Towards Physarum Robots: Computing and Manipulating on Water Surface Towards Physarum Robots: Computing and Manipulating on Water Surface

Towards Physarum Robots: Computing and Manipulating on Water Surface

  • 期刊名字:仿生工程学报
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  • 论文作者:Andrew Adamatzky,Jeff Jones
  • 作者单位:Department of Computer Science
  • 更新时间:2020-07-08
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Available online at www.sciencedirect.comScienceDirectJournal of Bionic Engineering 5 (2008) 348 -357Towards Physarum Robots: Computing and Manipulating on Water SurfaceAndrew Adamatzky, Jeff JonesDepartmnent of Computer Science, University of the West of England, Bristol BS16 1QY, United KingdomAbstractPlasmodium of Physanum polycephalum is an ideal biological substrate for implementing concurrent and parallel com-putation, incuding combinatorial geometry and optimization on graphs. The scoping experiments on Physarum computing inconditions of minimal friction, on the water surface were performed. The laboratory and computer experimental results showthat plasmodium of Physarum is capable of computing a basic spanning tree and manipulating of light-weight objects. Wespeculate that our results pave the pathways towards the design and implementation of amorphous biological robots.Keywords: biological computing, amorphous robots, unconventional computation, amoebaCopyright 02008, Jili University. Publisbed by Science Press and Elsevier Limited. All rights reserved.maze-solving23), calculation of efficient networkst ,1 Introductionconstruction of logical gates', formation of VoronoiPlasmodium, the vegetative stage of slime moulddiagraml'), and robot control9.Physarum polycephalum, is a single cell, with thousandsThe oscillatory cytoplasm of the plasmodium canof diploid nuclei, formed when individual flagellatedbe seen as a spatially extended nonlinear excitable me-cells or amoebas of Physarum polycephalum swarmdial01. In our previous papers we hypothesized that thetogether and fuse. The plasmodium is visible by nakedplasmodium of Physarum is a biological analogue of aye. When a plasmodium is placed on an appropriatechemical reaction-diffusion system encapsulated in ansubstrate, it propagates and searches for sources of nu-elastic and growing membranel2l. Such an encapsula-trients (bacteria). When such sources are located andtion enables the plasmodium to function as a mas-taken over, the plasmodium forms veins of protoplasm.sively-parallel reactiondifusion computer-ol and alsoThe veins can branch, and eventually the plasmodiumto solve few tasks which reaction-diffusion computersspans the sources of nutrients with a dynamic proximitycould not do, e.g. construction of spanning treesh4, andgraph, resembling, but not perfectly matching graphsimplementation of storage modification machinests.from the family of k-skeletons'.Also, under certain experimental conditions, the plas-A large size of the plasmodium allows the singlemodium exhibits tavlling self-localizations, imple-cell to be highly amorphous. The plasmodium showsments cllision-based logical circuits and thus is capablesynchronous oscillation of cytoplasm throughout its cellof universal computation'body, and oscillatory patterms control the behaviours ofBeing encapsulated in an elastic membrane thethe cell. All the parts of the cell behave cooperatively inplasmodium can be capable of not only computing overexploring the space, searching for nutrients and opti-spatially distributed data-sets but also physically ma-mizing network of streaming protoplasm. Due to itsnipulating elements of the data- sets. If a sensible, con-unique features and relative ease of experimentationtrollable and, ideall, programmable movement of thewith, the plasmodium becomes a test biological sub-plasmodium and manipulation by the plasmodium couldstrate for implementation of various computational tasks.be a中国煤化工for experimentalThe problems solved by the plasmodium includeimpleYHCNMHGotic devices. ThereCorresponding author: Andrew AdamatzkyE-mail: andrew.adamatzky@uwe.ac.ukAdamatzky and Jones: Towards Physarum Robots: Computing and Manipulating on Water Surface349are already seeds of an emerging theory of artificialPhysarum network conectivity, the laboratory experi-amoeboid rosl1-191.ment configurations were used to map a synthetic enIn present paper we undertook a set of scopingvironment for the model organism. Modelling resultsexperiments on establishing links between Physanumwere presented alongside the“wet" Physarum results tocomputing and Physarum robotics. We have chosensupport the approach. Detailed description of the modelwater surface as a physical substrate for the plasmodiumwas provided in Ref. [20], and a brief overview of thedevelopment to study how topology of the plasmodiummodel is given below.network can be dynamically updated, without beingThe model takes a multi-agent approach to modelstuck to a non-liquid substrate, and how small objectsemergent transport