Springer Handbookoƒ Computational Intelligence Kacprzyk Pedrycz Editors

"#$ 1291 . SwarmSwarm Intelligence in Optimization Intell and Robotics . | F Part Christian Blum, Roderich Groß

. Overview ......  Swarm intelligence is an arti cial intelligence dis- cipline, which was created on the basis of the laws . SI in Optimization......  that govern the behavior of, for example, social .. Ant Colony Optimization......  insects, sh schools, and ocks of birds. The or- .. Particle Swarm Optimization ......  ganization of these animal societies has always .. Arti cial Bee Colony Algorithm ...  mesmerized humans. Therefore, it is surprising .. Other SI Techniques that it has only been in the second half of the last for Optimization and Management Tasks ......  century that some of the most important prin- ciples of swarm intelligent behavior have been . SI in Robotics: Swarm Robotics ......  unraveled. A prime example is stigmergy, which .. Systems ......  refers to a self-organization of the animal society .. Tasks ......  via changes applied to the environment. . Research Challenges ......  In this chapter, we provide a concise introduc- References......  tion to swarm intelligence, with two main research lines in mind: optimization and robotics. Popular examples of optimization algorithms based on ious swarm intelligent behaviors for problem solv- swarm intelligence principles are ant colony opti- ing and organizing groups of robots. This has mization and particle swarm optimization. On the resulted in a separate research eld nowadays other side, the eld of robotics has adopted var- known as swarm robotics.

. Overview

Swarm intelligence (SI) [66.1–3] is a subfield of the unsophisticated individuals, yet they are able to achieve more general field of artificial intelligence [66.4]. The complex tasks in cooperation. Essential colony behav- term swarm intelligence was introduced and used for iors emerge from relatively simple interactions between the first time by Beni et al. [66.5–7] in the context the colony’s individual members. of cellular robotic systems. Nowadays, SI research is An important aspect of any SI system is self-orga- generally concerned with the design of intelligent mul- nization [66.8]. Originally, the term self-organization tiagent systems whose inspiration is taken from the was introduced by the German philosopher Immanuel collective behavior of social – or even eusocial – in- Kant [66.9] in an attempt to characterize what makes or- sects and other animal populations. Examples include ganisms so different from other objects. Nowadays, the ant colonies, bee hives, wasp colonies, frog popula- term self-organization refers to a process where some tions, flocks of birds, and fish schools. Among these, form of global order or coordination emerges from social insects have always played a prominent role in rather simple interactions between low-level compo- the inspiration of SI techniques. Even though their in- nents of an initially unordered system. Self-organizing trinsic ways of functioning have fascinated researchers processes are neither directed nor controlled by any for many years, the mechanisms that govern their be- agent or component, neither from inside nor from out- havior remained unknown for a long time. In colonies of side the system. They are often triggered by random social insects, for example, single colony members are fluctuations that are amplified by positive feedback and ]. Other exam- 10 is the ants’ foraging ACO ), the capabilities of termites 66.1 ]. 2 , 1 During the last 50 years or so, biologists discovered In the meantime, some of the above mentioned be- behavior, and in particular,can how find ants shortest of pathsnest. between many In food species order sources to andthe their search area for around food, theirWhile ants nest initially moving, by explore ants means ofsubstance leave random tiny on walks. drops the ofthese ground. pheromones. a Ants When pheromone are choosingattracted also their by way, able they paths to are centrations. marked scent When by having identified strong aevaluate pheromone food the source, con- ants quantity andcarry the some quality of ofturn it the trip, food back the and on to quantity the their of ground mayity nest. pheromone of depend During that the on food. ants the the The leave quantity re- pheromone and trails qual- will guide other development of theseobservation algorithms was of inspired antThey by colonies. live the Ants inby colonies are the and social their goal insects. cused behavior of on is the colony survival governed survival ofprovided rather individuals. the The inspiration than behavior for that being fo- tallization, molecular self-assembly,which neural and networks learn the toterns. recognize way complex pat- in that many aspects ofinsects the are collective self-organized activitiestion of as without social a well, central that control.weaver For is, ant example, the constructs they African nests func- Where by the pulling gap leaves between together. leavesof exceeds an the individual body ant, length multiplechains. ants organize Once into the pulling leavestogether are using silk in from contact, larvae,site which they by are other are carried workers to of glued the the colony [66. ples concern the recruitment offor fellow prey colony retrieval members (Fig. and wasps toof build bees sophisticated and nests, antsment. or to For more orient the examples, themselves we ability refer into the [66. their interested reader environ- haviors have been used asof inspiration technical for the problems, resolution especiallytimization in the and context in ofto robotics. op- reviewing This some chapter ofthors – is the most – dedicated interesting algorithms/systems intwo fields. from the these opinion of the au- SI SI tech- ]. The , which SI 14 – 12 techniques for op- SI negative feedback ) and particle swarm opti- ACO . SI ). More recently, other techniques such techniques for solving optimization prob- ] is one of the earliest in Optimization SI PSO 11 Ants cooperate for retrieving a heavy prey SI algorithms in the early 1990s [66. [66. as the artificialveloped. bee Apart from colony solving optimization algorithm problems, have been de- timization. Dorigo andACO colleagues developed the first techniques are being used for managementample, tasks, for in ex- distributed settings orThe in following sections online will optimization. give aapplication brief field overview of of this (photo courtesy of M. J. Blesa) possibly counterbalanced by generally aids inproperties exhibited stabilizing by self-organizing systems the arethe thus system. result The ofponents. global this As such, distributed self-organizationand interplay is able of typically to robust theirbations. survive com- and Historically, self-organization self-repair processes damagebeen have or studied pertur- in physical,and cognitive chemical, systems. biological, Well known social, examples are crys- niques have been usedand for continuous both optimization solving problemsdistributed combinatorial in settings. static and Two in of the most well-known . . Ant Colony Optimization ACO techniques for solvingcolony optimization optimization problems ( are ant . The use of Fig. . lems has already a rather extensive history. mization ( Swarm Intelligence Part F

