A Distributed Epigenetic Shape Formation and Regeneration Algorithm for a Swarm of Robots
Rahul Shivnarayan Mishra, Tushar Semwal, Shivashankar B. Nair
AA Distributed Epigenetic Shape Formation and RegenerationAlgorithm for a Swarm of Robots
Rahul Shivnarayan Mishra
Indian Institute of [email protected]
Tushar Semwal
Indian Institute of [email protected]
Shivashankar B. Nair
Indian Institute of [email protected]
ABSTRACT
Living cells exhibit both growth and regeneration of body tissues.Epigenetic Tracking (ET), models this growth and regenerativequalities of living cells and has been used to generate complex 2Dand 3D shapes. In this paper, we present an ET based algorithm thataids a swarm of identically-programmed robots to form arbitraryshapes and regenerate them when cut. The algorithm works in adistributed manner using only local interactions and computationswithout any central control and aids the robots to form the shapein a triangular lattice structure. In case of damage or splitting of theshape, it helps each set of the remaining robots to regenerate andposition themselves to build scaled down versions of the originalshape. The paper presents the shapes formed and regenerated bythe algorithm using the Kilombo simulator.
CCS CONCEPTS • Theory of computation → Self-organization ; •
Computersystems organization → Robotics ; KEYWORDS
Epigenetic Tracking, Swarm Robotics, Nature-inspired, Distributed,Decentralized
ACM Reference Format:
Rahul Shivnarayan Mishra, Tushar Semwal, and Shivashankar B. Nair. 2018.A Distributed Epigenetic Shape Formation and Regeneration Algorithm fora Swarm of Robots. In
GECCO ’18 Companion: Genetic and EvolutionaryComputation Conference Companion, July 15–19, 2018, Kyoto, Japan,
JenniferB. Sartor, Theo D’Hondt, and Wolfgang De Meuter (Eds.). ACM, New York,NY, USA, 8 pages. https://doi.org/10.1145/3205651.3208300
Almost all biological beings are aware of their shape and size. Manyresearchers have strived to mimic these complex physical and cog-nitive living entities in the form of a Single Robot Systems (SRS).An SRS is aesthetically and physically closer to these beings butis indeed a highly sophisticated system. Simple small robots withinsufficient capabilities may not be able to perform complex tasksthat an SRS could perform, but a collection of a large number of
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GECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan © 2018 Association for Computing Machinery.ACM ISBN 978-1-4503-5764-7/18/07...$15.00https://doi.org/10.1145/3205651.3208300 simpler robots having limited capabilities which cooperate to fulfila goal might be able to perform as effective and efficient as an SRS.The goal could be some form of self-organization such as to main-tain a particular shape formation . If we consider each robot in sucha swarm to be the basic unit of a body, then the swarm metaphorizethe biological being. A swarm of robots collectively executing a taskcan be more robust, adaptive and efficient as compared to the SRS.Swarms play a significant role in applications such as exploration ofinaccessible areas and mapping [4, 21], hazardous tasks executions[12], pattern formation [17], collective transportation [7], etc.Algorithms for shape formation could be classified into thosethat use leader/neighbour-following methods, potential field basedones and those that are nature-inspired. In the first type [1, 3, 10],the primary goal is to follow the leader which in turn has all theinformation required to make the moves. The robots need to ar-rive at a consensus and the notion of a leader gives the overallsystem a centralized flavour. However, these works constitute rig-orous theoretical proofs which makes them relatively complex [16].In the potential field based methods [8, 11, 15], the robots followpotential field gradients which constitute the resultant of virtualattractive and repulsive forces. Though successfully implementedin several scenarios, the robots may get stuck at local optimal points[16]. Nature-inspired shape formation algorithms are based on themanner in which swarms function in an inherently distributed anddecentralized manner. A swarm can be made to achieve a goal usingeither a centralized or a decentralized approach. The former mayseem simple and faster but is not always an appropriate solutionsince the swarm is dependent on a single controlling entity. If thisentity fails, the entire system can collapse. Further, centralized con-trol is difficult and expensive to scale. A decentralized approachseems much more efficient and robust. Nature solves a gamut ofproblems using such decentralized and distributed approaches. Re-searchers have thus proposed several bio-inspired algorithms.Cheng et al. [2] describe a pheromone and flocking inspiredgas expansion model for coordinating a swarm of identically pro-grammed robots to spatially self-aggregate into arbitrary shapesusing only local interactions. Rubinstein et al. [17] have proposeda self-assembly