networks. A population of agents,floating on the surface can be manipulated by the plas-adopting simople stimulus-response behaviours, is cou-modium's pseudopodia. Laboratory experiments usingpled to a two-dimensional discrete map representing thePhysarum may sometimes prove difficult due to the factproblem configuration (the “data” map). Food sourcethat the computing substrate is a living organism subjectstimuli are projected to another coupled map (the“uail"to the influence by changes in environmental conditions.map) at their locations at every step of the scheduler, andAlthough Physarum is a very resilient organism, thethe stimuli are diffused by means of a simple 3x3 meanexperimental results show natural variation. For thisfilter kernel. The food source stimulus is dampedreason, laboratory prototypes were supplemented by a(food_ source_ valuex0.1) to maintain a steep diffusionsimple model of Physarum like network behaviours,gradient away from the food source.using the emergent multi-agent approach to constructThe agent population (size: %p, where “p" is thedynamic transport networks'ou. Video recordings ofarea in pixels of the environment) is initialised withlaboratory experiments and computer simulations arrandom agent positions and random agent orientations.available at htp:/:/uncomp.uwe.ac.u/jbe/Agents can be inoculated at particular locations (forexample food sources) and new agents are initialised at2 Methodsthe front of plasmodium growth according to local 0C-Plasmodium of Physarum polycephalum was cul-cupancy measures. These measures are based on a localtivated on a wet paper towel in dark ventilated containers,window surrounding each agent (0w), a minimum OC-oat flakes were supplied as a substrate for bacteria oncupancy threshold (omin), and a maximum thresholdwhich the plasmodium feeds. We used several test are-(0mx). In tbese results Ow = 3x3 window, 0mim> 0 andnas for observing behaviour of the plasmodium and0max<4.scoping experiments on plasmodium induced manipu-The morphology of each agent is shown in Fig. 1.lation of floating objects. These are Petri dishes withThe agents sense the concentration of stimuli in the trailbase diameters of 20 mm and 90 mm, and rectangularmap by three forward oriented sensors (offset 9 pixels inplastic containers with size of 200 mm x 150 mm. Thethese examples and set, directly in front, to the left and todishes and containers were flld by 1/3 with distilledthe right at 45 degree angles). At each scheduler step thewater. Data points, to be spanned by the plasmodium,agents orient themselves towards the strongest trailwere represented by 5 mm to 10 mm sized pieces ofsource by rotating left or right (by 45 degrees), de-plastic foam, which were either fixed to bottom of Petripending on the source of the stimuli. After the sensorydishes or left floating on water surface (in case of largestage every agent attempts to move forward in its currentcontainers). Oat flakes were placed on top of the foamdirection (represented by an intermal state from 0 degreespieces. Foam pieces, where plasmodium was initiallyto 360 degres). If the new cell is not occupied, the agentplaced, and the pieces with oat flakes were anchored tomoves to the new cell and denosits trail onto the trailthe bottom of containers. Tiny foam pieces to be ma-mapa中国煤化工cannot move for-nipulated by plasmodium were left free floating.wards;YHCNMHGonismadeontheTo provide the computer model approximation oftrail map. Inertial movement for each agent is provided350Joumal of Bionic Engineering (2008) VoL.5 No.4by maintaining a floating point representation of thecordings, the brightness is inverted, ie. brightest valuescurrent position, as well as the discrete position corre-indicate food sources and the greatest plasmodium flux.sponding to the image structure. This efectively allows" The borders of the model“dish" are indicated by uni-the agents to“"slide past" one another even when the nextform greyscale values.cell is occupied (the occupation can only actually hap-3 Results: Computing and manipulatingpen when a cell becomes free). The inertial behaviourresults in the emergence of surging movements in theTo demonstrate that a substrate is suitable for ro-population and corresponds to the spatial oscillationsbotics implermentations one must demonstrate that theseen in Physarum. The strength of the oscillations can besubstrate is capable of sensing of environment and re-reduced by firing a“change direction" event (pCD) withsponse to extermal stimulus, solving complex computa-probability 0.05 (in these result). When a pCD event istional tasks in spatially distributed data sets, locomotion,triggered for an agent, the floating point position is re-and manipulation of objects. We provide basic demon-stored to the discrete position and a new direction is strations which may indicate that plasmodium of Phy-randomly selected. The efect is to dampen the surge ofsarum polycephalum can be successfully used in futuremovement caused by the