Communication-Aware Distributed PSO for Dynamic Robotic Search

Transcription

1 Communcaton-Aware Dstrbuted PSO for Dynamc Robotc Search Logan Perreault Montana State Unversty Bozeman, Montana Mke P. Wtte Montana State Unversty Bozeman, Montana John Sheppard Montana State Unversty Bozeman, Montana Abstract The use of swarm robotcs n search tasks s an actve area of research. A varety of algorthms have been developed that effectvely drect robots toward a desred target by leveragng ther collaboratve sensng capabltes. Unfortunately, these algorthms often neglect the task of communcatng possble task solutons outsde of the swarm. Many scenaros requre a montorng staton that must receve updates from robots wthn the swarm. Ths task s trval n constraned locatons, but becomes dffcult as the search area ncreases and communcaton between nodes s not always possble. A second shortcomng of exstng algorthms s the nablty to fnd and track moble targets. We propose an extenson to the dstrbuted Partcle Swarm Optmzaton algorthm that s both communcatonaware and capable of trackng moble targets wthn a search space. Smulated experments show that our algorthm returns more accurate solutons to a montorng staton than exstng algorthms, especally n scenaros, where the target value or locaton changes over tme. I. INTRODUCTION Many tasks are more sutable for robots than humans. Search problems such as detecton of explosves and radoactve sources can be made safer by usng robots operatng under a well-performng algorthm. Consder a scenaro where a radoactve object s lost or stolen and must be recovered quckly to protect the health and safety of the publc. Arborne robots equpped wth radaton sensors could be deployed to search for the object. These robots must locate the object and relay ts locaton to a montorng staton. Search reportng s dffcult when the search area s much larger than the communcaton range of the robots. Addtonally, the target may be moble durng the search process, whch means that robots must not only report the target s poston, but also track t. Emergng technology has revealed that swarms of small, nexpensve robots may be more effectve at performng search tasks than ther larger counterparts [1]. These swarms utlze concepts from many dfferent felds and may be appled to a wde varety of applcatons [2]. Unfortunately, these robotc swarms are only as effectve as the dstrbuted algorthms that enable ther emergent functonalty. Ths dependency ntroduces a need for practcal algorthms capable of controllng a swarm s behavor to solve a varety of tasks. In regards to the search problem, robots must effectvely fnd a soluton as well as transmt ths soluton back to a montorng staton. The communcaton component of the problem can be dffcult n large areas, especally when workng wth nexpensve, power constraned robots that may have a relatvely short transmsson range. When the target soluton s moble throughout the search process, the problem of trackng becomes more dffcult stll. Fndng a target and transmttng the soluton to a server are dstnct goals that may have conflctng optmal solutons, and effectve dstrbuted algorthms must balance both objectves. An exstng algorthm called dstrbuted Partcle Swarm Optmzaton dpso) has been shown to perform reasonably well n smulated envronments [3 7]. However, prevous work does not address the problem of communcatng a soluton back to a central server. Once a swarm of autonomous robots has found a soluton to a problem, that soluton must be relayed back to a montorng node that s capable of processng the nformaton or ntatng an external acton. Another potental shortcomng of the current dpso algorthm s the nablty to track moble targets. The orgnal PSO algorthm cannot be appled drectly to moble target search, as ths typcally requres reevaluaton of a partcular locaton s ftness at a later tmestep, or postng sentnels dedcated to detectng change [8]. Exstng studes have focused strctly on statc targets wthn a search space. Ths s acceptable for scenaros where optma are statc, but may not be suffcent for robotc search, where a target may move durng the search process. The combnaton of search and connectvty objectves s a novel problem addressed by ths paper. We propose an mproved dpso algorthm capable of trackng moble targets as well as transmttng solutons to a server throughout the course of the search process. Ths new communcatonorented dpso algorthm C-dPSO) uses a modfed velocty update equaton to mantan consstent communcaton wth the server. We also propose decayng ftness values to track targets whose locaton, or emtted ftness value changes over tme. The result s a dstrbuted algorthm for robotc swarms that mantans communcaton wth a central server, whle solvng the problem of search wth dynamc optma. The computaton placed on each robot s relatvely lghtweght and well-suted to nexpensve, power constraned robots. The contrbutons made n ths paper provde the means for such robots to solve dffcult search problems over large areas. The remander of ths paper s organzed as follows. In