algorithm to build shapes using a swarm of Kilo-bots robots that have limited capabilities. Their algorithm doesnot support regeneration and thus cannot evolve to form the sameshape when some portion of it is cut off. The improvised versionof this work is described in [19] wherein the authors augmenta self-repairing feature. The repair of the mutilated shape, how-ever, requires the human being to intervene and provide the num-ber of remaining robots in the swarm, thus making the systemsemi-autonomous. George et al. [6] describe a cell-based program-ming model capable of creating symmetrical shapes such as cubes, a r X i v : . [ c s . R O ] O c t ECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan Rahul Shivnarayan Mishra, Tushar Semwal, and Shivashankar B. Nair spheres, etc. using numerous cells. If the shape were to be cut ordamaged, the cells within detect the same and regenerate or self-heal the destroyed portion. Apart from these, a few bio-inspiredalgorithms based on hormones [18, 20, 22] and cellular mechanisms[14, 23] have also been reported. Gene regulatory networks havealso been employed for shape formation in changing environments[9, 16, 23]. Though they augment their work with real-robot experi-ments, the differential equations used to implement the kinematicsinvolved can make the system complex.An algorithm for a set of robots to generate and regenerateshapes needs to be simple, distributed and decentralized, autonomousand be capable of handling variable-sized complex shapes. Nature-inspired algorithms provide for comparatively simple mechanismswith lower computational overheads [24]. They are inherently dis-tributed and decentralized and hence have an edge over other con-ventional methods for shape formation and regeneration.Epigenetic Tracking (ET), first introduced by Fontana [5], is onesuch algorithm which models the growth and regenerative qualitiesexhibited by a colony of cells found in a living body. ET is definedas the method to generate arbitrary 2D and 3D shapes by usingevolutionary techniques. It explains the process by which a seedgrows into a whole living being. In nature, we can find certainpeculiar species which have a peculiar tendency to grow their bodyparts. For example, a lizard regrows its tail after it sheds it off, whilea starfish regenerates its leg if it is cut off. Human babies when insidethe mother’s womb, are capable of regenerating their limbs. Allthis regeneration is done by the body cells themselves without therequirement of any central system. Each cell contains a gene whichdecides the shape of a being. A cell divides and replicates itself asper the gene within the cell. A gene is similar to an instructionmanual which aids cells to reproduce and form arbitrary shapes.In this paper, a distributed novel Epigenetic Tracking based shapeformation and regeneration algorithm has been proposed for aswarm of robots. Each robot is modelled in the form of a cell con-taining a gene. The algorithm is tested on Kilobots [17] which aresmall robots with limited computation and wireless communica-tion capabilities. Experimental results performed using a simulatorhave been presented. To the best of our knowledge, this is the firstoccurrence of a work where ET has been used for shape formationand regeneration in a swarm of robots.Subsequent sections of this paper describe the shape formationand regeneration problem, the algorithm and associated terminolo-gies and the results and conclusions.
In this section, we have discussed the problem of shape formationand regeneration by a swarm of robots using a decentralized algo-rithm. The same is followed by a detailed description of the variousterms and methods used in the algorithm.
This paper focuses on the problem of shape formation and shaperegeneration exhibited by a swarm of robots without a centralcontroller. All the robots are aware of the target shape, and theywork collectively to form a given shape and is capable of detectingany damage done to the shape. The damage could be in the form
Figure 1: A sample input bitmap image of shape ‘T’ of removal or failure of robots. After detecting the damage, theremaining robots work collectively to form a smaller scaled versionof the specified shape. The primary objective is thus to use onlylocal interactions and computations onboard the robots to onceagain reorganize, assemble and regenerate the original shape withthe remaining robots in the swarm.We propose the use of an Epigenetic Tracking based algorithmcapable of running on small, low-cost robotic platforms such asKilobots [17]. Kilobot is one such robotic platform which has limitedcomputational capabilities and is capable of achieving short-rangeomnidirectional communication with their neighbours via infraredrays. They are devoid of any other sensor. The algorithm is state-based, meaning that a robot is always in a unique state. A robot thusperforms an action(s) based on its current state and the informationobtained from the neighbouring robots.
