of a means for position _sensing, a means for _attaching itselfto other _chunxels, and a communication system capable of _sending and _receiving informationfrom thesystem control and a_computing system(Stiebitz_P.H., Carrano _A.L.,

Alejandro _B.E., 2002). The second generationwill be 12mm cubes also manufactured _by

conventional _machining and _{molding techniques,} while the third generation will begin

making the transition to MEMS (Micro Electro Mechanical

Systems)

fabrication

techniques _reducing the size to 4 mm and _{finally shrinking} it to 1mm in the fourth

Figure 2:CurrentGenerationChunxels

This section presents the hardware and the control details of the chunxel device. The

understandingofthehardware details ofthe chunxel andthe control system usedtopropel thechunxels inthe fluidenvironmentwill_helpin

discussing

thescope ofthisresearch.

Eachchunxel hastwomajoroperational modes as follows:

The propulsionmode: theexternal andinternal coilswillbeused aselectromagnets; and

The positioningmode:theexternal coilswillbeused as a generator of magnetic field.

Propulsion:

For thepropulsion _purpose, a48V DC power _{supply is} used to generate a magnetic force

and drive the coil. Each external coil will have an intermittent DC signal. The chunxel

could then use one ofthe internal coils as an electromagnet to move _along the magnetic

field created _by the external coil. Power from the front or back coil gives a movement

along the x-direction, power from the west or east coil gives a _ymovement and north and south a z movement.Thepower_{supply is}a48 VDCpower_{supply(Yvanoff,} Marie 2002).

Positioning:

Forthe_positioningpurpose, anACpower_{supply is} usedto drivethecoil.This second_way to power the external coils will generate a time varying magnetic field inside the _tank, whichinduces an emfintheinternalchunxel coils.Asthischunxel comes closerto thecoil powered, the emfinduced in the three internal coils increases. These coils are orthogonal and representthe_X, YandZ-axis ofthechunxel(Yvanoff,Marie2002).

Communications betweena system controller andthe chunxels is achieved_bythe _pulsing the external coils in a structured fashion. By _{counting the} induced emf pulses on the

chunxel_coil, a series of pulses canbe decodedto extract a message transmittedby ahost

3.1. External coils

driving

_sequence

Todrivethe six external _coils,anAC andDC sequenceis _used,theAC forthe_positioning

sensingandthe _{DC for propulsion,} as_{described intheprevious}

section. TheDC energizes the external coils in the sequence _{West, North, Back,}

East, South, Forward. The three orthogonal coils within the chunxel are _{optionally energized in concert with the external} coils to produce thrust _sequentially in the six _{directions. In the second operational}

mode, the chunxel's spatial position is determined _{by applying} an _alternating current to the external coils_{sequentially,} and then_sensingtheinduced emfinthe chunxel coils(power is

not applied to the chunxel coil in this mode). The control

driving

sequence andthe time

delays are shownin Figure3 andFigure4_{respectively (Yvanoff,Marie 2002).}

fcfefce Portionsa^ir.s Propulsion _{Rasitien sansing} Proptfiston _{Basiiiiffl searing} Propulsion Fositcr.sosae

->

*--+> <- -*- -+- -*-

<-K S EV.'

F B VSfestI>C :: S BWF E NwthDC N S E W F E EickDC N S E WF B

Positionsensing fteputeunn _{Posttkai sensing} RrapuUior. _{PosHtun sensing} Propulsion _{P-oatior. sensing} Cemsm.

-?-- ? --

-+--* ? A-

->-*< >

<-EV.'

F E Ei-tDC N S BW F E Sooth DC N S EV.'

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< ? A ?

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KXtoS

lWms

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U 15 IS

Figure 4:_{Timing Delay}

3.2. _{Robot assembly}and construction

Inside the chunxel, two 19mmsquares of single layercircuitboardsandbatteriesconstitute

the electrical components. Oneofthebatteries is usedto drive the internalcoils when_they

are used as electromagnets. Two other batteries are used to _supply current to a micro

controller and signal amplifiers. Eachofthree indented facesofthe cube containsthe three smallinternal coils while the two out-dentedfacescontainthe circuitboards andthe small

batteries, and on the third one there is a_battery used to drive the coils. Design detail and

constructionofthechunxelsisshownin Figure 5.(Yvanoff,Marie2002)

Coil 1of3

Circuit Boardwith

components

Battery

Circuit Boardwith

components

3.3. Results ofInitial Trial

The initial trial ofthe chunxel device was conducted in March/August 2002. The goal of

this demonstrationwas fora proofofconceptforthe chunxel device. It turnedoutthat the

chunxelswere

behaving

as expected. Some ofthe observations thatwere made_duringthis

runare asfollows:

The wakeupsignal waked_upthe_chunxels;

Thechunxel_timingscheme was synchronizedwiththe _drivingsequence;

Thespeedofthechunxels

during

thepropulsion was as _expected;

Thechunxel seemedtomovearoundthe targetareabutneverstopped; and

One ofthechunxel locatednearthecorner ofthe tankspun around.