Part F | . 1292 Swarm Intelligence in Optimization and Robotics 66.2 SI in Optimization 1293

ants to the food source. It has been shown in [66.15] consideration by assembling them from the set of solu- . | F Part that the indirect communication between the ants via tion components. In general, ACO algorithms attempt pheromone trails – known as stigmergy [66.16] – en- to solve an optimization problem by iterating the fol- ables them to find the shortest paths between their lowing two steps: nest and food sources. Initially, ACO algorithms were developed with the aim of solving discrete optimiza-  Candidate solutions are constructed using tion problems. It should be mentioned, however, that a pheromone model, that is, a parameterized nowadays the class of ACO algorithms also comprise probability distribution over the search space. methods for the application to problems arising in net-  The candidate solutions are used to update the works, such as routing and load balancing [66.17], and pheromone values in a way that is deemed to bias for the application to continuous optimization prob- future sampling toward high-quality solutions. lems [66.18]. ACO algorithms may be regarded from different The pheromone update aims to concentrate the perspectives. First of all, as mentioned above, they are search in regions of the search space containing high- SI techniques. However, seen from an operations re- quality solutions. In particular, the reinforcement of so- search perspective, ACO algorithms belong to the class lution components depending on the solution quality of metaheuristics [66.19–21]. The term metaheuristic, is an important ingredient of ACO algorithms. It im- first introduced in [66.22], has been derived from the plicitly assumes that good solutions consist of good composition of two Greek words. Heuristic derives solution components. To learn which components con- from the verb heuriskein ./ which means to tribute to good solutions can help assemble them into find, while the prefix meta means beyond, in an upper better solutions. The main steps of any ACO algorithm level. Before this term was widely adopted, metaheuris- are shown in Algorithm 66.1. DaemonActions (see tics were often called modern heuristics [66.23]. In line 5 of Algorithm 66.1) may include, for example, the addition to ACO, other algorithms such as evolutionary application of local search to solutions constructed in computation, iterated local search, simulated annealing, function AntBasedSolutionConstruction(). and tabu search, are often regarded as metaheuristics. The class of ACO algorithms comprises several For books and surveys on metaheuristics, we refer the variants. Among the most popular ones are MAX– reader to [66.19–21, 23]. MIN Ant System (MMAS) [66.24] and ant colony system (ACS) [66.25]. For more comprehensive infor- Algorithm . Ant colony optimization (ACO) mation, we refer the interested reader to [66.26]. 1: while termination conditions not met do 2: ScheduleActivities . . Particle Swarm Optimization 3: AntBasedSolutionConstruction() 4: PheromoneUpdate() PSO [66.2, 27] is an SI technique for optimization that 5: DaemonActions()foptionalg is inspired by the collective behavior of flocks of birds 6: end ScheduleActivities and/or fish schools. The first PSO algorithm was intro- 7: end while duced in 1995 by Kennedy and Eberhart [66.28] for the purpose of optimizing the weights of a neural network, From a technical perspective, ACO algorithms work that is, for continuous optimization. In the meantime, as follows. Given a combinatorial optimization problem PSO has also been adapted for its application to discrete to be solved, first a finite set C of the so-called solution optimization problems [66.29]. components, used for assembling solutions to the prob- In PSO, solutions to the problem under consider- lem, must be defined. Second, a set T of pheromone ation are labeled particles. The algorithm works on values must be defined. This set of values is commonly a whole set of particles at the same time, the so-called called the pheromone model, which is – from a mathe- swarm. Therefore, PSO can be seen as a population- matical point of view – a parameterized probabilistic based optimization technique. During the run time of model. The pheromone model is one of the central the algorithm, particles move through the search space components of any ACO algorithm. The pheromone on the search for an optimal, or good enough, so- values i 2 T are commonly associated with solution lution. Moreover, particles communicate their current components. The pheromone model is used to prob- positions to neighboring particles. The position of each abilistically generate solutions to the problem under particle is updated according to three terms: its so- ) , ), ]. so- 38 von 33 fully PSO 66.1 ], variants 34 term, and the algorithm. do [66. PSO von Neumann Frankenstein’s in 2005 [66. PSO part, i PSO carries the particle x i cognitive cognitive v ) algorithm was first

