ProgrammingMethodologyfor Biologically-InspiredSelf-AssemblingSystems

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RadhikaNagpal�

, Attila Kondacs,CatherineChang

October4, 2002

Cellswith identicalDNA cooperateto form complex structures,suchasourselves,with incrediblereliability inthe faceof constantlydying andreplacingparts. Emerging technologiesaremakingit possibleto bulk-manufactureand embedmillions of tiny computingand sensingagentsinto materialsand the environment. We would like tobuild novel applicationsfrom thesetechnologies,like smartmaterials,self-reconfiguringrobotsandself-assemblingstructures,thatachieve thekind of complexity andreliability thatcellsachieve. This posessignificantchallenges:a)How doesoneachieve a particular globalgoal from the local interactionsof vastnumbersof parts?b) Whataretheappropriatelocalandglobalprogrammingparadigmsfor engineeringrobustsystems?

We will presenttwo examplesof usinga programminglanguagesapproachto designingself-assemblingsystems.We usemorphogenesisanddevelopmentalbiology asa sourceof mechanismsandgeneralprinciplesfor organizingrobustlocalbehavior. Howeverunlikecurrentapproachesto emergentsystems,thegeneralprinciplesareformalizedasprogramming languages — with explicit primitives,meansof combination,andmeansof abstraction— thusprovidinga framework for thedesignandanalysisof self-organizingsystems.We believethatthis methodologywill impactthedesignof reconfigurableroboticsand smart-matterapplications,and also influenceour engineeringprinciplesforrobustdesign.

Thefirst systemprovidesa languagefor specifyingshapeformationonanintelligentsheetcomposedof thousandsof identically-programmedbut locally-interactingflexible agents[1,2].Thesystemusesa novel approach:thedesiredglobal shapeis specifiedat an “abstract” level as a folding constructionon a continuoussheetof paper, which isthenautomatically compiled to producetheprogramrun by the identically-programmedagents.Theglobal-to-localcompilationis achievedby usinga setof five robust local primitives,inspiredby cell differentiationin multicellularorganismssuchastheDrosophila. Thecompilercomposestheseprimitive building blocksin a principledway usinga setof geometryaxiomsfrom paper-folding (origami)mathematics.Theresultingprocessis not only versatilein theshapesandpatternsthatcanbeformed,but alsoextremelyreliablein thefaceof randomagentdistributions,varyingnumbersof agentsandrandomagentdeath,without relying on globalcoordinatesor centralizedcontrol.Theprocessalsoexhibits interestingbiological traits; for example,it is scale-independent — the shapescalesto the numberofagentsand proportionsof the initial sheetwithout any modificationto the agentprogram. Many examplesand adetailedanalysisof thesystemcanbefoundin [1].

Thesecondsystem,currentlyunderdevelopment,appliesthesameapproachto a differentdomain:thesynthesisof arbitrary3D volumetricshapesfrom cell growth. Thegoalis to compileapredeterminedglobalshapeto produceaprogramfor a seedagentthatthen“grows” thestructurethroughreplication.Thecompilationproceedsin two stages:first anarbitrary3D shapeis automaticallydecomposedinto anefficientpackingof covering-spheres,usingtechniquesfrom computergraphics. Neighboringspheresare linked into a bidirectionalnetwork using local referencepointsrelative to eachsphere.This sphere-representationis key becauseit permitsthe formationof the entirestructurebycellsrecursively executingonly two simple primitives: growing into asphere,andtriangulatingthecentersof adjacentspheres.Locally theagentsusereplication,gradientsandcompetitionto achieve theseprimitivesrobustly andallowfor local self-repairin the event of agentdeath. Apart from being scale-independentand robust, this systemalsomodelsregeneration. In biology, many speciesshow incredibleabilitiesto regeneratelimbs; a starfishcanregeneratetheentirestructurefrom partof a limb. Ourartificial systemcanalsoregeneratebrokenstructures,becausethesphere-network representationallows thestructureto begrown startingfrom any sphereandeverycell containsall necessaryinformationto reproducethemissingstructure.Currentlywe arecompletingthesimulationsof 2D shapeformationandextendingthe processto 3D. The next stepis to replacecell growth/deathwith a model for a self-assemblingmodularrobotwheretheagentscanattach,detachandwander.