As it turned out, the concept of chunxel device was _{working properly} and provedthat it

4. STATEMENT OF PROBLEM

In chunxel _technology the behavior ofthe chunxel _{is primarily based} on the concept of

swarms. Swarm _{engineering has} two formal steps. The first involves the generation of a

swarm condition. Swarm condition is a set of rules or _behaviors, which the individual

agents in the swarm must follow in order to form a co-operative structure within the

swarm. This isa condition_which,when _satisfied, will guidethe generation of a swarm of

agents which is capable of_carrying out the desired action or actions. The second _{step in}

swarm_engineeringinvolvesthefabricationof abehavioror set ofbehaviorsthat_satisfythe

given swarm condition. Alsothe generation of swarm behavior is adynamicproblem and

in order to ensure the completion of the task in reasonable time _by the swarm, it is

imperativeto_developa robust navigation strategy.

The collective behaviors of components ina dynamic system (like a swarm_behavior) can

influence the environment and when this occurs the constraints on the components in a

system are not _fixed, and thus attempts to analyze the system, must provide an _ongoing

mutable parameterization ofthe environment(A Tutorial IntroductiontoSwarm). _Thus, in

order to understand the dynamics ofthe swarm system under a given navigation _strategy

and test the performance of the algorithm it is important to simulate this process.

Simulation is a process of _designing a computer model based on some _underlying

computational logic of a real system and _conducting experiments with this simulation

model forthepurpose ofunderstanding the behaviorofthe system and evaluatingvarious

strategies fortheoperationofthesystem.

The swarm behavior is the logic behind the motion ofthe chunxel. The intelligence given

tothe chunxel is _nothing buta set of swarm rules and behaviorinorderto decide the next

direction in whichithas to move. Butthe actual physical motion ofthe chunxelinside the

liquidmediais dependantonparameterslikethecycle_time, radius and number ofturns of

the external and internal coil and also the current carried bythese coils. It is importantto

evaluate the effect ofthese parameters on the motion ofthe chunxels inside the _display

11

showedthatthe chunxels _{continuously hunted fortheir}

pre-programmed targets. This was

believedto bedue toahighpropulsionforce control set_point,whichis proportionaltothe

radius,currentand number ofwindingsofthe external andinternal chunxel coils_(Yvanoff,

Marie 2002). In order to build a stable 3D structure it is imperative to minimize hunting.

Thephysical andeconomical limitationsofthe _{existingprototype,} and construction of new

prototypes, also makes it _necessary to

develop

a simulation _tool, which would aid in

understanding the effects of the various parameters mentioned above. This _testing of algorithms with different values for the physical parameters will _help in optimizing the

device and come_up withoptimum valuesfor allthevariables that affectthemotion ofthe

chunxel so as to reduce the _hunting effect and atthe same time reduce the time inwhich

the chunxelreachesthe target.

The basic problem that was addressed in this research was that ofbasic navigation and

motion control of the individual chunxel units based on swarm behavior. The overall

problem includedidentificationoftargetlocations forthe chunxelsto _fill,the broadcastof these target locations to the available _chunxels, selection of target location _by the

individual chunxels, movement to the target _{location using} proportional control scheme

andbroadcast_bythechunxelthat the target isoccupied.

The most innovative part ofthis research however was the dynamic behavior ofthe 3-D

structures formed. The chunxels demonstrated collective synergisticbehavior tofulfill the

swarm condition and completetasks, whichwere not possible_byindividualthechunxels.

Thustheobjectivesthathavetobe fulfilled_bythisresearch canbe summarized asbelow:

> Developmentof a2Dsimulation_tool;

> Developmentof anavigation_strategyforgenerationof2D_shapes;

> Demonstrationofsynergisticbehaviorby developinga control algorithm inthe2D

simulation_tool;

> Developmentof a3D simulation_tool;and

For _{this reason, the} scope oftheproblem _{included both static structure}

13

5. LITERATURE REVIEW

This research deals with swarms _{behavior, multi robot}

cooperation, navigation strategies,

and control algorithms for

forming

3-D structures. The creation of artificial swarms has

becomean

interesting

topicofresearchinthelast fifteenyears. Thisresearchfindsitsroots

in the seminal work of_{Rodney Brooks (Brooks R, 1986), whichadvocated the creation of}

simple robots with simple behaviors intheplace ofrobots ofcomplex abstract models and

interpreters for intelligent behavior. The method is called behavior-basedcontrol and has

become_widelyaccepted, due to the _simplicityof_{the approach, theflexibility} and potential

for generalizationto _learning and the _capability of researchers to create swarms of simple

behavior based robots capable of _carrying out _interesting behaviors. Several researchers

have proposed _interesting methods of_creating control algorithms for such simple robots,

including learning and _evolutionary algorithms _{(Harvey I., 1994),} and work continues on

bothofthese general methods.

