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Keywords: collective ffecision making, bio-inspireff control theory, ffesign, nonlinear ffynamics, Keywords: collective ffecision making, bio-inspireff control theory, ffesign, nonlinear ffynamics, Keywords: collective ffecision making, bio-inspireff control theory, ffesign, nonlinear ffynamics, bifurcation control bifurcation control 1. INTRODUCTION 1. INTRODUCTION A funffamental tas1k. foINr mTRanOyDmUuCltTi-IaOgeNnt system networks A funffamental task for many multi-agent system networks A funffamental task for many multi-agent system networks is successful collective ffecision-making among alternatives is successful collective ffecision-making among alternatives uofsiinngffiivniffofurmalaatgioentfsf,isitnribapuptelifcfatciroonsssitnhcelunffeintwgotrrka.nGsproorutpas- using information ffistributeff across the network. Groups of inffiviffual agents, in applications incluffing transporta- of inffiviffual agents, in applications incluffing transporta- tion, mobile-sensing, power anff synthetic biological net- tion, mobile-sensing, power anff synthetic biological net- waloterkrns,atairveeso,fstuenchreaqsucihreofofstinogmwahkiechaospintigolne icshotricue,awmhoinchg works, are often requireff to make a single choice among alternatives, such as choosing which option is true, which alternatives, such as choosing which option is true, which action to take or ffirection to follow, or when something in action to take or ffirection to follow, or when something in the environment or system has changeff. For purposes of ffesigning ffistributeff multi-agent ffecision- For purposes of ffesigning ffistributeff multi-agent ffecision- For purposes of ffesigning ffistributeff multi-agent ffecision- mgraokuipnsg,wwhoesseeesukrtvoivalelvreerlaiegse omnecshuaccneissmsfuslucsoelflfecbtyivaenfifmecai-l making, we seek to leverage mechanisms useff by animal groups whose survival relies on successful collective ffeci- groups whose survival relies on successful collective ffeci- sions among alternatives. House-hunting honeybees (See- sions among alternatives. House-hunting honeybees (See- l2e0y11a)n,fafnBffumhirgmraatno,ry20b0ir1f)fs, (sEchikoeonlainagr eftisahl.,(C20o1u4z)inmaekteaelf.-, ley anff Buhrman, 2001), schooling fish (Couzin et al., 2fi0c1ie1n)t, fafnecffismioingsraffteosrpyitbeirffffist(uEribkaenncaeasroertsaigl.n, i2f0ic1a4n)tmchaaknegeefs- 2011), anff migratory birffs (Eikenaar et al., 2014) make ef- ficient ffecisions ffespite ffisturbances or significant changes ficient ffecisions ffespite ffisturbances or significant changes in their environment. They employ ffecentralizeff strategies in their environment. They employ ffecentralizeff strategies anff face limitations on sensing, communication, anff com- anff face limitations on sensing, communication, anff com- pyeuttatthioeny (sStiullmpetrefror(m201w0i)t,h Kspraeuefsfe, acncffurRacuyx,tornob(u2s0tn02es)s), putation (Sumpter (2010), Krause anff Ruxton (2002)), yaentff tahffeayptsatbililliptyer(fPoramrriswhitahnfsfpEefeffefl,staecicnu-Kraecsyh,erto, b1u9s9t9n)e.ss, yet they still perform with speeff, accuracy, robustness, anff affaptability (Parrish anff Effelstein-Keshet, 1999). anff affaptability (Parrish anff Effelstein-Keshet, 1999). Typical mechanisms useff to stuffy collective animal be- Typical mechanisms useff to stuffy collective animal be- Typical mechanisms useff to stuffy collective animal be- havior ffepenff on the animals’ social interactions anff on havior ffepenff on the animals’ social interactions anff on tohuesirunpfefrecresptatniofnfisngofofthtehiresexftfeerpneanlffeennvciireosnmmaeknets. Aporsisgiborle- their perceptions of their external environment. A rigor- ous unfferstanffing of these ffepenffencies makes possible ous unfferstanffing of these ffepenffencies makes possible tinhsepitrreafnf sflfaetsiiogn omf etthheomffoelcohgaynifsomr suisnetoina esnygsitneemearetfifc nbeiot- the translation of the mechanisms into a systematic bio- inspireff ffesign methoffology for use in engineereff net- ★inspireff ffesign methoffology for use in engineereff net- ★ This research has been supported in part by NSF grant CMMI- 1★6T5h0i5s6r,eOseNarRchgrhaanstbNee0n00s1u4p-1p4o-r1t-e0d63in5,paanrdt UbyNNASMF-DgGraAntPACMgrManIt- This research has been supported in part by NSF grant CMMI- P6A3P50II5T6,ROAN1R05g8r1a6nt N00014-14-1-0635, and UNAM-DGAPA grant 1635056, ONR grant N00014-14-1-0635, and UNAM-DGAPA grant PAPIIT RA105816 PAPIIT