social i ) ) p Basturk , the term ABC adaptive hierarchical parti- ]. Moreover, / 66.2 66.1 variant that was created by do 35 and then i algorithms is characterized by / i ], and p [66. Inertia Weight of a particle is composed of three . neighbors PSO i f /; p 33 /; i i v . PSO momentum x x momentum summarizes the basic / <  [66.  i Karaboga g i x . p p ] is a = min . . f 66.2 ]. termination conditions not met each particle g 36 . The use of rather small neighborhoodtopolo- PSO if Update velocity ( Update position ( p ˝ ˝ 37 2 1 for end for [66. R R 2 1 terms. The end while Randomly generate an initial swarm while c c The class of 4: 3: 6: 7: 8: 9: 1: 2: 5: and combining (someFor of) more information, them thesult in [66. interested a reader beneficial may con- way. analyzing the components of existing toward the previous direction; the informed represents a forcetoward the that best influences positionious of the neighboring different new particles. neighborhood Var- for direction topologies this may purpose. Examples beNeumann include used ring, star,gies and – suchneighborhood as – the has onebetter induced generally results by been the when showndressed, to rather whereas lead complex larger to problems neighborhoodsto are a generally ad- better lead performance for simpler problems [66. cle swarm optimizer represents a force that pullssonal-best position; the finally, particle the toward its per- point-wise vector multiplication. As shown in ( cial The artificial bee colony ( the velocity term Algorithm . Particle swarm optimization ( PSO . . Articial Bee Colony Algorithm components: the a multitude ofsible different to variants, mention renderingvariants all it include of impos- the them here. However, popular proposed by Algorithm per- algo- parti- (.) (.) studies cellular refers to /; i th particle PSO i x ˝ are the so- 2  models. Early c g p denotes the . i ]: p and ˝ 28 1 2 Grenander’s c R 2 , are updated according c n for solving optimization and artificial life C seemed to be the most ap- / is the best position found by i g x ;:::; PSO p 1  i ], suggested that bird flocking is D . Moreover, on the flocking model known as p  Heppner are independent functions return- i . 31 particle 1 was used due to making use of the denotes the velocity of the ; 2 ˝ i 0 denotes its position, is – in some way – similar to R Œ v 1 ]. i , for , the difference between its current po- i ; ), which are often used for generating as- R x i x 1 32 ], and v c and CA PSO Reynolds was chosen by Kennedy and Eberhart for the position, and 30 particle ( C s may be characterized by the following three C and 1 is closely related to i i i v x R velocity v [66. CA .

values of the cell and its neighbors. cells [66. These three attributes also hold for the particles in Henceforth, PSO i i v x automata problems. main attributes: 1. Cells are2. updated in parallel. The value of each new cell depends3. only on the There old is no difference in rules for updating different PSO on rules governingsynchronously large [66. numbers of birds flocking an emergent behavior resultingbetween from local the interactions birds.for These the studies development laid of the foundation tonishing self-replicating patterns based on simplerules. local boids works by to the following two equations [66. particles in its neighborhood. In the original called acceleration coefficients. The symbol sonal best where called sition and the best positionfrom it the has best found position so foundthe far, by and effect its that that, neighbors. This duringthe has the swarm increasingly execution focuses ofspace on containing the high-quality areas algorithm, solutions. The of term thecle swarm search following reason. Their initialthe intention movements was of to flockstheir model of model birds further evolved and toward an fishtimization, algorithm the schools. for visual op- As plots producedthe from the algorithm results rather of resembledThe swarms term of mosquitoes. term velocity, and in the swarm, propriate term in this context. ing a vector of values,from generated the uniformly range at random, rithm, Swarm Intelligence Part F

Part F | . 1294 Swarm Intelligence in Optimization and Robotics 66.2 SI in Optimization 1295