2 Secton II, we dscuss related work and dentfy areas for mprovement wthn the swarm robotc lterature. In Secton III we ntroduce our C-dPSO and n Secton IV we dscuss the concept of decayng target values. Secton V states the hypotheses of ths study. Our experments are descrbed n Secton VI and the results are presented n Secton VII. Fnally, we dscuss the mplcaton of these fndngs n Secton VIII and conclude wth future work n Secton IX. II. RELATED WORK The related work for ths research can be separated nto three man groups. The frst, descrbed n Secton II-A, deals wth PSO dstrbuted across a swarm of robots. In ths case, the algorthms vew each robot as a separate partcle n the PSO algorthm. Our C-dPSO algorthm behaves n ths fashon, and therefore s most closely related to these works. Secton II-B dscusses several algorthms that use PSO to perform partcular tasks for robots but do not necessarly dstrbute the algorthm onto ndvdual robots. Although somewhat dfferent from our approach, these algorthms solve related problems. Fnally, Secton II-C dscusses some of the methods beng used to perform message routng that were nfluental to our work. A. Dstrbuted PSO Ths work focuses prmarly on an extenson of Kennedy and Eberhart s PSO algorthm nto a physcal envronment [9]. Rather than usng vrtual partcles that model physcal movement, dpso attempts to perform the same tasks usng swarms of robots wth actual parameters. The prncples are smlar to the orgnal algorthm, but the replacement of partcles wth robots ntroduces a new set of problems Although dpso stll uses the same velocty update equaton, the performance of such an update may be unrelable gven a nosy or varable performance of hardware components. Communcaton between agents n a robotc swarm s also not guaranteed as they are n PSO, whch makes t dffcult to transmt the global best poston to other agents or a central montorng node. A relatvely recent study provdes an excellent revew of PSO applcatons, and shows that publcatons nvolvng robotcs account for approxmately 3.4% of the lterature [10]. Many of these works deal wth robotc control, and only a small subset are dedcated to the search problem. Several studes have been conducted that focus on applyng PSO to the robot search problem. Hereford frst proposed the concept of dpso as a soluton to the robotc search problem [3]. The prmary contrbuton was the noton that robots can represent partcles when workng n a physcal search space. 1 The proposed algorthm s decentralzed by pushng computaton from a supervsng node onto the ndvdual robots. These robots calculate new target locatons and update personal best values wthout any nteracton wth an outsde controller/coordnator. A broadcast of poston and value are sent only when a robot fnds a new global best, whch reduces the number of transmssons sent among nodes. Experments 1 Throughout the course of ths paper, we use the terms robot and partcle nterchangeably. wth smulated robots were used wthn a 2D space to track 10 dfferent statc targets that each produced a detectable emsson. An extenson of Hereford s work mplements ths algorthm on three physcal robots that attempted to fnd lght sources wthn a room [4]. In both the smulated and physcal envronment, robots were able to locate targets by workng cooperatvely. Another study was conducted n parallel to, but ndependent from Hereford. Here, the authors developed a PSO nspred robotc olfactory search algorthm [5]. Ths study focused manly on the specfc case of odor detecton and search. Although ther algorthm was proposed for use wth exstng hardware, all experments were conducted usng smulatons. Odor sources remaned statonary throughout the numerous experments. A paper by Pugh and Martnol [7] extended ther prevous work [6] and ntroduces another mplementaton of dpso. Smlar to Hereford s work, ths study also focused on the problem of fndng multple statc targets wthn a search space. The algorthm was mplemented on a smulated envronment usng e-puck robots [11]. Unlke Hereford s work, ths mplementaton had robots communcate wth one another at every tmestep. Ths paper s related to ther prevous work, n whch the authors use PSO as a nose resstant robot learnng algorthm [12]. Whle smlar to our own work, ths paper dd not deal wth robotc search and dd not dstrbute the PSO algorthm among the varous nodes. Our mplementaton of dpso dffers from all prevous work n that t ncorporates a communcaton scheme that wll allow transmsson of a soluton back to a montorng