inertial behaviour.experiments on laboratory implementations of amor-Sensor widhpbous biological robots.The surface of water is in tension therefore itFL所Rphysically supports propagating plasmodium, when itscontact weight to contact area ratio is small. WhenSensor fset lengthplaced in an experimental container the plasmodiumsmorumangle hforms pseudopodia aimed to search for sources of nu-trients. In most experiments“growth part” of the pseu-dopodia has tree-like structure for fine detection ofchemo-gradients in the medium, which also minimizesFig, 1 Morphology of agent particle. For these simulations, sen-weight to area ratio. Examples of tree-like propagatingsor width = I, sensor arm angle = 45 degrees, rotation angle = 45pseudopodia are shown in Fig.2.degrees, sensor offset distance = 9 pixels, and the distance movedper step was 1 pixel.The list comprising the agent population is trav-ersed in a random order for both the sensory andmovement stages to avoid any influence from sequentialpositional updates. In the current model the maximumpopulation size is manually assigned, based on a pro-portion of the size of the problem configuration area.a)Work is in progress to automatically assign the popula-tion size in relation to food source availability. To visu-alise the evolution of the system behaviour the values ofthe trail map are dynamically scaled (based on themaximum and minimum curtent trail values) to the 8-bitrange, and the trail levels are interpreted as a greyscalebrightmess map. In the printed matter results foodsources are indicated by very dark grey values for clarity中国煤化工and the darkest regions of the synthetic plasmodiumFig. :CHC N M H Gneatal arena by prop-.indicate areas with the greatest flux. For the video re-gating tre-ike pseudopodia.Adamatzky and Jones: Towards Physarum Robots: Computing and Manipulating on Water SurfaceIn Fig. 2b we can see that pseudopodia not alwaysWhen the plasmodium spans sources of nutrients, itgrow towards sources of outrients, there is a pseudopo-produces many “redundant" brancbes Fig. 3). Thesedia growing south-west, where no sources of nutrientsbranches of pseudopodia are necessary for space ex-located. This happens possibly because in large sizedploration but do not represent minimal edges connctingcontainers air volume is too large to support a reliablethe nodes of the spanning tree. These “redundantand stationary gradient of chemo-attractants. This maybranches are removed at later stages of the spanning treepose a difficulty for the plasmodium to locate and spandevelopment. See a well. established spanning tree ofall sources of outrients in large- sized containers.data-points in Fig. 4. lnitially the plasmodium wasIn Petri dishes air volume is small and, supposedlyplaced in the westerm domain, and the plasmodium hasthe air is stationary, therefore plasmodium easily locatesconstructed the spanning tree in 15 bours. Fig. 5 showssources of nutrients Fig.3). It thus builds spanning treesthe model organism migrating to connect the tree andwhere graph nodes (to be spanned) are presented byminimising the surface area of the tree.pieces of foam with oat flakes on top. In Fig. 3 we cansee that originally the plasmodium was positioned at tbesoutherm domain. In twelve hours the plasmodium buildsa link with westem domain, and then starts to propagatepseudopodia to the eastern domain.Fig. 4 Spanning tree of three points constructed by the plasmo-dium.(a) Start●●●(a) Inoculation + 180 stepsFig. 5 Evolution of model Plhysarum connecting the spanning tee.Oat flakes are shown by black discs. Plasmodium is seen asamorphous mass. The plasmodium was inoculated on the west-most flake (a). It exhibits strong foraging behaviour (b, c) andevenhWhen all sources of(b) 12 hoursnutrie中国煤化工: dep cocactivitprotoplasmic tube (e).Fig. 3 Plasmodium builds links comecting its original domain ofOn theYHresidence with two new sites.as darker parts of the plasmodium.352Journal of Bionic Engineering (2008) Vol.5 No.4We demonstrated that the plasmodium does explorespace and computes a spanning tree on the water surface,when placed itally on one of the floating objects.Would the plasmodium be as well operational whenplaced just on the surface of water? As shown in Fig. 6the plasmodium works perfectly. We placed a piece ofplasmodium on bare surface of water (Fig. 6, start). Inthree hours the plasmodium forms an almost circularfront of propagating pseudopodia, which reach two sta-tionary domains with oat in eight hours (Fig. 6).(b) 490 stps(c) 1050 steps(a) Sturt(d) 2040 steps(b)3 hours中国煤化工(C) 3590 stepsFig..FYHCNMHGonthewatersurf.ceFig 5 Continued.and occupics two sources of nutrients.Adamatlky and Jones: Towards Physarum Robots: Computing and Manipulating on Water Surface353(b) 12 hours later(d) 8 hoursFig. 