Artificial swarm designhas thus far been _{largely along} two different lines ofdesign. The

firstofthese isthepractical approach_{(Kelly I.,}and _{KeatingD., 1996, 1998, 1998,}Mataric M., 1995, 1995a, 1997a), in which a particular task is identified and a _group of robots is

builtwith the task inmind. This work_typically contains multiple iterations ofdesignand

redesign ofthe physical robot and/or its controllerto complete the task _{(Goldberg D.,} and

Mataric _M., 1997). The second of these is the theoretical approach in which a task is

examined _{theoretically,} and a condition is derived which will yield the global goal. The

design ofthe robots is then an exercise in_obtaining robots whose real dynamics matches

the desired_dynamics, which can take one iteration. Themain difference between these is thatinthe firstapproach, an_{understanding} ofthe_underlying systemdynamics is generated

throughthe _buildingand improvementof various versions ofthe system, whilethe second

attempts to generate an understanding ofthese _dynamics, and _{subsequently build} robotic systems based onthis understanding. In this way, the second approach is more similar to

traditional methods inrobotics, in which the system dynamics are worked out before the

generation ofa robot. The use ofthis approach in swarm robotics would seem to provide

precision. Rather, they _may be seen as anextension ofthose methods to tasks_requiring a

smaller degree of individual precision.Many _{studies have been undertaken}

using the

practical approach to swarm construction.

Among

these are studies _{investigating}

navigation and exploration _tasks,

rudimentary construction _tasks, task allocation studies,

and communicationstudies.

The closestknown research is reported

by

_{Mitre Corporation(www.jisan.org) in}the area

of_{self-assembly} ofMicrosystems and Nanosystems. The objective ofthe research was to

determine ifalarge number of mobile micro_{robots, the} sizeof a grain of a _salt,could

self-assemble under distributed control in order to fabricate more complex structures (qtd. in

StiebitzP.H., Carrano _A.L., Alejandro _B.E., 2002). The Intelligent Autonomous Systems

Engineering Laboratory atthe _University ofWest England has undertaken studies similar

to MITRE. O.E. Holland and C.R. Melhuish discuss _swarming simulations conducted

under the _following minimalist assumptions: a beacon in the environment transmits an

omni directional signal, agents have the _ability to sense that a signal is above a threshold

but cannot discern _direction, agents are propelled _by repeated _impulses, the direction of

motion is in the direction of stronger signal except for a small random perturbations and

the environment consists of a circular two dimensional space. Simulations of Multiple

types offield attenuation, noise and signal _following rules produced conditions in which

agents_{very efficiently}convergetothe signal _source,even whenthe source is moving (qtd.

in Stiebitz_P.H., Carrano_A.L.,AlejandroB.E.,2002).

Murataet aldiscussthe developmentofidenticalrobots capable of_formingarbitrary,large

scale, complex, three-dimensional forms and dynamic mechanical structures. Their

approach utilized cubic shells couples by _rotating mechanical joints. These _couplings,

along withthe imbeddedintelligence, allowthe cubes to climb over one anotherto create

new forms (qtd. in Stiebitz P.H., Carrano A.L., Alejandro B.E., 2002). Chirikhjian et al

have also examined the problem of self-reconfiguration of collection of identical

mechatronic modular robots that have the _{ability to connect,} disconnect and climb over adjacent modules without the outside help (qtd. in StiebitzP.H., Carrano A.L., Alejandro

15

Plane"

KazuoHosokawa et al havepresented anovel conceptof_{self-organizing}collective

robots with morphogenesis in a _{vertical plane. It is potentially applicable to autonomous} mobile robots. For physical reconfiguration of a swarm of robots against _gravity, new typesofmechanismsand_{control strategies are proposed anddemonstrated.}

Coates et al in their paper "The Use of Cellular Automata to Explore Bottom _Up Architecture Rules," discuss the use of three-dimensional cellular automata to construct three-dimensional shapes. Cellular automata are entities that have been given a set of internal and external rules _by which _they form spatial relationships with other cellular

automata. In _{this way,} it is thought possible to provide each _entity with sufficient local information to guide its participation in the construction of the overall form (qtd. in Stiebitz _P.H., Carrano _A.L., Alejandro _B.E., 2002). Antonio Sgorbissa and Ronald C.

Arkin have showed how robots _navigating within an unknown environment with local

communication capabilities can cooperate _{by helping} each other to achieve their own goals. Cohenreports ona_mapping andnavigationtaskinwhich swarm of robots spreads itselfina_maze, and _collectivelymapsthe terrain. _{The map is detailed} enoughto allow an

agentto travelfrom a pointinthe_mapto_anyother pointinthe _{map in}a minimum amount of_time, while _using minimal individual processing, and _taking advantage of an elegant

communication scheme(CohenW., 1996).

There are other _{publications,} which propose different control strategies for problem

specific tasks to be solved by swarm robotics. G. Dudek et al present _taxonomy to the different ways in which a collection of autonomous robotic agents can be structured (Dudek _G., 1993). Gage details the design of a multiple robot system for mine detection.

This work focuses on _illustrating the benefits in time and correctness ofcoordinated and

communicating multiple robot detection schemes. The use of communication and coordination is found to be a serious advantage over the lack of _it, in terms both of

detection speed, correctness, and cost/success ratio (Gage D., 1995). A method based on

approachisthatthese equations_{maybe completely}

solved, yieldingthe_stationary states of

the system,andthe modes ofevolutionofthe system. As

long

asthe robots are capable of

following the dynamic equations of_motion, the methodwill provide the desiredbehavior (Spears_W.,andGordon _D., 1999).