node. Although some of these studes assumed a lmted transmsson range between robots themselves, all experments extracted the fnal soluton by usng an oracle that only exsted wthn the smulaton. In addton, prevous studes attempted to solve problems where the target soluton was statc. Scenaros exst n whch robots are requred to track moble targets. The orgnal dpso algorthm [3] cannot be modfed trvally to perform moble target search. It does seem possble to adapt Pugh and Martnol s algorthm [7] to work wth dynamc targets, but the reportng problem would reman unaddressed. B. PSO for Robotc Control A related paper [13] uses PSO to learn optmal parameters for the search problem, but not as a soluton to the search problem tself. Other bologcally nspred models nclude Dgtal Hormone Models [14], Pheromone Models [15], [16], and Stochastc Cellular Automata SCA) [17]. These models, whle smlar, use dfferent communcaton mechansms for cooperaton and n most cases have not been appled to the problem of search. A number of statstcal models have also been developed [18 21] for use n robotc swarms. These probablstc models are dfferent from bologcally nspred models ncludng PSO) n that they are used to plan robot behavor n an offlne settng pror to runtme. Behavor for each robot s planned accordng to rules dscovered pror

3 to the search tself, and communcaton between robots s unnecessary durng the modelng process. Several papers have been publshed focusng on the robot path plannng problem usng PSO [22 25]. Ths s a dfferent problem than dpso. In path plannng, a PSO algorthm s used to determne the optmal next locaton for a robot at any gven tmestep. The PSO algorthm tself stll uses vrtual partcles to accomplsh ths, and the result s smply passed to a sngle robot as a plan of acton. Dstrbuted PSO ams to use robots as a replacement for partcles wth the logc of the PSO algorthm tself beng dstrbuted among them. Work by Nasrollahy and Javad s relevant to robotc search because t addresses moble targets [22]. Ther approach, however, s dfferent from our problem n that PSO s run at each teraton. Although the target may move over tme, the PSO algorthm s solvng for a statc target at each tmestep. We seek to deal wth nstances where a target may move durng the course of the PSO algorthm. C. Routng Protocols Our work uses concepts lkes opportunstc forwardng and delay tolerant networkng to acheve communcaton wthn the network. These notons are promnent n wreless sensor networks WSNs), and we adopt some of the technques descrbed n ths lterature for communcaton between robots. PSO has been used n WSNs for postonng moble nodes for optmal coverage and qualty of servce [26]. Two publcatons use WSNs to fnd and track a movng target but use WSNs that have been prevously deployed wth a known topology [27], [28]. The communcaton model our system uses was nspred by Boudrga et. al. [29]. Our system assumes that robots are able to know ther poston accurately n physcal space. The problem of fndng node localty n WSNs s challengng n practce and much work has been done to attempt to solve t [30]. Fnally, Haberman and Sheppard ntroduced a routng protocol for power-constraned sensor networks [31]. Ths work uses a dstrbuted form of PSO that mantans a seres of overlappng swarms, one for each node n the network. Ths s smlar to our approach n that each node represents a sngle partcle and the fnal goal s to provde communcaton wth a data collecton pont. Ths algorthm was shown to reduce the energy consumpton n sensor networks. Our algorthm dffers from ths research n that we use C-dPSO to drect the movement of robots such that communcaton wth a server s avalable. III. COMMUNICATION-ORIENTED DPSO We propose a dpso algorthm that ncorporates a communcaton objectve nto the velocty update equaton. Rather than smply pursung solutons to a specfc problem, nodes strve to reman n contact wth the server. PSO tradtonally operates by movng partcles usng a velocty update equaton. The drecton n whch partcles move corresponds to local and global best solutons as determned by a ftness functon, whch returns hgher values for better solutons. In the case of robotc search, we assume all nodes are equpped wth a sensor that detects the value of a poston. A logcal extenson for dpso s to augment the velocty update equaton wth nformaton relatng to server connecton. Ths wll have the effect of pullng ndvduals toward ether the target soluton or a locaton wth server connecton as necessary. Messages may be passed from robot to robot n an ad-hoc fashon, so drect connecton to the server s not necessary to attan nformaton exchange. Ths s related to work n delay tolerant networks, whch attempt to mantan data flow even though a contguous path may not exst [32]. The orgnal PSO algorthm