6 Contimued.In usual conditions (on a wet solid or gel substrate)edges of spanning trees, presented by protoplasmic tubes,adhere to the surface of the subatartel:.14,15. Thereforethe edges cannot move, and the only way the plasmo-dium can do a dynamical update is to make a proto-plasmic tube inoperative and form a new edge instead(membrane shell of the ceased link will remain on thesubstrate, e.g Ref. [15]). When plasmodium operates on(C)water suface, the cohesion between the water surfaceand the membrane of protoplasmic tubes is small enoughfor the protoplasmic tubes to move freely. Thus theplasmodium can make the tubes almost straight and thusminimize costs of tbe transfer and communication be-tween its distant parts. Two examples of the straighten-ing of the protoplasmic tubes are shown in Fig. 7. Suchstraightening is a result as the tubes become shorter dueto contraction. The straightening of protoplasmic tubeswas also observed in the model organism (Fig. 8).(d) 12 hours laterFig. 7 Continued.Fig.7 Examples of straightening of protoplasmic tubes. In pho-中国煤化工tographs (a) and (c) tubes are longer than necessary. In photo-graphs (b) and (d) the tubes corTespond to minimal shortest pathFig..MHCNMHGodel! as the tube com-betweea the sites they are connecting.neccting the two food sources is tightened.354Journal of Bionic Engineering (2008) Vol.5 No.4(b) 720 steps(a)0 hours(c) 1590 steps(b)5 hours(2)9 hous(d) 3650 stepsFig 8 Continued.The presence of contraction may indicate that iftwo floating objects (both with sources of nutrients) areconnected by a protoplasmic tube then the objects willbe pulled together due to shortening of the protoplasmictube. We did not manage to demonstrate this exactphenomenon of pulling two floating objects together,however we got experimental evidence of pushing andpulling of single floating object by the plasmodium's中国煤化工pseudopodia. The plasmodium-induced pushing ande plasmodium can push.MYHCN M H C be pushed s ndicacepuling are exemplified in Figs. 9 and 10.by white arow in the furst pbotograph.Adamatzky and Jones: Towards Physarum Robots: Computing and Manipulating on Water Surface355(e) 16 hours(d) 22 hoursFig. 9 Continued.(a)0 hoursFig 10 Continued.To demonstrate pushing we placed a verylight-weight piece of plastic foam on the water surfacenearby the plasmodium (Fig. 9, 0 bours). The plasmo-dium develops a pseudopodium which propagates to-wards the light-weight piece of foam (Fig. 9, 5 hours).Due to gravity force acting on the pseudopodia a rippleis formed on the water surface (Fig. 9, 9 hours), whichcauses pushing the piece of foam away from the growingpseudopodia's tip Fig.9, 13 hours). Due to the absence(b)15 hoursof any nutrients on the pushed piece of foam, the plas-modium abandons its attempt to occupy the piece andretracts the pseudopodia (Fig. 9, 16 hours). The pieceremains stationary: it becomes shifted away from itsoriginal position.In the second example, Fig. 10, we observe thepulling of the light-weight object. The piece of foam tobe pulled is placed between two anchored objects (Fig.10, 0 hours). One object hosts the plasmodium another(C) 17 hoursobject b中国煤化工acts the plasmo-dium).le plasmodium'sFlg. 10 Photographs demwonstrate that the plasmodium can pulllightweight object. The object to be pulled is indicated by whiteoniginalMYHCN MH Gn the surerarToW in the first pbotograph.utrients. The pseudopodium occupies the piece of foam356Joumal of Bionic Engneing (2008) Vol.5 No.4(Fig. 10, 15 hours) and then continues is propagationerations. To translocate nodes selectively in the storagetowards the source of nutrients. When the source ofstructures we may need to assign certain atributes. Thisnutrients is reached (Fig. l0, 22 hours) the protoplasmiccan be done by marking nodes with different species oftubes connecting two anchored objects contract andcolors. In Ref. [15] we demonstrated that the plasmo-straighten thus causing the light-weight objects to bedium exhibits strong preferences to certain food col-pulled towards the source of nutrients (Fig. 10, 32 hours). ouring, is neutral to others, and that some food colour-The pushing and pulling capabilities of the plasmodiumings repel the plasmodium. Such preference hierarchycan be utilized in constructions of water-surface basedcan be mapped onto the mobile data storage structure.distributed manpulatr(1321.More future experiments are required indeed todevelop ideas derived from our scoping experiments to4 Discussionthe full working prototypes of the Physarum robots andInspired by biomechanics of surface walking in-mechanical Kolmogorov-Uspenski machines.sect229, our previous studies on implementation ofReferencescomputing tasks in the plasmodiumls, and our ideas[] Kirkparick D G Radke J D. A famnewok for computaionalon design and fabrication of biological amorphous r0-morpbology. In: Toussaint GT (ed), Computational Geometry,bots20), we decided to explore operational capabilities ofNorth-Holland, Amsterdam, 1985.plasmodium of Physarum polycephalum on the water[2] Nakagaki T, Yamada H, Toth A. Maze-solving by ansurface. We were interested to demonstrate that theamoceboid organism. 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