The most _interesting and _closely related research is Touchable User Interface _Using Self Movable Robotic Modules. This device (Patent: _6,243,622) consists of a touchable user interface _including multiple robotic modules that can "walk" over each other to allow

reconfigurationofthe interface.Eachmodule_preferablyincludesmotivedevicesas well as

connective devices communication between the modules and a control unit that sends

commands to the _{interface, thereby enabling} its reconfiguration. Space filling robotic polyhedral modules (Patent: _6,233,503) consists of a movable robotic module _including a framework _defining a set of vertex elements, a set of edge _elements, or a set of face

elements, with the _{framework substantially} shapedto permitface centered cubic packing. Each module includes a pivot mechanism on its framework to permit rotation of the

framework with respect to other movable robotic modules. A power unit supplies

operational powerto each_{module, the}power_beingused forrotation of_{the module,} sensor and/or a control unit connected to the pivot mechanism and/or the power unit to control

rotationoftheframework (Yim etal).

There is much researchdone inthe area of swarms andMicrosystems as discussed above,

butthere are no known disclosuresofthe system ofthe type being studied and researched inthis thesis. The major source ofinformationcomes fromthevariouspapers,projects and

experiments conducted on chunxel _technology itself. In "N-Body Simulations of Microsystems Self-Assembly" a paper directly related to the chunxel _project, J.C. Tillet

and P.H. Stiebitz have discussed the equations ofmotion, the transition between various

stages of motion, and an efficient method of _detecting collisions _among spherical

Microsystems, which are capable ofself-navigationand self-propulsionin3-D space. This

paper also discusses the various control strategies viz. Directed, Cooperative and

Autonomous. This thesis is a part of an extension of this paper and compliments the

17

Stiebitz P.H. also foundthat the collision avoidance and post collision _recovery plays an

extremelycritical roleinthe _abilityofthepopulationto_efficiently self-assemble. Itisalso stated that because of the limited _computing power of _{the chunxels,} development of parsimonious control algorithms is required for their navigation and self-assembly. In

order to improve the _probability of _completing the 3-Dimensional _geometry in a

This research _{dealt primarily with the}

development of a robust control algorithm for the chunxels to _successfully complete _{the three dimensional geometry. As}

earlier stated the control algorithm was verified _using a simulation tool. The development of a control algorithm and the simulationtool was a simultaneous and iterative process. The research was divided into five_{phases. Thisdistribution}

ofworkhelped_{in clearlydefining}the goals and objectives for each phase and a timeline within which the research was to be

completed.

Thefivephasesforthecompletionoftheresearchare asfollows:

Phase 1 - Development

of aTwo_{Dimensional SimulationTool:}

This was the first _step towards

building

a full fledge 3-D simulation tool for the chunxel

project. The motionofthe chunxels intwo axes viz. X andYwas studied with the_help of this program. The program was developed _{using Java 2 SDK. The basic swarm rule of}

occupying the nearest available target was incorporated in this _program, which the chunxels wouldfollowthus

beginning

theprocess of_developing a control algorithm _using swarmsbehavior. Thisphase also tookinto accountthe physical detailsofthe system like collision detectionand minimal _programmingeffort of_avoidingthe collisionswas used so thatafairrepresentation oftheactual system couldbe obtained.

Phase 2 - Demonstration

ofSvnergetic behaviorusing2-D SimulationTool:

The second phase was to demonstratethe synergetic behaviorofthe chunxels _{by giving}a set oftargets to thechunxels inordertoretrieve adeadchunxel froma random position in

the tank and_pushing itupward abovethe surface ofliquid inside the tank. Thisphase was carried outto

help

understandthedynamicnature ofthe chunxels while_workingintandem with each other. _{The already developed 2-D} simulation tool was used to observe this

behavior.

. 19

The 2-D simulation logic was extended to _incorporate a third axes _{viz, thus moving} the

simulation into the realms of 3-D space. Java 3D API was used to program the 3-D

simulation tool. The control algorithm and simulation program was _{simultaneously} developed. Basic swarms

behavior,

method for _{reducing hunting} of _targets, was

incorporated in the program in this phase. _{Other programming details like collision}

detection, application of _{electro-magnetic force}

equations, physical phenomena of

buoyancy, and fluid _dynamics ofthe chunxel inside the liquid _medium, were also taken

into considerationinthisphasethus

developing

asimulationmodel_representingthe actual

chunxel device for experimentation purposes. The final _{step in} the development ofthe

simulation program was

designing

an interface. _{This interface helped in dynamically}

changingthevarious parameters ofthemodel. Thevariousparameters consideredwerethe

radius, current, turns in internal and external _coils, mass of_{the chunxel, density} ofthe

liquid_medium, andthecycletime_{for energizing} ofthe external coils.