Epigenetic Tracking (ET) models the biological development pro-cess found in living cells. Coupled with evolutionary techniques,the model is capable of generating complex 2D or 3D shapes fromartificial cells. In this model, an entire shape emerges from a singlecell through a sequence of two actions, mitosis and apoptosis . Mi-tosis is the process of cell division where a cell produces a cloneof itself. Apoptosis is programmed cell death, which keeps controlof cell population. The two actions are driven and directed by agene. A gene is a long strand of encoded information used by a cellto decide whether it has to perform mitosis or apoptosis. After aseries of cell actions, the desired target shape emerges from a singlecell. A gene is similar to an instruction manual which guides theprocess for the shape formation.Inspired by this simple distributed and robust shape formationtechniques modelled by ET, we propose a biologically inspiredalgorithm for shape formation and regeneration exhibited by aswarm of robots. Each robot has a unique ID and is modelled as acell containing a gene which has encoded information about thetarget shape. The algorithm takes the input in the form of a binaryimage with given rows and columns while the output is a swarmof robots positioned in the manner similar to the image. A sampleinput in the form of a binary image to form a ‘T’ shape is shownin Fig. 1. Since the pixel values are either or , the image will bereferred to as a bitmap array where denotes the presence of arobot which is part of the shape while a represents a void space. Distributed Epigenetic Shape Formation and Regeneration Algorithm for a Swarm of RobotsGECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan
Figure 2: Transformation of arrangement used in the pro-posed algorithm
The number of s indicate the consensus of robots required to formthe shape, and thus each robot initially knows about the currentswarm population.Given an input binary image, the gene required for the shapeformation is computed and transferred to all the robots constitutingthe swarm. The robots (or cells) then use this gene to form a shapein a distributed and decentralized manner. In this work, we havetaken the coordinates of the central pixel of the input bitmap (redcoloured in Fig. 1) as the reference or origin. The position of theremaining pixels is described and used with reference to this origin.It may be noted that coordinates of any pixel could be chosen asthe origin. Though the use of the Cartesianarrangement shown in Fig. 1 is straightforward, it suffers fromthe fact that all the neighbours of a are not equidistant. The sat the diagonal points are at a farther distance than the s at theedges. This can lead to instability especially while real robots areused to form shape. Before computing the gene, the input imageis thus, skewed in a manner that every robot is equidistant fromthe other. We followed a simple process to generate the skewedimage. Consider the input shape in Fig. 2. The top row of the imageis first shifted left by half the distance between the two pixels (ortwo adjacent s or s in the row). We then shift this row leftwardsalong with the one just below it together by another half distance.In the next step, the top row and the two rows immediately belowit are shifted leftwards together, by the same distance. This shiftingprocess is repeated till eventually, the whole image gets skewed toform a triangular lattice structure.The computation steps involved in the making of the gene aredescribed in the following subsections. In the current context, the metaphorgene is a collection of 1-Dimensional ( D ) vectors each with threefields of information – a Tag (Tg) which denotes a pair of X and Y location coordinates, a Flag (F) and the number of
Nearest Neighbors (NN) of a robot at the corresponding (X,Y) location. To compute agene from an input binary image, the Tд , the F and the NN fields ofinformation for each pixel value in the input image is calculated andconcatenated to create a table of 1- D vectors. This table forms thegene for a given shape. The significance of each of the constituentsof these vectors is presented below:(1) Tag ( Tд ): Tag is the (X,Y) pixel coordinate of the input bitmap.For e.g., Tд for the origin is (0,0). It aids the robot in deter-mining its position within the swarm.(2) Flag ( F ): If a bit at a coordinate (X,Y) is equal to 1, the re-spective flag is set to 1 else it is set to 0. The flag represents (a) (b) Figure 3: (a) A skewed input bitmap image of an arbitraryshape (b) Computed gene whether a robot at a position (X,Y) is inside the shape (F = 1)or outside the shape (F = 0).(3) Number of Nearest neighbors ( NN ): This is a value rangingfrom 0 to 6 which indicates the number of nearest neighborsa robot at a position (X,Y) is allowed to have. The NN valuefor a bit at location (i,j) in the input bitmap image is equal tothe number of s at the location (i-1,j), (i-1,j+1), (i,j+1), (i+1,j),(i+1,j-1) and (i,j-1).Fig. 3a and 3b shows an input bitmap image and the computedgene, respectively. As an example, the (X,Y), F and the NN valuesfor the bit at the centre of the bitmap image shown in Fig. 3a are(0,0), 1 and 6, respectively.A robot at a location (X,Y) is aware of the count of closest neigh-bours it is supposed to have by looking into the gene with thetag (X,Y). These neighbours should be at an equal distance say aconstant d so that the robot can differentiate them from the rest ofthe swarm. Since all the robots maintain a distance of d from eachother, they form a triangular lattice structure as shown in Fig. 2.After forming the shape, the robot keeps monitoring this count. Ifit decreases, the robot discerns that formed shape is harmed. Thus,damage detection forms the primary aim of triangular lattice ar-rangement. The sole purpose of the SCS was to have a coordinatesystem which allows unique referencing of robots in the triangularlattice arrangement. In this section, we propose an ET based distributed and decentral-ized algorithm for shape formation and regeneration in a swarm ofrobots.