operates by movng partcles based on a current velocty. Let p be the local best poston seen by partcle and p g be the global best poston seen by any partcle. The followng s the velocty update rule for partcle. v = ωv + U0, φ 1 ) p x ) + U0, φ 2 ) p g x ) where s a pont-wse multplcaton of elements. Here, ω acts as nerta and φ 1 and φ 2 denote the amount of nfluence the personal and global best postons have. Randomly samplng from a unform dstrbuton U ntroduces addtonal exploraton that may otherwse be domnated by the explotaton of a partcular soluton. The term that makes use of the personal best locaton s often called the cogntve component, whle the term contanng the global best poston s called the socal component. For smplcty, we can rewrte the velocty update equaton as follows. We use Φ to represent the random varables for readablty. v = ωv + Φ 1 Cogntve) + Φ 2 Socal) Ths update occurs durng each teraton of the algorthm pror to a partcle s movement. In the context of dstrbuted PSO, tme s dscretzed nto slces wth each tmestep servng as an teraton of the algorthm. Ideally we would lke communcaton wth the server at all tmesteps, but ths s unrealstc for problems where the search space s larger than the communcaton range of a robot. As an alternatve, we set a target number c of maxmum tmesteps before communcaton wth the server s restored, thereby lmtng the amount of tme where no communcaton s avalable. To acheve ths addtonal goal, some of the searchng power of the system needs to be dverted to the task of restorng connecton. Ths means that c s a tunable parameter, where lower values allow for more frequent communcaton wth the server and hgher values correspond to a more robust search of the avalable space. Better performance can be acheved by varyng the target number of tmesteps for each partcle. We can acheve ths by addng a unque offset θ to each c that s dfferent for each partcle so that robots attempt to communcate wth the server at dfferent tmes. By ntroducng unque offsets, robots wll travel back to the server one after another. Ideally ths maxmzes the effectveness of the adhoc communcaton by

4 creatng a chan of robots back to the server. Assumng that the sze of the swarm s known to be N, and each robot s assgned a unque dentfer R d that ranges from 0 to N 1, we can determne the tmestep offset for each robot as θ = R d c/n. By usng ths offset, each robot wll start searchng for the server at evenly spaced ntervals at the begnnng of the algorthm. As tme contnues, partcles swtch to searchng for the server based on when communcaton wth the server was last establshed. Ths communcaton-orented behavor can be acheved by modfyng the velocty update equaton to nclude a communcaton component. v = ωv + 1 mn t )) tc 1, Φ 1 Cogntve) 1, t )) tc + 1 mn Φ 2 Socal) t ) tc + mn 1, Φ 3 Communcaton) Both the cogntve and socal components are pursung a soluton wthn the space, and as such we may smplfy the equaton even further by combnng these terms nto a Goal) component. v = ωv + + mn t )) tc 1, Φ x Goal) t ) tc 1, Φ 3 Communcaton) 1 mn Here, t s the current tmestep and t c s the last tmestep n whch successful communcaton wth the server occurred. Ths new velocty update now relates the tradeoff between search and communcaton objectves. When t t c < communcaton wth the server has been establshed wthn the threshold number of tmesteps), the velocty update reverts back to the orgnal PSO verson where only the goal component s used. When t t c the target number of tmesteps have occurred snce the last successful communcaton wth the server), the goal objectve s entrely gnored and the robot focuses all efforts on reganng communcaton wth the server. The addtonal communcaton component requres a new ftness functon that denotes how good a locaton s n terms of communcaton. A value of 0.0 s awarded to a poston that s unable to communcate wth the server. If a robot s capable of communcatng wth the server drectly, t s gven a value of 1.0. It s possble to establsh a connecton wth the server va ntermedary nodes, but each addtonal hop detracts from the communcaton value. The ftness value reducton can be represented usng the followng decay formula, ftness c = e e H where e s the mathematcal constant approxmately equal to and H denotes the number of hops requred for communcaton wth the server. When H = 1 drect communcaton), a value of 1.0 s receved as expected. As H ncreases there s an exponental drop-off such that as H approaches nfnty the value goes to zero. In realty, there are a fnte number of robots, meanng that a large enough ncrease n the number of hops wll eventually result n faled communcaton wth the server. Ths wll also produce a zero value for the gven poston. When any connecton s made to the server, t c s set to