Phase4- Verification

ofthe3-D Simulation Tool:

Phase 4 dealtwith _verifying the program and _{checking its} validity. _{Data pertaining} to the

propulsion force experienced _by the chunxel at various locations inthe _tank, the average

velocity ofthe chunxel inside the _tank, the _drag forces generated were compared to the actual data collected_during the prototype runs ofthe chunxel device andto thecalculated

values from thephysical equations presentinthe literature. Alsovisual inspectionwas one

of the tools used to observe the behavior ofthe chunxels and see if compares to the

expected motion as seen in the prototype run. This was the most important phase ofthe

research as it was the foundation for obtaining reliable results from the experimentations

thatwere conductedinthelastphase ofthisresearch.

Phase 5 - Experimentation_andOptimizationusingthe 3-D Simulation Tool:

This phase was critical for the future ofthe "Chunxel" Technology. Experiments were

carried out in _{this phase, using} the simulation tool, with different configurations ofthe

hardware parameters to find out an optimal configuration forthe next generation chunxel

6.1. Phase 1:

Development

of a _{Two Dimensional Simulation}

Tool

Themainobjectiveto be achieved

by

theend ofthe firstphase of research was to _develop

abasic framework forthe finalthreedimensionalsimulationtoolforthechunxel device.A two-dimensionalsimulationtool was _developed as the first _stepinthe research sothat the basic functionalities of the chunxel could be visualized and checked. _Also, this 2D

program was the

building

block upon which the complete structure ofthe 3D simulation tool wasbasedupon. The 3D simulation_{tool was, in}a_sense, an extension ofthebasic 2D

program with more functionalities and physical phenomenon incorporated in it. Here it is importanttomentionthat the 2D simulationtool was a methodto evaluatethebehaviorof

the chunxel under the proposed control strategies and not to evaluate the physical

parameters ofthe device. Inthe 2D simulation the chunxel moves _{only in} four directions viz. _{North, South, East,} and _West, unlike the actual device where the chunxel is free to

move in the six directions proposed to be _{North, South, East, West,} Forward and Backward. The chunxel coordinates arethus _{denoted using only}xand_ycoordinates inthe

XandY Axesrespectively.

6.1.1. Javaand2D Simulation Tool

The 2D program was written in Java 2 (Version 1.4.1 SDK), as an applet. In the later

stagesofthisresearchtheprogram was designedto runas aJavaapplicationbecauseofthe

need to read and write files fromthe local machine arose, which will be discussed inthe Phase 4 ofthis research. Java applets are notdesignedto read or write files, because as a

general _rule, Java applets run under a "better safe than sorry"

security model. Applets

cannotdo_anyofthe following:

Theycannot read or writefiles intheuser's filesystem.

They cannot communicate with an Internet site other than the one that served the

web pagethatincluded theapplet.

. 21

Theycannotloadprograms stored onthe user's _system,suchas executable programs

and sharedlibraries.

Java applications have none ofthe restrictions in place for applets. _They take the full

advantageofJava's capabilities.

The 2D simulation program was designed _using the Java classes that support graphical

features. The 2D program comprised of

displaying

small squares that represented the

chunxels in the applet window and animate these _squares, i.e. move them on the screen

depending

on the control logic proposed in the research. Animation in Java is

accomplished _{by using} the Abstract _Windowing Toolkit _{(AWT), Swing} and the Threads

class inthejava.lang.package.

It will be helpful at this stage to understand a little bit about the Java coordinate system

that is used _by the AWT and _Swing packages. It is imperative to know how graphical

objects like rectangles that are used to represent the chunxels in this 2D program, are

displayedonthescreen. Theother_thingto considerhere is howtheJavacoordinate system

isrelatedto the directionalconventionsusedinthechunxel device.

6.1.2. Javacoordinate system& directionalconventions

Java's coordinate system used pixels asits unit of measure. The origin coordinate 0,0 is in

the upper-left corner of the Applet window. The value of x coordinates increases to the

right of0,0 and _y coordinates increases in adownward direction. This differs from other

drawing systems in which the 0,0 origin is atthe lower left and _yvalues increases in an

upwarddirection. Allpixel values are integers;decimal numbers cannotbe usedto _display

something between integer values. Hence the motion ofthe chunxel is proposed to be

incrementsordecrementsof one pixel unit.

The chunxels are shown onthe screen by_using fillRect() methodinJavathat draws solid

The x and_ycoordinates oftherectangle's_top left corner; thus the x and_ypositions

ofthechunxels andthe targetsarethe_topleftcorner ofthesquares.

Thewidthoftherectangle (Chunxelwidth= _{1 0}

pixel_units)

Theheightoftherectangle _{(Chunxel height}= ₁₀

pixel_units)

The four directions that are used in the chunxel device are shown in the Figure 6 along

with the Java coordinate system. The North direction ofthe chunxel device is directed

upwards _{towards the origin,} and the other directions are relative to this North direction. According to the above convention andthe Java coordinate _system, amovementin North

is affected _{by subtracting} one pixel unit from the _y coordinate of the current chunxel

position, the South movement _{by adding} one pixel unit to the _y coordinate. _Similarlythe Westmotionisbrought about_{by subtracting}onepixel unit fromthe x coordinateandEast

motion_byaddingonepixelunitto thexcoordinate ofthechunxel position.