The overall process of shape formation and regeneration exhibitedby a swarm of robots using the proposed algorithm, follows a Dis-crete Finite Automaton (DFA) with eight states namely,
Queued , Search , Inactive , Active , Quasi , Stable , Danдer and
Leader . Table1 provides an abstract description of each of these states. Since
ECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan Rahul Shivnarayan Mishra, Tushar Semwal, and Shivashankar B. Nair the process of regeneration is after shape formation and for thesake of clarity, the algorithms for both the processes, i.e., formationand regeneration has been explained separately using the statesdescribed in Table 1.We also introduce a gradient value termed the Timestep (TS) inthe proposed algorithm. Every robot which has been placed in theshape has a gradient value TS to assist robots in reaching
Stable state according to their order of arrival. Robots in the
Search stateswho are trying to determine their new locations during the shapeformation process always try to locate themselves near a robot inthe
Active state with minimum TS value compared to their otherneighbours in
Active state. Consider two robots R A and R B in the Active state with TS values 4 and 5 respectively. This indicatesthat the NN criteria for R A needs to be fulfilled first as R A wasplaced into the shape/cluster before R B . The TS thus prevents theformation of holes or gaps in the shape which would then causethe shape to become irregular at the end. The proposed algorithm for shape for-mation needs a minimum of three seed robots which need to beplaced at the vertex of an equilateral triangle. These seed robots actas an initial frame of reference for the trilateration process executedby other robots to know their location information. The seed robotsare respectively initialized with an (X,Y) coordinate, a state, an NN value and a TS. The (X,Y) coordinate for one of the seed robotsis chosen randomly from the gene. The coordinates of the othertwo are taken from the appropriate neighbours from the gene. Thelocation of the seed robots decides the position and orientationfrom where the shape formation will commence. The NN valuesfor the corresponding coordinates are also taken from the gene andstored within, by each robot. One of these robots is set to the Active state with TS equal to 1, while the other two are initialized to the
Inactive state with a TS of 2. After the seed robots are initialized, therest of the robots in the
Queued state concurrently start to executethe Algorithm 1 to eventually form the shape represented by thegene.Robots in the
Queued state, one after another, transits to the
Search state and start searching for a location to occupy around thealready placed robots (initially the seed robots). A robot decideson which location to place itself by using the process explained inSec. 3.1.3. After the robot places itself, it moves to the
Inactive stateif its neighbour count is less the NN value of the correspondingtag (X,Y) acquired by the same robot and one of its neighbours isin the Active state. The same robot transits to the
Stable state ifits neighbour count becomes equal to the NN value. This series oftransitions from Search state to the
Stable state is followed by eachof the robots in
Queued state until they all are in the
Stable stateand the shape formation is accomplished.
In practical scenarios, a shape formedby a swarm of robots could get damaged due to various reasons suchas malfunctioning of a robot(s), removal of a robot(s), discharge ofthe batteries, etc. Hence, it is necessary that the same algorithmshould facilitate the robots first to detect the damage to the shapeand secondly allow them to reorganize to form a scaled-downversion of the same shape with the remaining number of robots. If arobot(s) in the
Stable state finds that its neighbour count has becomeless than the value NN stored within, it transits to the
Danger state,
Table 1: States and their descriptionState Description
Queued
All robots are initially in a swarm repository in a con-nected form. Using broadcasts, these robots find theone having the lowest ID. This robot changes its stateto
Search and moves out of the repository towards theseed robots to localize itself. The robot with the nextlowermost ID moves out after a predetermined amountof time.