t. If the connecton value s the best seen throughout the course of the algorthm, the new communcaton best locaton s stored as s. Ths trackng of the last known poston where communcaton was avalable s analogous to target trackng, n that each robot has ts own opnon of where t beleves t should go. For ths reason, future work may nvestgate the C-dPSO s ablty to track moble servers as well as targets. The fnal, un-smplfed velocty update equaton wth the ncorporated communcaton component s as follows. V = ωv t )) tc + 1 mn 1, U0, φ 1 ) p x ) t )) tc + 1 mn 1, U0, φ 2 ) p g x ) t ) tc + mn 1, U0, φ 3 ) s x ) It should be noted that communcaton to the server s only necessary when a new global best s found. There s no need to report back wth no new nformaton. Ths s accomplshed by settng t c to t for every tmestep untl a new best locaton s found. Essentally ths means the tmestep count does not begn untl a vald soluton s found. Ths allows a robot tmesteps to explot the new area n search of a better soluton before defaultng back to the communcaton goal. Communcaton between nodes may vod the need to connect to the server f a path through other robots can reach the server or f a better soluton s found by another node pror to makng contact wth the server. To accomplsh ths, robots communcate ther last known connecton tme wth the server as well as what ftness value the server had stored at that pont. Usng ths nformaton, robots may determne f better nformaton has already been relayed to the server. If so, t c s set to t and the robot resumes the task of searchng. When a new global best s found by a robot, the robot broadcasts a message wth the new global best value and ts poston to all the peer robots wthn range. Upon recevng a broadcast message that a new global best was found, the robot wll rebroadcast the message. All duplcate messages are gnored. If the new global best message manages to propagate to the server, an acknowledgment wll be sent to the orgnal robot. Upon recevng the acknowledgment the robot resets t c to the tmestep when the new global best was dscovered. Tes for the best ftness value use the one most recently observed. Ths s useful n dynamc scenaros, and s especally mportant for the communcaton ftness value where frequent tes occur.

5 IV. EXTENSION TO DYNAMIC SEARCH In addton to beng communcaton aware, t s also desrable for dpso to extend to problems wth non-statc targets. A moble target creates a dynamc search problem wth respect to poston. It s also possble for targets to change ther emtted ftness throughout tme, whch ntroduces another dynamc element to the task. In tradtonal PSO, a best locaton p or p g ) s stored based on the hghest ftness value experenced by a partcle f or f g respectvely). If the target s n moton, the partcles may reman fxed on a worthless locaton belevng t stll to have value. Typcally ths problem s solved by reevaluatng stored best postons to verfy ts ftness at later tmesteps. Ths soluton apples to targets wth changng ftness values as well. Unfortunately ths s not possble n a physcal envronment because a partcle s unable to evaluate the ftness of a locaton t s not currently at. To avod ths ssue, we decay the f and f g values throughout the executon of the algorthm. Eventually, the worth of a locaton dsspates over tme and nodes become nterested n more valuable locatons. If the target remans n the general vcnty, addtonal best locatons wll be found n the area and the values wll be boosted back to ther orgnal startng postons. Ths change to the ftness values does not affect the velocty update equaton drectly and can be appled to ether the orgnal dpso or the communcaton-orented verson. Durng each tmestep, ftness values are decayed as follows, f β 1 f f g β 2 f g f c β 3 f c where β k 0, 1] s a decay factor. If the target soluton s known to be statonary, β 1 = β 2 = 1. Smlarly f the communcaton server s known to be statonary, β 3 = 1. By reducng as a percentage of the prevous value at each tmestep, the ftness values are modeled by a nonlnear decay functon. The reducton n ftness can be thought of as a reducton n the confdence we have about the orgnal observed value. As tme contnues, the nformaton becomes less fresh, and a more recently observed poston may be more valuable despte havng a lower ftness. Ths desred effect s acheved by decayng the values as descrbed. The values for β k become new hyperparameters for the equaton, and should be tuned based on how quckly the search task s changng n the system. For systems where the target s movng quckly, β k must be set to a low value for the robots to value the freshness of nformaton more. In stuatons where the ftness value s decreasng, β k must be set so that the perceved ftness decays at least as quckly as the true ftness