North

West East

South

X,Y

Height=10

Chunxel 10x10 Pixels Square

[image:34.526.58.493.344.583.2]

Width=10

Figure 6: Javacoordinate system&Chunxel DimensionsinJava 2D

6.1.3. BasicControl Algorithm

Theessence ofthe chunxeldevice istoform a3D geometryby givinga setofcoordinates

23

orderto_occupy the specific_{targets, the chunxelshaveto}

move withinthe tank inspecific

directions. Thus simple controllogic forthismotionis asfollows:

1. Identifyingthetargettobe

occupied; 2. _Movingtowardsthe_target; and 3.

Occupying

thetarget.

Fornnumberoftargets with nnumber ofchunxels insidethe_tank,thechunxels will select

the target nearestto its current position. Since the chunxels are autonomous _agents, allthe

chunxels inside the tank are given information about all the targetpositions. Basedonthe "Nearest Target"

rule the chunxel will

identify

the _target, which itdesires to occupy. The

distance betweenthecurrent chunxel positionandthe targetis given_by

Dist(CT)=

Sqrt((cnx+tnx)2+(cny+tny)2₎

Where,

cnisthechunxel withidentificationnumber_n,

tn isthe targetwithidentificationnumber_n,and

x and_yarethecoordinatesofthechunxel andtarget.

In the Java source code the square root is not considered, sincethe squared values ofthe

distances are _directly compared with each other. This is done in order to reduce the

computational loadontheprogram. The distances betweeneach chunxel and allthe targets

are compared and the _target, which is at the least distance from the chunxel under

consideration,is selected_bythatchunxel.

There can be a situation wheretwochunxels can select the same target_location; in such a

situation, the chunxel that reaches the target first, occupies the target. Once a target is

occupied, the occupied target andthe chunxel that occupies the target are "Locked". This

means that the chunxel that occupies the target and the occupied target are no longer

coordinates were supplied withinthe program. Ineither case it was _necessaryto initialize

the target locations and initial _{chunxel positions. This was done by}

creating two arrays

with two dimensions and n _elements, one _array for the chunxels and the other for the

targets; n is the number oftargets and chunxels to be initialized. It is assumed in this

program that the number of chunxels initialized is equal to the number targets to be

achieved.The first dimension isthereference numberoridentificationnumberofthe target

andthe chunxel. The seconddimension storesthexand_ycoordinates of_{the corresponding}

chunxel ortarget. Thus the_arraycanberepresentedina matrix shownin Table 1.

Table1: 2D_{Arrayfor storing Chunxel Information in Java}

1st

Dimension 2ndDimension

Identification# _{[0] [1] [2] [n]}

[1] X _y - ~

[2] X _y - ~

[n] X _y ~ ~

Addingtheabove control strategies to the simple control logic loop givesthebasiccontrol

algorithmthat the chunxelsandthechunxeldevice haveto follow.

BasiccontrolAlgorithm:

Step 1 Initializetargetpositions;

Step2

"Unlock"

alltargets, i.e. non-occupied;

Step3 Initializechunxelspositions;

Step4 "Free" all chunxels. i.e. chunxels are not occupying any targetposition andfree to

move;

Step5 Check_{ifany of}the targetsare occupied;

Step6 _Iftargetisoccupied;

"Lock"

thetargetandthechunxel_occupyingthattarget;

Step 7 _Ifalltargetsare occupied gotostep 18;

Step8 Broadcast the

"Unlocked"

targets to the "Free

"

chunxels;

Step9 Selecttarget locations to be achievedby the chunxel based onthe "Nearest Target"

25

Step10 Decide the directionsfor the individual chunxels to move in towards the selected target;

Step 11 Storetheaboveinformationinthechunxelmemory; Step 12 Energizenorth_coil;

Step 13 Energizeeastcoil; Step 14 Energizesouthcoil; Step 15 Energizewestcoil; Step16 Goto_step6; and Step1 7 Endsimulation.

The direction to be pursued _by the chunxel is decided _by the relative position ofthe chunxel andthe target. Ifthechunxel isto the leftofthe target the chunxelhas to movein the East direction and if it is to the right ofthe target then it as to move in the west direction. Similarly,ifthe chunxelis belowthe_target,it hasto moveinnorthdirection and if it isabovethe target thenit hastomove south. _{Mathematically,}

If,

ex- tx>0

=>chunxelis tothe right, Movewest cx-tx<0=>chunxelis tothe _left, move east

cy-ty>₀=>chunxelisbelow, move north

cy-ty <0=>chunxelisabove, move south

6.1.4. Collision Detection

In any simulation of a physical phenomenon or physical model it is necessaryto see that twoobjects do not_overlap orinterpenetrate. Collision detectionisa system of

determining

whether two or more objects collide. Collision detection is a computational geometry

problem. To make _any simulation of a physical model realistic collision detection is essential.

Most collision detection methods _usually deal with the temporary positions reflecting

1) Futureposition_calculation;

2) Collision_detection;and

3) Collisionhandling.

The_{logic governing}object motion wouldproceedina

loop

likethis:

Entity oldPosition =

Entity currentPosition

Modify Entity

depending

uponthecontrollogic

IfEntitycollidesthen_Entity =

Entity oldPosition

Insimple wordsthelogic canbeexplained as follows:

Save thecurrent positionina_{temporaryvariable;}

Calculatethenewposition andsave itas current_position; and

Ifat this current position the _entity collides with _any other _entity then change the

current positionto thevalue storedinthe_temporaryvariable.