39]. The inspiration for the ABC algorithm is to be Division of Labor (Ants/Wasps) . | F Part found in the foraging behavior of honey bees, which In colonies of ants and wasps, for example, there are essentially consists of three components: food source various tasks to be dealt with by the colony members. positions, amount of nectar and three types of honey However, the urgency to engage in certain tasks may bees, that is, employed bees, onlookers, and scouts. In change over time. In 1984, Wilson [66.43] showed that short, the algorithm works as follows. Feasible solu- the concept of division of labor in colonies of Pheidole tions to the problem under consideration are modeled as genus ants allows the colony to adapt to these changing food source positions. Moreover, the quality of a feasi- demands. Division of labor was later modeled in [66.44, ble solution is modeled as the amount of nectar present 45] by means of response threshold models. at the corresponding food source position. Each type These models were later used in several techni- of bee is responsible for one particular operation in the cal applications. In the following, we mention a few context of generating new candidate food source po- of them. Nouyan et al. [66.46] consider static and dy- sitions, that is, new candidate solutions. Specifically, namic task allocation problems in which trucks have employed bees will search in the vicinity of the food to be painted in painting booths. Another applica- source position that is presently in their memory; mean- tion concerns media streaming in peer-to-peer net- while they pass information about good food source works [66.47]. A multiagent system for the schedul- positions to onlooker bees. Onlooker bees tend to se- ing of dynamic job shops with flexible routing and lect good food source positions from those found by sequence-dependent setups is considered in [66.48]. the employed bees, and then further search for bet- Merkle et al. [66.49] made use of a response threshold ter food source positions around the selected food model for self-organized task allocation in the context source position. In case the employed bee and the of computing systems with reconfigurable components. onlookers associated with a food source position are Finally, [66.50] present a system for task allocation in not able to find a better food source position, their distributed environments. current food source position is abandoned and the em- ployed bee associated with this food source becomes Cemetery Formation (Ants) a scout bee that performs a search for discovering The term cemetery formation refers to a behavior which new food source positions. If a scout identifies a new has been observed in ant colonies of the species Phei- food source position, it turns into an employed bee dole pallidula, among others, which cluster the bodies again. of dead nest mates. This self-organized behavior has Essentially, the difference between the ABC algo- given rise to several applications, especially in the con- rithm and other population-based optimization tech- text of clustering and sorting. In 1991, a model for the niques is to be found in the specific way of managing clustering and sorting behavior of ants was published the resources of the algorithm, as suggested by the in [66.51]. Note that clustering refers in this context to foraging behavior of honey bees. Due to its simplic- the formation of piles, and sorting, on the other hand, ity and ease of implementation, the ABC algorithm refers to the spatial arrangement of objects according to has captured much attention recently. It should also their properties. be mentioned that, although the algorithm has initially Mainly based on the model from [66.51], several been introduced for continuous optimization, in the algorithms for clustering and sorting were proposed in meantime it has been adapted for its application to com- the literature. The first one was presented in [66.52], binatorial optimization problems as well [66.40, 41]. extending the original model to handle numerical data. For a recent survey, we refer to [66.42]. More recent papers include [66.53] which deals with clustering and topographic mapping. Finally, the ceme- . . Other SI Techniques tery formation behavior of ants has also inspired an for Optimization algorithm for dynamic load balancing [66.54]. and Management Tasks Flashing in Fireies In the following, we briefly mention other applica- Fireflies are winged beetles that make use of biolumi- tions of SI techniques for optimization and management nescence to attract mates or prey. Moreover, tropical tasks, the latter especially for what concerns distributed fireflies, in particular the ones from Southeast Asia, environments. They are grouped with respect to their synchronize their light flashes in large groups of indi- natural inspiration. viduals. This is a self-organized phenomenon which is ]– 66 ]. How- ], image 69 62 , 68 ] is currently the 69 , or simply tortoise, ] built two autonomous 75 ] introduced a first formal 67 [66. ]. 65 ]. ]. It is nowadays generally ac- ], and generally to continuous op- 74 70 – [66. 63 Walter ]. The second algorithm is known as ], multiuser detection [66. 71 et al. [66. 64 61 Machina speculatrix Aihara Nest Building (Termites/Wasps) Models for nest building based on stigmergy have Self-Desynchronized Croaking (Japanese Tree Frogs) state of the art for this problem. Both termites andin wasps cooperation. build The highly constructionbeyond of complex the such nests nests capabilitiesnests is of well of an bothplex individual termites internal insect. and The structure.extremely wasps large have Moreover, in a termiteScientists very comparison nests studying com- to are theup individual with nest-building insects. probabilistic behavior modelsthe for came behavior describing (parts [66. of) segmentation [66. have dealt with the croaking ofmale Japanese individuals tree make frogs. use The of theirtract croaks females. in Moreover, order females to of at- thiscan family recognize of the frogs sourceto of determine such the a current croakmale. location However, this and of is are only the possible able if corresponding are no close two frogs enough (that to theIn female) such croak a at case, the the female samecroaks is time. came not able from. to detect Thisevolved where is a the why, self-organized over way time,croaks. of male desynchronizing frogs their ever, the algorithm proposed in [66. model based on acapturing this set behavior. So of far, this pulse-coupled modelapplied has to oscillators only distributed been for graph coloring [66. cepted thatbuilding. stigmergy plays a centralbeen role used in mainly inautomated nest software building of tools certain for structures.be Examples simulating found can the in [66. timization [66. been applied tonetworks the [66. training of feed-forward neural fish school search Different biological studies – for example, [66. robots called which exhibited behaviors resembling those of simple . . Systems In the late 1940s, ]. 60 tech- artifi- school- SI phase-cou- ], which is in- 59 ], the synchroniza- ) [66. ). It has, for example, 56 ], and dynamic pricing FA 57 ]. The benefits of this self- AFSA 55 ( ]. Second, the literature offers 58 . Such a fish aggregation is called . Shoaling fish are aware of each models [66. in Robotics: Swarm Robotics shoaling SI Fish Schooling There are basically two different algorithms for op- The literature contains, at least, two types of tech- . Schooling is a self-organized behavior that results aggregation of fish A group of fish that havean gathered are commonly called unstructured in the case invarious which species the of group fish consistsexample, of having in randomly the gathered,some vicinity for social of component a tosaid food this to source. gathering, be If the there fish is are other’s presence, adjusting,ming for behavior example, to their eachHowever, swim- other their in relation order isan to rather aggregation stay of loose. fish together. If, isample, more in when tightly all contrast, organized, fish for move at ex- direction, the same speed then in the the same ing aggregation is saidfrom local to interactions be ior between comes the with fish.a several This means advantages behav- for such socialing, interactions, as and more providing predator successful avoidance. forag- timization based on fishliterature. The schooling first to algorithm is becial referred fish found to swarm as in algorithm the the in online markets [66. tion in overlay networks [66. spired by the way in which firefliesThis attract algorithm mates or was prey. initiallyoptimization. introduced It for has, continuous however, beenplication adapted to for combinatorial optimization the as ap- well [66. the so-called firefly algorithm ( niques for thefollowing coordination sections provide of a brief groups overview ofwith of this a field, robots. focus The onthey accomplish. swarm robotic systems and the tasks synchronization are nothypotheses yet fully consider understood. diet,tude. Current social interaction, and alti- nical applications that areof inspired by the different flashing aspects ofthat fireflies. require First, some there type areples of applications include, self-synchronization. but Exam- areprotocol not in limited sensor to, networks a [66. synchronization Swarm robotics refers to the study and use of . mathematically described by thepled oscillator so-called Swarm Intelligence Part F