rate of change. Ths s not an ssue wth ncreasng ftness values, as the beleved ftness would be lower than the true ftness at a gven pont and the newer nformaton would be stored. If values are decayed too slowly, partcles wll stll face the ssue of trackng outdated nformaton. Alternatvely, f values are decayed too quckly, partcles wll lose possbly vald nformaton and essentally wll be startng over wth a random search when t may not be necessary. As targets move more quckly or ther ftness values degrade at a hgher rate, the β k values must be set lower and lower, makng t dffcult to reuse collected nformaton. V. HYPOTHESES The purpose of our evaluaton s to determne the effectveness of the proposed communcaton component and dpso s ablty to track moble targets. A number of hypotheses have been created to test these elements ndvdually. Solutons for all hypotheses are n reference to the robotc search problem. Error s determned usng the Eucldean dstance between the returned soluton and actual target poston. Frst, we hypothesze that the addton of decay mproves the performance of dpso for moble problems. We predct that dpso wth a tuned decay parameter wll perform better than dpso wth no decay when trackng a moble target, a target wth a slowly decreasng ftness value, a target wth a quckly decreasng ftness value, and a moble target wth a quckly decreasng ftness value. These problems represent a wde range of possble dynamc search problems, and the results form the foundaton for our clams. Next, we hypothesze that dpso wth a communcaton mechansm wll perform better than dpso wthout one. Performance s measured n terms of the server s knowledge of the target locaton, so communcaton s a vald concern. Fve tests are run on the same scenaros as before, plus an addtonal statc scenaro where the target s statonary wth a fxed ftness value. VI. EXPERIMENTAL APPROACH Experments are conducted n a smulated envronment. Rather than targetng a specfc robot, addtonal constrants have been added to the classc PSO algorthm to whch realworld robots must adhere. Specfcally, only partcles wthn a specfed range of each other are allowed to exchange nformaton, and the noton of a global best must be propagated through the network rather than beng mmedately avalable to all nodes. Ths smulates the potentally lmted communcaton range that robots must adhere to, but ths local best topology s often used n other PSO mplementatons as well to mprove performance. Communcaton between nodes may fal wth some small random chance, but message transfers are assumed to be successful after the start of the transmsson. Also, the velocty for each partcle s clamped to smulate a top speed for the robot. An addtonal node s constructed that acts as the server. The smulator does not consder movement constrants that may be mposed by specfc robots such as turn radus), and gnores the problem of collson as ths can typcally be handled by dedcated collson detecton algorthms. For all experments, the robots operate n a two-dmensonal space n search of a sngle target. Future work may nvestgate an extenson nto a three-dmensonal space or problems

6 wth multple targets or servers. Swarms are composed of a fxed number of eght robots. These robots, along wth the server, have a communcaton range that s 25% of the total wdth/heght of the search space. For each experment, the search problem s solved 1000 tmes, where the target s randomly assgned to a new locaton for each teraton. These targets have a fxed ftness value that degrades non-lnearly wth dstance from the source. In addton to these targets, nose s added to the search space by assgnng a large number of randomly placed nodes that produce a small ftness value. We seed the random placement of these nodes such that each experment wll be solvng the same 1000 problems each tme. We record several measurements durng the course of the experments, ncludng soluton error n terms of Eucldean dstance between the correct target locaton and the server s belef of the soluton locaton. For farness, we allot 2000 tmesteps to every algorthm, whch should be suffcent for convergence n all cases. Ths s because there s a tradeoff between the qualty of the soluton and the tme avalable, and we opt to provde suffcent tme to better study the qualty of the soluton. To properly evaluate the dynamc scenaros, the error s measured durng every tmestep from tmestep 1800 to 2000 and then averaged. Ths allows us to determne how well each algorthm s trackng a moble target after an ntal search perod. A Student s t-test was used to test statstcal sgnfcance n all cases. Four experments were conducted to test clams about the decay component. Each experment uses the newly proposed communcaton-aware dpso. The performance of C-dPSO wth a tuned decay