�Submission:2003AAAI SpringSymp:Computational Synthesis: From Basic Building Blocks to High Level Functionality�contact:Dr. RadhikaNagpal,Artificial IntelligenceLaboratory, MassachusettsInstituteof Technology, Cambridge,MA 02114,radhiai.mit.edu

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Figure 1: Shapeand patternformation on a surfaceof identically-programmedlocally-interactingagents(a) dif-ferentiatinginto an inverterchainpatternand(b) folding into an envelope. In both examples,the agentprogramisautomaticallygeneratedfrom anabstractdescriptionof thedesiredstructure.Thepatternscalesautomatically(withoutmodificationof theagentprogram)to thesizeandproportionsof surface.Theprocessis robustto randomplacementandrandomdeathof agents[1].

This researchis motivatedby technologies,suchasMEMs1 devices, that aremaking it feasibleto build novelapplicationssuchassensorcoveredbridgesthat monitor load andmodularrobotsthat canreconfiguretheir shape.Theseapplicationswill requirecoherentandrobustbehavior from thelocal interactionsof vastnumbersof agentsandtheir interactionswith theenvironment.Approachesbasedoncentralizedcontrolandplanningarenotscalableto largenumbersof agents.In addition,they aredifficult tomakefaulttolerantbecauseof thestrongtendency todependoncen-tralizedinformation,suchasglobalclocks,positioninformation,anduniqueidentifiers.Thesestrategiesput pressureon systemdesignersto build complex, precise(andthusexpensive)agentsratherthancheap,mass-produced,unreli-ablecomputingagentsthatonecanconceiveof just throwing at a problem.By contrast,biologicalsystemsregularlyachieve coherent,reliableandcomplex behavior from the cooperationof large numbersof identically-programmedunreliableagents.During embryogenesis,cells form incrediblycomplex structures,in thefaceof largevariationsincell behavior andbiologistsarebeginningto uncovermany of theunderlyingmechanisms[3,4]. Howeversimplymim-icking biologicalbehavior is not sufficient. Cellularautomatamodelsandartificial life researchhave beendifficult togeneralizebecauselocal rulesareconstructedempirically, without providing a framework for designinglocal rulestoobtainany desiredgoal.Evolutionaryandgeneticapproacheson theotherhand,evolve local ruleswithoutproducingany understandingof how or why they work; thismakesthecorrectnessandrobustnessof theevolvedsystemdifficultto verify andanalyze.

This researchrepresentsa differentapproachto engineeringself-organizingsystems.Ratherthantrying to mapa desiredgoaldirectly to thebehavior of individual agents,theproblemis brokenup into two pieces:a) how to de-composethegoalglobally b) how to maptheconstructionstepsto local rules. In bothexamples,we take advantageof currentunderstandingin otherdisciplinesof how to decomposea problem.This approachsuggeststhatexploringnew globalparadigmsis at leastasimportantasexperimentingwith local rules.Our currentresearchhasfocussedonself-assembly, however the sameapproachcould be appliedto achieving global behavior from ant-like robots. Theglobal-to-localcompilationis thekey to achieving complexity while still beingableto analyzethebehavior of thesys-tem. By encodingtheseprocessesasprogramminglanguageswe cancombineprinciplesfor controllingcomplexity,drawn from computerscience,with techniquesfor robustdesign,inspiredby biology.

Bibliography[1] Programmable Self-Assembly Using Biologically-Inspired Multiagent Control, Nagpal,AutonomousAgentsandMultiagentSystems(AAMAS), 2002.Also PhDThesis,MIT, June2001.[2] Amorphous Computing, Abelsonet. al., Comms.of theACM, Vol 43,no 5, May 2000.[3] Principles of Development, Wolpert,Oxford UniversityPress,2002.[4] The Making of a Fly: the Genetics of Animal Design, Lawrence,BlackwellScience,1992.

1Micro-electronicMechanicalDevices.Integratesmechanicalsensors/actuatorswith silicon basedintegratedcircuits.

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