Inthe above algorithm for collision_detection, when objects _{collide, they} are moved back

to theprevious_position,becauseifthosewerethe safe spotsfortheobjects a moment ago,

they will _probably be still safe. But there are complications inthemethod that we chose:

for_example, when an objectismovedbacktoits _startingposition,care hastobetaken that

it is _really still _safe; if not (because an object might have moved in that space in the

meantime), then theoffendingobjectmustbe movedbacktoitsown _startingposition. The

worstthatcanhappen is that all theobjects haveto bereverted backto theirown _starting

points. This is an _extremely slow _{way because it involves} significant iteration (Blow

Jonathan, 1997)

The other_way to overcome the problem of collision detection inthe case ofchunxel 2D

simulation is collision avoidance. The principle is tomove _{only those chunxels,}which do

nothave anypotentialcollision, takingplace with_anyother chunxel. Itis also_{very easy}to

predict the collision inthe case of chunxel simulationbecause all the chunxel are _moving

inthe same directionor not_moving at all at_anypoint oftime inthe simulation.This logic

. 27

factor to be considered in the 2D simulation _program, the collision avoidance _strategy is

bettersuitedforthisapplication.

Eithercollision detection orcollision _{avoidance, there has to be a}

waytopredict whether

the objects interpenetrate or _{overlap each other. This is achieved}

by using the "Bounding

box"

approach. Asimple _waytocheck whetherthe

bounding

_{boxes intersect is}"ifthe tops

are higher than the bottoms and the lefts are 'letter' _{than the rights, then the boxes}

intersect."

(Magarshak_Greg, 2000). Figure7depictsthe

bounding

boxapproach.

Figure 7:_BoundingBox Collision Detection

A method for the chunxel collision detection was developed. This method checks for

future collisions that _may take place and _{correspondingly} modifies the position of the

chunxelunder consideration. Thecollisiondetectionor avoidancealgorithmisas follows:

Step 1 Takethechunxelidentificationnumberas an argumentforthedetectionmethod; Step2 Checkthedirection inwhichthechunxelismoving;

Step3 _Ifchunxel_{moving in}north or southdirectiongoto_step5; Step4 _Ifchunxel_{moving in}east or westdirectiongoto_step6;

Step5 _Moving north or south: check _ifany other chunxel position is between the _colliding ranges.

Thiscanbeachievedby

a) Checkingifthex-coordinate_{of any}other chunxellies betweenthe (x-coordinate_ofthe

current chunxel- 9_pixel

units)and(x-coordinate ofthecurrent chunxel+9pixel_units)

AND

b) Checkingifthey-coordinate_{of any}other chunxelisequalto10pixel unitsfromthe

Step6 _Moving east or west: check _{ifany other chunxel position is between the}

colliding

ranges.

Thiscanbeachieved_by

a) Checking ifthey-coordinate_{of any}other chunxelliesbetweenthe(y-coordinate_ofthe

currentchunxel- 9

pixel_units)and(y-coordinate_ofthecurrent chunxel+9pixel_units)

AND

b) Checking ifthex-coordinate_{of any}otherchunxelis equalto10pixel unitsfromthe

x-coordinate_ofthecurrentchunxel

Step 7 _Ifcollision isnotdetectedadvance theposition _ofthechunxel_byone unitinthe

pre-determineddirectionelsedonot changetheposition_ofthechunxel.

6.1.5. ProportionalMotion

The first prototype run showed that the chunxels _continuously oscillate about the target

position. This is because of the _gravity and _{buoyancy effects,} collisions and also the

constant cycle time that even after _being locked to a specifictarget the chunxels _keep on

hunting for the targetposition. To minimize this _"Hunting ofthe Target" a "Proportional

Motion"

method is implemented. Although in the 2D simulation _{program, the hunting}

effect cannotbe observed since_{only integer}values are acceptedforthecoordinate _byJava

even then the proportional motion logic was employed so that it could _help in extending

thesamelogicto the3D simulation program.

The logic behind proportional motion is to take bigger steps when the target _{is far way}

from the current chunxel position and as the chunxel approaches the target go on _taking

smaller and smaller steps. In an actual device this can be achieved _{by turning} ON the

internal coil for a certain percentage ofthe cycle time. Thus _{by controlling} the Time ON

forthe internal coil insidethe chunxel, the timeforwhichthemagneticforce ofpropulsion

thatacts onthe chunxel canbecontrolled. Inthis _waythe displacement ofthe chunxel can

be made smaller as itapproaches the target. Ifthe distance betweenthe chunxel andtarget

is greater than the size ofthe chunxel then the chunxel takes multiple steps towards the

target, else it takes _only one step. This distance was termed as the "threshold distance."