parameter s compared to C-dPSO wthout any decay when solvng dynamc problems. β k parameters were tuned by startng wth a value of 1.0 no decay), and decreased by 0.05 untl performance on a tranng set of smulatons acheved the hghest value. We note that smlar mprovements are seen wth any value smaller than 1.0, and that these hyperparameters are relatvely nsenstve to change. Experment Dynamc 1 attempts to fnd a moble target whose top velocty s 20% of the top speed of the robots. Experment Dynamc 2 attempts to track a target whose ftness value s degradng lnearly wth tme. In ths case, the ftness value wll be 1 3 of the orgnal value at the end of the 2000 tmsteps. Smlarly, experment Dynamc 3 wll also have a lnearly degradng ftness value. In ths case however, the ftness value wll reach zero by the tme 1500 tmesteps have occurred. Fnally, experment Dynamc 4 combnes the dffcultes ntroduced by Dynamc 1 and Dynamc 3. Ths wll attempt to track a target movng at 20% of the speed of the robots whose ftness value s degradng and wll have completely depleted by 1500 tmesteps. Addtonally, fve experments were performed to test the clams about the communcaton component. Each experment compares dpso wth the new communcaton-aware velocty update equaton wth the exstng standard dpso algorthm. Each algorthm uses the same optmally tuned decay parameters to observe the effects of the communcaton component on ts own. Experment Comm 0 deals wth a statc problem TABLE I: Summary of Experment Attrbutes Experment Communcaton Dynamc Target Dynamc 1 Moble Dynamc 2 Decay Dynamc 3 Fast Decay Dynamc 4 Moble Fast Decay Comm 0 Statc Comm 1 Moble Comm 2 Decay Comm 3 Fast Decay Comm 4 Moble Fast Decay where the target s statonary and has a fxed ftness value. Experments Comm 1, Comm 2, Comm 3 and Comm 4 operate on dentcal problems as Dynamc 1, Dynamc 2, Dynamc 3, and Dynamc 4 respectvely. The dfference s that nstead of analyzng the effects of decay, the communcaton aspect of the algorthm s now beng tested. These nne experments are summarzed n Table I, where the Communcaton column ndcates that the communcaton mechansm s beng vared and Dynamc ndcates that the decay component s beng tested. The last column descrbes the behavor of the target durng the search process. VII. EXPERIMENTAL RESULTS Results for the dynamc experments are shown n Table II. Recall that each experment tests the performance of the C-dPSO algorthm wth and wthout decayng the ftness values. At a sgnfcance level of 0.05, C-dPSO usng decay outperformed by reportng a more accurate soluton) the verson that dd not for the moble target experment Dynamc 1), the fast decay experment Dynamc 3) and the moble fast decay experment Dynamc 4). In the slow decay experment Dynamc 2), C-dPSO stll produces a smaller mean error, although ths value s not sgnfcant untl we consder a 0.1 sgnfcance level. Recall that experment Dynamc 2 was the case where the target s ftness value degrades slowly. It s lkely the dfference between the algorthms was smaller n ths case, because the problem was close enough to the statc case. Ths observaton s supported by the fact that the fast decay experment Dynamc 3) dd acheve statstcal sgnfcance, whch s smply the case where the target s ftness value degrades faster. These results show that decayed ftness s especally mportant when the target s n moton. Table III shows the communcaton results for the statc target Comm 0), moble target Comm 1), slow decay Comm 2), fast decay Comm 3) and moble fast decay Comm 4) experments. In ths case, dpso augmented wth the communcaton mechansm C-dPSO) performed better than the orgnal dpso algorthm for all experments at a 0.05 sgnfcance level. Ths s not surprsng, as the error s measured wth respect to the server s belef of the target poston. Wthout the communcaton component n the dpso velocty update equaton, the server s only notfed f a robot enters communcaton range by chance. Ths means that the orgnal dpso algorthm may

7 TABLE II: Dynamc Results n Eucldean Dstance Experment C-dPSO C-dPSO Decayed p-value Dynamc < 2.2e-16 Dynamc Dynamc Dynamc < 2.2e-16 TABLE III: Communcaton Results n Eucldean Dstance Experment dpso C-dPSO p-value Comm e-05 Comm e-12 Comm e-03 Comm e-05 Comm e-03 Fg. 1: Tme seres graph for moble target search problem. be capable of fndng a soluton but has no effectve method of relayng ths nformaton to a useful locaton. Fgure 1 s a tme seres graph for a sngle smulaton run on the moble target experment wth decay. Ths fgure llustrates the orgnal dpso algorthm s nablty to communcate consstently wth the server, as depcted by the spkes n soluton error over tme. Whle C-dPSO s requred to report back to the server at routne ntervals, standard dpso focuses solely on fndng the target. When measurng error from the