Part F | . 1296 Swarm Intelligence in Optimization and Robotics 66.3 SI in Robotics: Swarm Robotics 1297

animals. The robots had a driving/steering mechanism, swarm and swarm intelligence in this context [66.83, . | F Part a head light, a photoreceptor, and a bump sensor. They 84]. were designed to search for and approach light sources Other early physical implementations of distributed of moderate intensity. If a robot observed such a source, robotic systems include the CEBOT Mark II [66.85], its head light was turned off, otherwise it was turned on. ACTRESS [66.86], and GOFER [66.87]. In an experiment, the robots were set up in a dark envi- ronment, where they approached each other exhibiting Hardware Architectures complex motion patterns. Such mutual recognition al- Advances in technology, for example, in computers, lowed a population of machines to form a sort of manufacturing and mobile devices have made it af- community, which broke up once an external light fordable to study swarms of around 201000 physi- source was introduced [66.75, p. 129]. This two-robot cal robots [66.88] and up to around 1000000 robots system may be the first self-organizing multirobot sys- in simulation [66.93–95]. At present, most swarm tem. Interestingly, even a single robot was reported to robotic systems consist of mobile robots that operate exhibit complex interactions when facing its mirror im- on the ground. An example is the Kilobot platform age – such a behavior, if observed in an animal, might (Fig. 66.2a), which was designed to facilitate the fab- be accepted as evidence of some degree of self-aware- rication and operation of thousands of robots – includ- ness [66.75, pp. 128–129]. ing their charging, programming and activation all at In the 1950s, inspired by von Neumann’s kinematic once [66.88]. Other state-of-the-art robotic systems in- model of machine replication [66.76], the first physi- clude the r-one (Fig. 66.2b), which features, among cal models of self-replication were built. Penrose and others, a set of IR transmitters and receivers for com- Penrose [66.77] studied a system in which passive me- munication and relative localization [66.89], and the chanical parts move on a linear track when the latter is Khepera I-IV [66.96] and e-puck [66.97], which fea- subjected to side-to-side agitation. In their default posi- ture a range of sensors including a camera. Increasingly, tion, the parts do not link under the influence of shaking swarm robotic systems operate in spaces other than on alone. If a seed object composed of two complementary the ground, such as underwater [66.90, 98] (Fig. 66.2c) parts, one hooked up to the other, is added, it repli- or in the air [66.99, 100]. In some robotic systems, cates by interacting with the other parts on the track. the swarms operate and collaborate across multiple Jacobson [66.78] implemented a system in which self- spaces, such as on the ground and in the air [66.91, 101] propelled electromechanical parts move on a circular (Fig. 66.2d,e). track with several branches. A seed object composed According to their system architecture, most swarm of two parts could trigger other parts to assemble into robotic systems can be categorized into either multi- identical objects without human intervention. robot systems or modular reconfigurable robot systems. In the late 1980s, studies of Fukuda and Nak- Multirobot systems are composed of multiple distinct agawa [66.79–81], Beni [66.5], and Wang and robots, which are typically mobile and able to perform Beni [66.82] provided an enormous impetus for the field (collectively) more than one task in parallel (Fig. 66.2a– that developed into swarm robotics. Fukuda and Naka- c). Modular reconfigurable robot systems are composed gawa proposed a novel type of robotic system called dy- of component modules that can be physically linked namically reconfigurable robotic system (DRRS), which together to form a robot (Fig. 66.2f). A few hybrid sys- can dynamically reorganize its shape and structure tems exist, sharing properties of both multirobot and [::: ] for a given task and strategic purpose. DRRS modular reconfigurable robot systems [66.91, 102–104] is made of several cells with built-in intelligence and (Fig. 66.2d). the ability to autonomously connect to and detach from Of particular interest among systems of modular re- one another [66.81, pp. 55–56]. The authors also pre- configurable robots are those where the robots can build sented a first prototype of this system, the CEBOT themselves [66.105, 106]. The term self-reconfigurable Mark I [66.80]. At the same time, Beni introduced denotes the general ability of physical modules to re- the term cellular robotic system, referring to a sys- configure themselves, regardless of whether the process tem that can encode information as patterns of its is centrally controlled, for example, by an external com- own structural units [66.5, p. 59]; the units would be puter, or decentralized and autonomous. In the follow- structural elements, each with built-in intelligence, able ing, we use the term self-assembly to refer to processes to move in space and act asynchronously under dis- by which pre-existing components (separate or distinct tributed control. Beni and Wang also used the terms parts of a disordered structure) autonomously organize ], 90 r-one ) b ( ], and has ]; 8 88 [66. ], photo courtesy of 92 ]. Note that where the ]. 8 119 – 117 ]. , p. 12]. We include in this category ]. In other animals, no recognizable 116 ]. Pebbles (after [66. – ) Macrotermes bellicosus f 111 120 121 ( 112 s); [66. Lily developed in the CoCoRo project (after [66. ) interactions where agentsrectly, that sense is, where each theof current other another presence agent or can indi- motion be inferredenvironment. from Note changes in that the thecommunication boundary to is stigmergic blurred;the for situation where example, multiplesimultaneously consider agents [66. push an object Interaction via sensing refersthat to occur local interactions betweensensing one agents another, but as withoutcation a explicit communi- result of agents termites of In some social animals, the membersserve a of common a leader group individual. ob- Theirbe actions can highly dependentthe on leader, the as, observed forgroup behavior instance, [66. during of an attack of the been implemented intems several [66. swarm robotic sys- leader individual exists; instead, individuals observe nearby group members. The lattercal situation for is swarm typi- systems.for It is animal reported, groups forand that schooling instance, behavior exhibit [66. herding, flocking, In principle, interaction viaered sensing can an be implicit consid- form of communication, in par- groups are not homogeneous, even adividuals minority may of in- be ablegroup [66. to influence the rest of the c (  a heterogeneous system studied in the Swarmanoid project ) Kilobots developed by Harvard University [66. e ]. , ) d a ( ( 108 mem- ]: 111 ] and has widely ]. Stigmergic com- 107 refers to the transfer ] presented a detailed 16 et al. [66. 110 [66. ]: (i) systems in which the Cao 109 et al. [66. stigmergy Examples of swarm robotic systems: Dudek ], photo courtesy of M. Dorigo, Université Libre de Bruxelle ], photo courtesy of J. McLurkin, Rice University); 91 89 of the environment. In this case, robots leave Interaction via environment of information that isory mediated through the persistent signs that stimulaterobots. the This kind activity of of indirectreferred other communication to is also as munication is widely used infor social example, insect during societies, the construction of mounds by Sensing and Communication d) e) f) a) b) c) into patterns ortion. structures Self-assembly is without responsible for externalmuch the of interven- generation the of order in nature [66. taxonomy considering communication range, topology, and bandwidth. Incategorization the proposed following, by we adopt a simpler (after [66. been applied in theular synthesis of components. products Increasingly, fromassembly the molec- processes involving potential largerto of components the – self- centimeter-scale up – is being recognized [66. (after [66.  Fig. . a–f In most multirobot systems,other robots by interact using withmunication. each their sensors or some form of com- components that self-assemble are externally propelled, and (ii) systems insemble which are the self-propelled. components that self-as- In robotic systems, twobling distinct systems classes exist of [66. self-assem- D. Rus, MIT) photo courtesy of T. Schmickl, University of Graz); Swarm Intelligence Part F