29

eachtime the distance between the target and current chunxelposition is _checked, and if

the distance is greater than tenpixel _{units, then the} position ofthe chunxel is updated by

one pixel unit towards the target. Figure 8 makes it easierto understand the principle of

proportional motion method. Sincethe 2D simulationtool doesnottake into consideration

the cycle_time, and actual propulsionforce _arbitraryvalues were selected forthe threshold

distance, andthe number of maximum stepsthat the chunxel takes ifthe distance between

the chunxelandthetargetis less than the thresholddistance.

&

Multiplestepstobe _[J

taken

Chunxel

>Thresholddistance(td)

< ?

<td

P

1 steptobetaken

1 steptobetaken

| | Target

?

r

+\

Figure 8:Proportional FeedbackMotion in 2D Simulation Tool

The logic that was used to implement proportional motion can be expressed in the

followingalgorithm:

Step 1 For any directionalcoilthatisenergized:create a_loopcount= ₀

Step2 _Ifcount= _0goto step 4

Step3 _Ifcount> 0goto_{step 5}

Step4 Advancethe chunxel positionbyone pixel unitinthedetermined direction. Changethe

position_ofthechunxel_onlyifthere isnocollisiondetectedforthefutureposition.

Step5 _Ifthe difference between the targetposition and current chunxel position is

greater

than 10pixels unit after pixel units then onlyadvance theposition ofthe chunxel by

one unitinthe determined direction. Changethe

position_ofthechunxel_onlyifthere is

nocollisiondetectedforthefutureposition.

Step7 End: energizing ofthecoil.Moveto thenext coil_energizingsequence.

Combining the basic control algorithm with the collision detection and proportional

feedback motionalgorithms gives thebasic framework ofthe 2D simulation program. The

basic flow ofthe Java program is as shownin Figure 9. The detailed flow ofinstructions

and conditionallooping oftheprograminshown inAppendix A intheform ofaflowchart.

Start Main Program

Start Simulation

Make Targets Unoccupiedand

ChunxelsFreetoMove

Start Cycle

West, North,EastandSouth

Check OccupiedTargets &

Chunxels alre^yany Targets

I

Check forCollisions

ContinueCycletillallTargets

areoccupied

I

End Program

[image:42.525.197.342.204.643.2]

31

6.2. Phase 2:

Demonstration

_of

Synergistic

behavior using 2-D Simulation Tool

One of the most innovative _{parts ofthis research}

was, not _only the generation of static

structures,butalsothedynamic behaviorofthose structures. Theproposedapproach atthe

beginning ofthe research was to form a static structure and the _ability to demonstrate a

dynamic behavior forthe structure. The basic approach to navigation and control was to

implement a swarm style behavior that would allow all chunxels to stand on a common

non-hierarchical platform with one _{another, behave autonomouslyyet withcollective goals}

and synergistic functionality. This phase ofresearch was dedicated _solely to demonstrate

that the chunxels could exhibit collective synergistic behaviorand completetasks together

thatcould notbecompleted asindividuals.

One such task is _"building of a chunxel platform with an individual chunxel _atop the

platform. Once the structure is built the next _{step is} to raise the individual chunxel _up

above the level oftank medium."

This behavior would be impossible for an individual

chunxel, butcan beaccomplished_bythe _{group working}together.

An algorithm was developed in this phase to accomplish this task. _{During this phase,} a

strategy was also developed to overcome deadlock situations for the chunxels while

moving towards theirrespectivetargets. The deadlock situationis defined when achunxel

cannotreach its target location due to thepresence of some _{obstruction, generally} another

chunxel that is _stationary on its achieved target. A search sub-routine was developed to

findan alternative pathtowards thetargetto bereached.

6.2.1. Synergistic behavioralgorithm

The above-mentioned task of _lifting an individual chunxel above the liquid level was

demonstrated _{by developing} the synergistic behavior algorithm. In order to lift a chunxel

abovetheliquidmediuminsidethe tank thefollowing steps werefollowed:

Determinationofthetargetsinordertofromaplatformbeneaththatchunxel.

Broadcastingofthetargetstotheavailable chunxelsinsidethe tank.

Once theplatform has been_created,

broadcasting

adesired deltamovement foreach

chunxel.

Figure 10 belowshows thesimulation andtheformationoftheplatform andthemovement

ofthechunxelsinordertoliftachunxel above theliquidmedium.

slower_j faster

*

i yjU\

| slowBi_| faster _j

Figure 10: 2D Simulation Tool Screenshots

The incremental deltamovement is given_{by looping} theprogram insuch a _waythat once

one deltamovement is achieved thenext set ofdeltatargets is givento the chunxels. This

isrepeated untilthelastset oftargets orthe co-ordinatesofthe targetswheretheindividual

chunxelisabovetheliquid levelis achieved.

The formation of a platform is _{fairly easy} when the chunxel to be lifted is _away from the

walls ofthe tanks. But inthe scenario where the chunxelto be lifted is close to the walls

the platform cannot be made. In such special case scenarios the chunxel to be lifted is

pulled _away from the other chunxels andthenwhen it is _{sufficiently away} from thewalls

and enough room is available to form the platform beneath the original algorithm is run

33

Thus an addition to the _{original algorithm is made. Before}

broadcasting

the _targets, the

system sees the position ofthe chunxel which is to be lifted and ifit is