Search
Robots in this state search for a location within theshape by moving along the periphery of the currentlyformed shape. After finding an appropriate location, therobot places itself and transits to the
Inactive state.
Inactive
In this state, the robot continuously monitors all of itsnearest neighbours which are in the
Active state. Assoon as a neighbour in an
Active state transits to the
Stable state, the robot in the
Inactive state transits tothe
Active state. This transition avoids the chances ofgaps/holes appearing within the shape.
Active
A robot remains in this state till the NN value storedwithin it matches the actual number of neighbours.When these two values are equal, the robot transitsto the
Stable state. If a robot in the
Active state noticesone of its nearest neighbours to be in the same state buthaving a TS value less than its own, it transits to the
Quasi state.
Quasi
A robot in the
Quasi state transits to the
Active stateafter a predetermined time.
Stable
Robots in this state form part of the final shape. Theserobots continuously count their neighbours to ensurethat the shape is maintained. If they detect the absenceof any, they transit to the
Danger state.
Danger
Robots in this state participate in the process of leaderelection. The robot with the minimum ID amongst theserobots is elected the leader which in turn transits to the
Leader state.
Leader
The robot in this state estimates the number of remain-ing connected robots in the fragment of the shape, gen-erates a scaled-down version of the given shape (gene)and communicates the same with the remaining con-nected robots. Finally, it selects two of its neighboursto form the initial three seed robots to start the shapeformation once again using the remaining robots. TheLeader then transits to the
Active state. Those fromthe set of remaining robots whose coordinates matchthat within the new version of the shape transit to the
Inactive state while the rest move to the
Queued state.constituting the first step in the shape regeneration process. Thesecond step comprises execution of the following sequential phases:(1)
Leader Election : As soon as the damage is detected, therobots in
Danger state compete with those in the same stateand elect their leader. We have used the classical methoddescribed in [13] for this leader election, wherein each robot
Distributed Epigenetic Shape Formation and Regeneration Algorithm for a Swarm of RobotsGECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan
Algorithm 1
Algorithm for the shape formation by the swarm ofrobots while TRUE do if State ==
Queued then if Id == Minimum then State ← Search ; {the robot has the lowest Id among allthe
Queued robots} end if end if if State ==
Search then MoveTillActiveRobot () ; {Move along the periphery of al-ready formed shape until an Active state robot is encoun-tered} Flag ← Localization () ; {as per the Sec. 3.1.3} if Flag == 1 then
Initialize ( TS , N N ) ; State ← Inactive ; end if end if if State ==
Inactive then if Any neighbor move from
Active to Stable state then
State ← Active ; end if end if if State ==
Active then if TS of neighbor < TS then State ← Quasi ; end if if number of neighbors == NN then State ← Stable ; end if end if if State ==
Quasi then
W aitForTime ( T ) ; { T is a predetermined constant} State ← Active end if if State ==
Stable then if number of neighbors < NN then State ← Danger ; Alдorithm -2(); end if if New bitmap image received then
State ← Queued ; end if end if end while in the Danger state broadcasts its ID. Robots in the
Danger state, which receives an ID lower than their own, back offfrom the election process and retransmits the lower ID tothe others. Eventually, the one which does not receive anyID lower than its own for a certain defined time, transits tothe
Leader state.(2)
Census : The robot in the
Leader state now performs a countof the functional robots in the remnant of the shape it belongsto, by navigating around it and acquiring the Tд of all the Figure 4: Position determination by robots robots stationed on the periphery of this shape. When the
Leader reaches its original position again, it starts to mapthese coordinates onto the input bitmap image. By doing so,the Leader obtains the closed area bounded by the remnantshape. By counting the number of s on the boundary of thisclosed (remnant) shape, the Leader ascertains the number ofremaining robots and thereby concludes the census.(3) Generation of Scaled Image : Using the count (say n ) ofthe remaining robots in the remnant and the number ofrobots (say N ) in the original shape, the Leader estimates thenumber of robots, say K , that have been segregated ( K = N - n )and recreate a scaled-down version of the original shape. Theleader recreates the scaled image by deleting the s presenton the boundary of the current bitmap. The deletion is donesequentially and those s which makes the triangular latticearrangement unstable are skipped .(4) Sharing Scaled Shape and Seeding : The Leader shares thenew scaled down version of the image with all the n robotswithin the remnant, transforms itself to a seed robot andchooses two of its neighbours as the other two seeds. Theremaining n robots become aware of the change in shapeand hence transit to the Queued state, and the process ofshape generation commences again as in Algorithm 1.