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ticular, as an observed agent can change action threshold i. The particular threshold value i can either . | F Part and thereby influence the behavior of its observers. be fixed for each individual from the outset [66.135] or Arkin [66.122] referred to the interaction via sens- learned during its lifetime [66.136, 137]. In both cases, ing category as cooperation without communica- the mechanism can facilitate the emergent allocation of tion, and showed that it is sufficient to accom- tasks in groups of otherwise identical individuals (see plish tasks, that require the cooperation of multiple also Sect. 66.2.4). In addition, intentional approaches robots. Other examples of swarm robotic studies us- to task allocation have been considered [66.138, 139]. ing interaction via sensing include [66.123–126]. These require the agents to cooperate explicitly with  Interaction via communication refers to interac- each other. For example, the decentralized ALLIANCE tions involving explicit communication. Thereby, algorithm [66.140, 141] can be used for groups of het- information is either broadcast or transferred to erogenous robots to perform tasks and subtasks, which specific teammates. Information transfer can take may have ordering dependencies, in a fault-tolerant place through direct physical interactions, such as way. It assumes that the robots detect with some prob- touch. This latter form of communication can also ability the effect of their own actions as well as the be referred to as direct interaction [66.127]. Ex- actions of other team members. plicit communication can improve the performance Virtual potential fields [66.142, 143], and physi- of a multirobot system. This is typically the case comimetics [66.144], is another widely used behavior- where the system benefits from robots being re- based design method. The robots mimic a physical par- cruited to certain areas of the environment. Balch ticle under the influence of a potential field. The latter and Arkin [66.128] studied such an environment guides the particle toward a point of minimal poten- and showed that it can be sufficient for each robot tial energy. While the goal point, which the robot shall to signal its overall state. The transfer of more reach, would exert an attractive force on the particle, elaborate information however would not result in any obstacle would exert a repulsive force. Other robots any significant increase in task performance. Ex- can exert forces on the particle as well. Using this con- plicit communication is commonly used in modular cept, a wide repertoire of behaviors can be realized, reconfigurable robot systems, for example, to ex- such as the collective movement of robots arranged in change information between inter-connected mod- particular formations [66.145], or the tracking of mul- ules or to support the docking process of separate tiple moving targets [66.146]. The properties of the modules [66.129]. resulting swarm systems, for example, the cohesion of the swarm, can also be formally analyzed [66.147]. Control and Coordination Other design methods include the Growing Over the last two decades, a range of design methods Point Language [66.148], the Origami Shape Lan- have been proposed for the control of swarm robotic guage [66.149], and Proto [66.150]. These languages systems. They can be broadly classified into behavior- were developed in the context of Amorphous Comput- based design methods and automated design meth- ing [66.151], which considers systems of massively ods [66.130]. distributed, disordered, asynchronous, and locally In behavior-based design methods, the user ap- interacting computational devices. The Proto language proaches the problem in a bottom-up manner [66.131]. has been extended for use on mobile devices. This A repertoire of behaviors for individual robots is de- extension was validated with a swarm of 40 iRobot fined and often refined through a trial-and-error process. robots [66.152]. Some amorphous computing ap- A common approach is the use of finite state machines. proaches allow users to specify desired global system Each state defines a basic behavior. Transitions between properties in the language. A compiler then produces states can be triggered by probability, external events, the local rule set for the agents to achieve these time-outs, and combinations of these [66.132–134]. properties [66.149]. A prominent example is the use of response threshold Automated design methods can be grouped into functions, for example, reinforcement learning and evolutionary robotics. In re- s2 inforcement learning [66.153], an agent interacts with si=i i 1  exp or 2 2 ; its environment by choosing actions and receiving re- si C i wards. Matari´c [66.154, 155] applied reinforcement which define the probability for an individual to engage learning in a swarm robotic context. The robots had to in task i based on the perceived task stimulus si and learn how to collaborate in a foraging task. The robots ] pro- ]. Other 169 algorithm ]. One ap- 174 106 et al. [66. ] proposed a two-level Shen 172 role-based control communication and control, in ]. In principle, modular