server s pont-of-vew, ths results n a consstently low error for C- dpso and pecular spkes n error for dpso. These spkes occur as the target moves away from the locaton the server had stored prevously. On occason, a partcle concdentally comes n contact wth the server and s able to communcate an updated poston. Although ths reduces the error to a nearzero value, t begns to rse agan mmedately once the partcle moves away from the server. Ths behavor s consstent wth other runs for all experments. For ths reason, Fgure 1 serves as a representatve for all other runs n ths scenaro. The results shown n both tables strongly support the hypotheses presented n secton V. Specfally, the addton of decay mproves the performance of C-dPSO when faced wth suffcently dynamc search problems. Also, C-dPSO outperforms standard dpso, when algorthm error s measured based on a servers belef of the target locaton, or value. VIII. DISCUSSION The proposed communcaton scheme wll be useful f mplemented on smart robotc swarms where the soluton space s larger than the connecton range to the server. The proposed approach for relayng nformaton s dstrbuted among the robots and dynamcally adapts to changng condtons. In partcular, ths algorthm s agnostc wth respect to the number of robots, servers, and targets. The ftness evaluaton for the target can also be modfed easly wthout changng any other parts of the algorthm. The couplng between soluton and communcaton goals wll drect robots toward necessary locatons n the search space at all tmes. The dstrbuted nature of the algorthm ndcates that t should functon despte a varyng number of robots. In addton, the desgn of the algorthm does not place any restrctons on the sze of the search space and wll even allow for movng optma. Assumng the number of avalable robots s suffcent to provde reasonable coverage, the algorthm wll be able to functon n ncreasngly large search spaces. Unattended search drones are a partcularly useful applcaton for robots capable of these tasks [33 35]. These drones are ntended for use over a wde area and are often assgned to the task of fndng a moble target. Ths ntroduces stuatons where communcaton range s lmted [36] and wll necessarly requre the contnual trackng of a target. A specfc, applcable event occured on March 3, 2014 when Malaysa Arlnes Flght 370 went mssng [37]. The arcraft presumably went down n the Indan Ocean, but no crash ste was found. Automated underwater vehcles AUVs) were used to scan the ocean floor for the sgnal emtted by the blackbox, but unfortunately the batteres powerng the blackbox eventually depleted. In a scenaro such as ths, a form of dpso wth decayng ftness values may be an effectve method of drectng these autonomous vehcles to fnd the black box and export ts locaton to a search shp. IX. CONCLUSION In ths paper, we presented a verson of dstrbuted partcle swarm optmzaton that ncorporates a communcaton component nto the velocty update equaton. Ths addtonal term uses a separate ftness evaluaton that promotes communcaton wth the server. Experments showed that for a varety of problems, our method provded a superor server-stored soluton to that of standard dpso. We also ntroduced the concept of decayng ftness values to adapt dpso to track movng targets. In ths case, we found that decay s necessary to track effectvely moble targets or targets whose ftness s degradng over tme. In scenaros where a soluton s located outsde of the communcaton range of a montorng server, the dscovered solutons are only as good as the ablty to relay ths nformaton back to the server. Ths s partcularly true of moble trackng problems, where the server wll deally receve consstent updates on the whereabouts of the target. In future work, we wll nvestgate problems nvolvng one or several moble communcaton servers. Our algorthm

8 currently supports the trackng of a server n the same way target trackng s accomplshed. Ths may be useful n stuatons where a ploted vehcle s attemptng to fnd a target wth the assstance of several autonomous vehcles. Another nterestng extenson s to examne the effect of ncreased communcaton range for the server alone. It s feasble that the server node may have a larger communcaton range than the robots themselves, whch would allow server nformaton to be propagated more easly through the swarm. Fnally, we plan to extend these tests nto 3-dmensonal search problems. Ths extenson s trval as t smply requres an addtonal term n each partcle s poston and velocty vectors. Identcal experments would then be run to verfy the usefulness of our algorthm for applcatons nvolvng flght. We also hope to mplement ths algorthm on a set of real robots to elmnate any bas ntroduced by the smulator tself. 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