During the process of shapeformation, the moving robots determine their appropriate locationwithin the shape being formed using the trilateration to determinetheir position globally. The trilateration method used in this algo-rithm is different from the conventional one as since we use ourown SCS.The robot herein does not use the formulae in trilateration todetermine its (X,Y) coordinates. Instead, it localizes itself by usingthe coordinates of its neighbours. For instance in Fig. 4, R , R and R are the three robots already placed in the shape, each at adistance d from the other. Using SCS, the incoming robot R , detects R , R and R and discovers that it can possibly occupy positions(1,1) or (0,-1). However, since R occupying (0,-1) is also in thecommunication range of R , the latter founds that the position (0,-1) is already taken. Thus, R assumes that it can localize itself at(1,1). R can localize itself at (1,1) only if the flag stored against (1,1)within the gene is 1 and one of its neighbours is in the Active state.
Please refer to the supplementary file for a detailed graphical visualization.
ECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan Rahul Shivnarayan Mishra, Tushar Semwal, and Shivashankar B. Nair
Figure 5: Generation of alphabet ‘T’ in 2 hours 50 min-utes and 8 seconds Figure 6: Errors during generation of shape‘T’Algorithm 2
Algorithm for the shape regeneration by the swarmof robots while TRUE do if State ==
Danger then LId == LeaderElection () ; {the robot has the lowest Idamong all the Queued robots} if Id == LId then State ← Leader ; else State ← Queued ; Alдorithm -1(); end if end if if State ==
Leader then
CountPopulation () ; {Count the remaining population} GenerateScaledShape () ; {Scale down the input targetshape} Share the new shape with the remaining robot;
State ← Active ; Form new seed robots;
Alдorithm -1(); end if end while
Since this is true in the case shown in Fig. 4, R stores the associated NN value from the gene into its memory and commences to emitits coordinates. To test the efficacy of the proposed algorithm, we used the Kilo-mbo simulator. Kilombo is a C-based simulator developed to testswarm algorithms with Kilobots. The main reason behind the useof this simulator is that the code developed over Kilombo can bedirectly executed on an actual Kilobot. Kilobots are small 3.3 cmtall low-cost mobile robots with minimal computational capability.Instead of traditional wheels, they use vibration motors to effect
Figure 7: Regeneration of Shape ‘T’ sliding movements [17]. The robots can sense and communicatetheir distance from other robots using infrared light reflected offtheir surfaces. They can detect robots up to a distance of 7 cm. Inaddition, the robots can also broadcast messages to others.Each Kilobot was initially provided with the input bitmap imageof the desired shape to be formed and maintained. After feedingthe input image, the Kilobots convert the bitmap into a gene. Theremaining robots were organized in the form of a queue, and therobots were released one by one from the beginning of the queue. Itmay be noted that the remaining robots could be positioned in anydisordered manner provided that they are minimally connected.The initial testing of the algorithm was performed on alphabeticalshapes. Fig. 5 shows the results generated when the simulatedKilobots were fed the bitmap of the alphabet ‘T’.As can be seen from Fig. 5, the Kilobots cooperate and gener-ate the shape of the alphabet ‘T’ in a distributed manner. The line
Distributed Epigenetic Shape Formation and Regeneration Algorithm for a Swarm of RobotsGECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan
Figure 8: Dumbbell shape generation from the givenbitmap image Figure 9: Starfish Shape generation from the givenbitmap image connecting any two Kilobots indicates that they are in the com-munication range of the other. The five differently coloured robotsshown in Fig. 5(a) indicate their respective states. Further, in thesimulator, a moving Kilobot leaves behind a trail to show the pathfollowed by it. A queue of Orange coloured robots in the
Queued state can also be seen in Fig. 5(a), 5(b) and 5(c). The Shape formationof the algorithm starts with the transition of the robots placed atthe end of the queues from the
Queued state to the
Search state.Robots in the
Search state begin moving towards the already placedrobots and place themselves near any robot in the
Active state andthus transit from the
Search to the
Inactive state. The Kilobots startmoving from the end of the queue and place themselves due towhich the shape continues to form as seen in later stages in Fig.5. The proposed algorithm endeavours to be realistic by assumingthat there can be losses in transmission. We have taken an errorprobability of 0.2 (loss in communication) which leads to minor de-formities in the final shape formed. The results of a simulation runwherein, due to errors in message transmission, two of the robots(coloured violet and red) were not in a position to correctly sensethe state transitions of their neighbours is shown in Fig. 6. Thisresulted in their inability to transit to the