robots 173 et al. [66. . A global planner ensures that the robot , which, typically, have more advanced ]. Due to the combinatorial explosion of ] proposed a 171 Yoshida 170 hormone-inspired [66. Another class of algorithms addresses the problem than by search,be the reconfiguration attempted problem by can local also movement strategies, for ex- posed which artificial hormones help modulesactions to and synchronize discover changes inample, their a set topology. of For independent ex- caterpillar-likebe robots could connected intoits a gait single to entity, which thea connected would new entity topology. adapt was manually Inties split that a into continued smaller similar to enti- experiment, moveStøy as independent caterpillars. to let modular robotsterns. display periodic A locomotion module’s pat- to role synchronize specifies them with itsmunication, neighbor actions modules. a For and parent–child com- modules how architecture need is to be used; arrangedtended thus, in version acyclic of graphs. the Anwith control cycles. ex- algorithm can also cope of how to adjustchanging the the relative connection positions topology of [66. modules by possibilities, an exhaustive search ofpractical such graphs whenever the is number im- ofState-of-the-art modules is approaches not are small. thussider heuristic and ways con- ofexample, reducing the problem complexity. For proach is to formulate the problemFor as a example, search problem. inrobot order from to oneis reconfigure topology performed, a to where lattice-based responds another, the to a start the node graphend initial of search node topology the corresponds of graphrobot to the cor- [66. the robot desired and topology the of the gait control table specifiesmodule a for basic each action controlis to executed cycle either be from and performed. a central Thefashion. place In controller or the in latter a case, distributed the modulesactions synchronize using their internal timers. can solve the search problem on the fly [66. motion planner as a whole followsso, it a specifies predefined several 3Dvidual candidate trajectory. modules paths To from that do theA bring tail indi- motion to scheme the selectoreach head chooses module of a based the feasible on robot. ple a path is rule to for merge database. logically Another ameta-modules group exam- of nearby modules into locomotion abilities than theproblem individual is modules. then The reducedboth to meta-modules developing and controllersmeta-modules modular for [66. robots composed of ]. 158 , gait con- 157 ]. Early studies 160 , ]. ] demonstrated a sys- ]. Simulation environ- 159 156 166 163 ] went a step further in that – 165 161 ] proposed the use of ] evolved neural network con- et al. [66. 168 164 ]. The difficulties of using reinforce- ], where neural network controllers for ]. et al. [66. [66. 155 159 167 Griffith to correlate appropriate conditions for each to produce a range of animal-like locomotion ]. A recent survey of reinforcement learning Yim [66. et al. [66. Watson 130 Evolutionary robotics is an approach to design- Several design methods were developed specifically in robotics is reported in [66. ing robots,control) or using aspects evolutionary of algorithms [66. them (e.g., morphology, ment learning in a swarmin robotic [66. context are discussed were provided with ain set a of hand-coded behavior-basedlearn behaviors approach) how (as and wereof these required behaviors in to orderbehavior to optimize the higher-level in evolutionary roboticsior developed such collective astion behav- herding environments or [66. flocking in simplistic simula- This approach canswarm also robotic be systems.bypass applied In to both the principle,task the design and evolution problem of the can that of problem achieve decomposing of the subtasks identifying a [66. basic given behaviors ments with physicallyered embodied in agents [66. were consid- aggregation were firstrobots evolved in using a aof group simple these of simulation controllers five ing environment; were a the subsequently more best Quinn validated detailed us- simulation model of the robots. trollers for collectivesimulated motion robots and using subsequently tested anetwork the group best-rated in of 100robots. three trials with a group of three physical controllers for aevolved simple on phototaxis a task grouptoward were of a directly distributed eight evolution of physical robothardware, robots. morphologies in Working tem of template-replicating polymers, which wereof made reconfigurable modulesair that table slid andtrol executed passively their a on finite connectivity. an swarm state Recent robotics machine work considers toample, on cultural con- where evolutionary behaviors evolution, thatare for can subject ex- be to imitatedrobots (memes) engage an as both evolutionary teachers and process.memes learners [66. to In exchange these, the trol tables patterns, such as the walking gaits of hexapods. Each for, or mainly adoptedconfigurable in, robot the systems. contextaddresses One the of problem modular class of re- howsitions of to of adjust algorithms the modules relative withouttopology. po- changing their connection Swarm Intelligence Part F