RA105816 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. CCPooeeppryy rrreiiggvhhiettw ©© u 22n00d11e77r rIIFFesAApCConsibility of International Federation of Automa85728t5ic7 2Control. Copyright © 2017 IFAC 8572 10.1016/j.ifacol.2017.08.1392 works. This remains a challenge, however, in part because works. This remains a challenge, however, in part because works. This remains a challenge, however, in part because most stuffies of collective animal behavior are empirically baossetffsoturfrfieelsyoofncmolleeacnt-ivfielaffnmimoafflelbse.havior are empirically most stuffies of collective animal behavior are empirically baseff or rely on mean-fielff moffels. To affffress this challenge, we present a generalizable To affffress this challenge, we present a generalizable To affffress this challenge, we present a generalizable agent-baseff ffynamic moffel of ffistributeff ffecision-making agent-baseff ffynamic moffel of ffistributeff ffecision-making between two alternatives. In this type of ffecision-making, between two alternatives. In this type of ffecision-making, the pitchfork bifurcation is ubiquitous (Leonarff, 2014); the pitchfork bifurcation is ubiquitous (Leonarff, 2014); it appears, for example, in the ffecision-making ffynamics it appears, for example, in the ffecision-making ffynamics of house-hunting honeybees anff schooling golffen shiners of house-hunting honeybees anff schooling golffen shiners theleecatgienngt-bbeatsweeffenmofoffoeflf ssoouthrcaetsi.tOtouor eaxphpirboiatschthies ptoitcffhefroivrke selecting between fooff sources. Our approach is to fferive the agent-baseff moffel so that it too exhibits the pitchfork the agent-baseff moffel so that it too exhibits the pitchfork bifurcation. This allows the animal group ffynamics anff bifurcation. This allows the animal group ffynamics anff the multi-agent ffynamics to be rigorously connecteff by the multi-agent ffynamics to be rigorously connecteff by mapping to the normal form of the pitchfork bifurcation. mapping to the normal form of the pitchfork bifurcation. The major contributions of this work are as follows. The major contributions of this work are as follows. TFiherst,mwaejoprrescoennttribaugentionseraloifzabthisleawgeonrkt-baaseffre amos fofflellowfors. biiors-itn, swpierepffrecsoelnletctaivegefnfeecriasliiozna-bmleakaignegntff-ybnaasemfficms oafnfeffl ufoser First, we present a generalizable agent-baseff moffel for bio-inspireff collective ffecision-making ffynamics anff use bio-inspireff collective ffecision-making ffynamics anff use thoeffmelorfefeffluccatipotnuraensffthaesyamffpatpottiivce eaxnpfafnrsoiobnustofesahtouwrehsoowf moffel reffuction anff asymptotic expansion to show how thoeusme-ohfufenlticnagpthuorneseytbheee affffeacpistiiovne-manafkf inrogbuffsytnafemaitcusr.esRoe-f the moffel captures the affaptive anff robust features of moaurskea-bhluyn, thinogneyhboneeesybreeleiafbfelycisseiolenc-tmtahkeinhgighffeysntavmailcuse. nReest-house-hunting honeybee ffecision-making ffynamics. Remarkably, honeybees reliably select the highest value nest markably, honeybees reliably select the highest value nest site alternative, anff in the case of alternatives of equal site alternative, anff in the case of alternatives of equal vsalsuuef,ficthieenytlqyuhicikghly. mThakeseeahnonarebyibteraeryffycnhaomiciecsifhtahve vbaeleune value, they quickly make an arbitrary choice if the value sstusfufifefifcf iiennStleyelehyigahn.ffTBhuehsermhaonne(y2b0e0e1)f,fySneealmeyicest haal.v(e20b1e2e)n, is sufficiently high. These honeybee ffynamics have been stuffieff in Seeley anff Buhrman (2001), Seeley et al. (2012), stuffieff in Seeley anff Buhrman (2001), Seeley et al. (2012), anff Pais et al. (2013), anff leverageff in Reina et al. (2015). anff Pais et al. (2013), anff leverageff in Reina et al. (2015). Seconff, we present for this moffel an investigation of Seconff, we present for this moffel an investigation of Seconff, we present for this moffel an investigation of how the value of the alternatives, inffiviffual preferences, how the value of the alternatives, inffiviffual preferences, anff interaction topology influence the ffecision-making anff interaction topology influence the ffecision-making ffynamics. This is motivateff by the problem of ffesigning ffynamics. This is motivateff by the problem of ffesigning collective decision-making dynamics, as these parameters could serve as control parameters in engineered systems.
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