Stable state even thoughthe shape was formed. It may be noted that the resulting shape isnot similar to the one observed in the bitmap. The bitmap is in aCartesian coordinate system which gets skewed after adjusting inan SCS, as also shown in Fig. 2. The robots then follow this skewedbitmap and arrange themselves in a triangular lattice form whichfinally results in a skewed target shape.The damage considered in this system consists of the cutting ofthe shape initially formed by the robots, thereby separating theminto two parts. Each of these parts is separately capable of regener-ating the original shape depending on the numbers of remainingrobots in the respective parts. The regeneration of one such partis shown in Fig. 7. The shape was damaged by cutting it vertically(left branch in Fig. 7) and then cutting it horizontally (right branch).The Kilobots whose neighbours went missing, detect this damageand trigger the regeneration algorithm which in turn estimates thenumber of remaining Kilobots in the remnant to eventually reorga-nize to the new scaled down version of the original shape. Duringregeneration, the new shape can have an entirely new orientation as it depends on the coordinates of the initial three seed Kilobots’which mark the start of the shape regeneration algorithm. Othershapes that were considered include the dumbbell and starfishwhose matrix representation and final shapes are shown in Fig. 8and 9. A video on the various shapes formed and regenerated bythe algorithm can be found at the link .The proposed algorithm is able to form and regenerate shapeswith continuous surfaces. While filled shapes were formed withoutissues, those having unfilled and enclosed areas, such as the letter‘O’, seemed to be deformed. Prima facie observations revealed thatwhile the robots move to align the inside of an enclosed unfilledshape, the open area gets enclosed and the robots get trapped within.Since we have introduced noise into the system, this entrapment ofrobot(s) could lead them to non-determinism. In addition when therobots are about to connect the enclosed portion of the shape, it mayhappen that some of them do not find enough space to enter theenclosure so as to complete the shape. This lack of space could makethe stable robots to move away and avoid collision. This in turncan lead to an irregularity in the triangular lattice structure. If suchstable robots move away beyond the communication range of theirstable neighbours, the latter could detect this as a damage to theshape and initiate an undesired regeneration process. The problemcould be solved if an additional state is introduced to categorize therobots in the periphery of the enclosed unfilled area so that furtherrobots entering this area will detect this state and not venture tostation themselves. This would mean a corresponding addition of aflag in the gene to indicate such enclosed and unfilled areas.
Given a set of robots, the proposed algorithm is not only able togenerate the given shape but also to ensure that any divisive dam-age caused to the shape can make each remnant to regenerate ascaled-down version of the same shape without external interven-tion. Damage could occur in the form of a robot or a set of robotsmalfunctioning or lose charge. All activities in the algorithm areperformed in a distributed and decentralized manner. The trian-gular lattice structure based on which the shape is formed helps https://goo.gl/Qv7LMW
ECCO ’18 Companion, July 15–19, 2018, Kyoto, Japan Rahul Shivnarayan Mishra, Tushar Semwal, and Shivashankar B. Nair identify the extent of loss of robots and also trigger the regenera-tion mechanism. The algorithm is novel because it handles boththe generation and regeneration of a given shape without any in-tervention, much like biological cell division. The algorithm can beused in robotic swarms which need to divide and regroup in somegiven patterns. By providing, more than one image map, it maybe possible for a leader robot to optimally decide the best shapethe remaining set of robots should form. Such an algorithm couldbe useful in applications targeting exploration of inaccessible orrisk prone areas. We are currently in the process of enhancing thealgorithm so that the two scaled-down shapes can merge again toform the original shape. This feature would be useful when a swarmof robots travelling in a specific formation (shape) is split into two,due to an obstacle in their path, thus forming two scaled downversions. We are also working towards enhancing the algorithm toform and regenerate shapes with high complexity such as the oneswith holes.
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