Part F | . 1300 Swarm Intelligence in Optimization and Robotics 66.3 SI in Robotics: Swarm Robotics 1301

ample, random walks [66.175, 176], cellular automata Following the pioneering simulation works on . | F Part rules [66.177], gradient rules [66.178, 179], or combi- boids [66.30], Turgut et al. [66.183] demonstrated how nations of these [66.180]. These approaches naturally a group of robots can flock through a real environment lead to decentralized implementations, as is desired in using simple rules. To align with each other, the robots swarm robotics. used virtual heading sensors, each comprising a digital compass and a wireless communication module. Flock- . . Tasks ing was demonstrated with 9 Kobot robots in a bounded environment (Fig. 66.3d). A range of capabilities have already been demonstrated Krieger et al. [66.184] studied algorithms that al- with swarm robotic systems. In the following, a brief low a group of robots to forage (Fig. 66.3e). The robots overview is given. More detailed information is pro- rested in a central place, the nest. A robot would leave vided in Chaps. 71–74 of Part F of this handbook. the nest if the total energy of the colony dropped below Garnier et al. [66.189] demonstrated how a group of 20 a threshold. Each robot had its own threshold, which ef- Alice robots aggregate in a homogeneous environment. fectively enabled the division of labor within the group. The robots mimic the aggregation behavior of cock- In addition, a robot would leave the nest when being roaches, which are reported to join and leave clusters recruited by another robot that had found a cluster of with probabilities that depend on the sizes of clus- food. The pair of robots would then perform a tandem ters [66.190]. Such probabilistic algorithms have the ad- run to reach the cluster. The algorithms were tested on vantage that, as long as the environment is bounded, it groups of up to 12 Khepera robots. The groups were is not required that the robots initially form a connected reported to perform more efficiently when employing graph in terms of their sensing and/or communication. the division of labor and recruitment mechanisms than A deterministic algorithm for aggregation is considered without such mechanisms. in [66.181]. It requires robots to have one binary sen- Groß et al. demonstrated how a group of 16 sor, which informs them whether or not there is another s-bot robots self-assemble into a single composite en- robot in their line of sight. The robots do not need mem- tity [66.185]. The process was seeded by one of the ory and do not need to perform arithmetic computation. robots activating its light emitting diode (LED) ring They rotate on the spot when they perceive another in red. Other robots activated their LED rings in blue. robot, and move backward along a circular trajectory Once a robot would connect to the seed structure, it otherwise. This algorithm was validated with groups of became red too, thereby attracting other robots to the 40 e-puck robots (Fig. 66.3a). structure as it grows (Fig. 66.3f). The problem of self- Werfel et al. [66.116] developed a system of robots assembling into arbitrary morphologies of s-bot robots that can simultaneously construct and navigate struc- was considered in [66.194]. tures from a supply of building blocks (Fig. 66.3b). The Holland and Melhuish [66.186] studied algorithms robots are inspired by termites, which use stigmergic that allow groups of robots to sort (and cluster) ob- rules to construct sophisticated structures, in particular, jects of different types (Fig. 66.3g). Six robots were the mounds they inhabit. Given a desired target struc- programmed using simple rules, which regulated the ture, it is possible to generate automatically a set of conditions under which objects of different types were rules to be uploaded onto each robot. Using only local picked up and deposited. information, these rules allow the robots to coordinate Following the pioneering work of Kube their activities in a way that avoids conflict. A group of et al. [66.195, 196], Chen et al. [66.187] proposed three robots constructed several structures, one resem- an algorithm for a group of robots to transport ob- bling a castle. jects larger than themselves toward a goal location Halloy et al. [66.182] showed that hybrid societies (Fig. 66.3h). The robots were programmed to only comprising both cockroaches and robots can collec- push the object across the portion of its surface where tively decide to aggregate under either of two shel- the direct line of sight to the goal is occluded by the ters (Fig. 66.3c) and that it is possible for the robots object. The algorithm was proven to work for objects to influence the decision-making process. In general, of arbitrary convex shape and it was tested with 20 such interactive robots could be used to study and e-puck robots. control animal groups [66.182, 191], including live- Ijspeert et al. [66.188] studied an algorithm that al- stock [66.192, 193], and to inform ecological conserva- lows a group of robots to pull sticks out of the ground tion policy. collaboratively (Fig. 66.3i). Upon encountering a stick, ) ) b h ( ( ]); ry); 181 self-assembly ) f ]; photo courtesy ( 182 aggregation (after [66. ]; reprinted with permission from ) a c) ( 188 tems: i) decision making (after [66. ]. f) ]; photo courtesy of E. Middle ¸Sahin, East Tech- ) c ( 197 183 With regard to swarm robotics, a major challenge waiting time for the firstalytic robot model was of the derived system. from The anusing algorithm an- a was validated system of six Khepera robots. for example, operations research. Themay interested find reader various references toin such [66. kind of techniques is the transitionindoor from systems environments, operating asries, in typically to structured found the inreal more laborato- world. complex environments Overare found the expected in next to the decades, havescenarios, swarms impact including of in cognitive robots a factories, range deep of application sea ex- ]; photo courtesy of C. Melhuish, Bristol Robotics Laborato 186 flocking (after [66. ) d ]; photo courtesy of L. Keller, University of Lausanne); ( 184 pulling sticks out of the ground (after [66. ) i ( ]); 187 ]; reprinted with permission from AAAS); 116 foraging (after [66. ) sorting of objects (after [66. e ) ( g ( Examples of capabilities demonstrated by swarm robotic sys ]); 185 g) h) d) e) a) b) nical University); of J. Halloy, Université Libre de Bruxelles); Springer) a robot would onlythe be ground. able Itarrive to would and pull then pull wait it the for partially stick out a out of second completely. robot The to optimal (after [66. . Research Challenges Research challenges concerning the use ofligence swarm in intel- optimization are mainlytheir related to efficiency. increasing More specifically,viding in an addition innovative to wayintelligence pro- approaches of must problem also be solving,ing, efficient swarm concern- for example,able to computation compete with state-of-the-art timeniques. optimization tech- in This order mayswarm intelligence to often approaches be with befrom components achieved taken optimization by algorithms hybridizing in other fields such as, Fig. . a–i transport of objects (after [66. construction (after [66. Swarm Intelligence Part F

Part F | . 1302 Swarm Intelligence in Optimization and Robotics References 1303

ploration, disaster management, precision farming, and sized robots. The swarm robotics approach, however,  | F Part space systems. Working toward more complex environ- should be equally applicable to intelligent autonomous ments also concerns the ability of swarms of robots to devices operating at scales from a millimeter down to interact safely with humans. Another challenge con- a micrometer. This could have profound implications, cerns the miniaturization of swarm robotic systems. for example, on advanced materials and healthcare Most of the current systems comprise of centimeter- technologies.

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