A Mobile Robots Experimental Environment with Event-Based Wireless Communication

Transcription

1 Sensos 2013, 13, ; do: /s Atcle OPEN ACCESS sensos ISSN A Moble Robots Expemental Envonment wth Event-Based Weless Communcaton Maía Gunaldo 1, *, Enesto Fábegas 1, Gonzalo Faas 2, Sebastán Domdo-Canto 1, Dctno Chaos 1, JoséSánchez 1 and Sebastán Domdo Depatment of Compute Scence and Automatc Contol, UNED, Juan del Rosal 16, Madd 28040, Span; E-Mals: efabegas@bec.uned.es (E.F.); sebas@da.uned.es (S.D-C.); dchaos@da.uned.es (D.C.); jsanchez@da.uned.es (J.S.); sdomdo@da.uned.es (S.D.) School of Electcal Engneeng, Pontfca Unvesdad Católca de Valpaaso, Av. Basl 2147, Valpaaso, Chle; E-Mal: gonzalo.faas@ucv.cl * Autho to whom coespondence should be addessed; E-Mal: mgunaldo@da.uned.es; Tel.: ; Fax: Receved: 15 Ma 2013; n evsed fom: 12 Jul 2013 / Accepted: 18 Jul 2013 / Publshed: 22 Jul 2013 Abstact: An expemental platfom to communcate between a set of moble obots though a weless netwok has been developed. The moble obots get the poston though a camea whch pefoms as senso. The vdeo mages ae pocessed n a PC and a Waspmote cad sends the coespondng poston to each obot usng the ZgBee standad. A dstbuted contol algothm based on event-tggeed communcatons has been desgned and mplemented to bng the obots nto the desed fomaton. Each obot communcates to ts neghbos onl at event tmes. Futhemoe, a smulaton tool has been developed to desgn and pefom expements wth the sstem. An example of usage s pesented. Kewods: dstbuted contol sstems; moble obots; mult-agent sstems; weless communcatons; embedded sstems 1. Intoducton Sgnfcant developments n the felds of communcaton technolog, weless technolog, embedded devces, and man othes, have enabled the development of autonomous a, gound, o

2 Sensos 2013, undewate vehcles. Goups of such vehcles, efeed to as agents, can be utlzed to solve a vaet of poblems ve effcentl, such as fo example exploaton and montong tasks. One of the man poblems n these sstems s when the contol task s centalzed. Ths centalzaton demands a ve poweful communcaton netwok to send state nfomaton n a tmel manne and detaled models of the moble obot nteactons. Both of these equements can geatl lmt the scalablt of centalzed appoaches n netwoked contol sstems. An altenatve wa s to use a dstbuted appoach [1,2], whee each moble obot decdes ts actons based onl on hs own state and the dect neghbos nfomaton, whle guaanteeng that the whole goup fulflls a common goup objectve. One example of a goup objectve fo mult-agent sstems s state ageement o consensus,.e., all agents ae supposed to convege to a common pont o state. Such consensus poblems have a vaet of applcatons n flockng, atttude snchonzaton n satellte swams, dstbuted senso netwoks, congeston contol n communcaton netwoks, o fomaton contol [3]. We ae patculal nteested n the last feld of applcaton snce achevng a stable fomaton s analogous to eachng consensus. In ths consensus poblem the agents communcate though a netwok exchangng nfomaton to each the desed fomaton. Specfcall, we popose to ncopoate weless lnks between the moble obots to suppot the communcatons, the embedded sstems, and the contol. Moeove, all eal netwoks have bandwdth lmtatons that can cause delas n message delve poducng a majo mpact on oveall sstem stablt [4]. In ths sense, t s desable to know how fequentl moble obots should communcate such that the sstem mantans a desed level of pefomance. In ths lght, event-based communcatons ae an altenatve to tme-scheduled contol [5], and the have been n the focus of man eseaches n ecent eas such as [6 11], to menton just a few. In the lteatue, seveal smplfcatons ae usuall done n both the obot dnamcs and the netwok models of a mult-agent obot sstem. Howeve, a eal obot has ts own phscal pats, ncludng sensos, pocessos, actuatos, and communcaton devces. Theefoe, ts lmtatons must be consdeed, such as those elated to computatonal powe, senso eos, and actuatng and communcatng devces. Ths pape pesents a mult-agent appoach though the use of a decentalzed contol wth event-tggeed communcaton n a moble obot fomaton contol wth a consensus algothm. The decentalzed contol s less vulneable to a node falue and ease to scale than the centalzed appoaches pesented n [12 14]. In [12] the fomaton contol of a mult-khepea obot sstem s solved wthout communcaton between obots. Howeve, each obot executes an algothm peodcall that eques the knowledge of the complete gaph of the fomaton, so t s computatonall ntensve fo lage numbe of obots. Centalzed appoaches ae poposed n [13,14]. In [13] all complext of sensng, contol, and computaton s elegated to the leade of a goup of obots, and [13] teats the obots fomaton as a sngle vtual gd stuctue. A decentalzed appoach fo coopeatve contol s pesented n [15] and a detaled hadwae descpton s gven and seveal expemental examples of mult-vehcle contol fo TXT-1 monste tucks fom Tama, Inc, ae gven fo both communcaton and vson fomaton contol. In [16] a hadwae platfom fo a sngle vehcle s developed and a PID event-based contol s mplemented. Howeve, none of these woks consde dstbuted event-based contol n a mult-obot envonment. Hence, the man contbuton of ths pape s the mplementaton of dstbuted event-tggeed

3 Sensos 2013, algothms n a eal moble obots platfom snce, to the best knowledge of the authos, all the esults n ths feld ae manl theoetcal and onl pesent smulaton esults. The expemental esults show the goodness of the event-tgge appoach compaed to tme-dven contol, educng the communcaton between agents. Futhemoe, n contast to othe woks, as fo example [12,15], n whch a costl platfom fo ndoo o outdoo expementaton s used, we gve a detaled descpton of ou low-cost hadwae platfom, and how t was mplemented n LEGO obots, n ode to help eades who ae consdeng buldng a smla sstem fo eseach, educatonal puposes [17], o to mmc eal wold exploato applcatons [18]. An nteactve smulaton, whch s avalable at s also pesented as a complement to the expemental setup. Ths smulaton helped n the desgn and tal of dffeent expements wth vaable sstem and netwok condtons. The pape s oganzed as follows. Secton 2 descbes n detal the expemental envonment and ts components. Secton 3 gves a backgound on event-based contol and mult-agent sstems, and the extenson of these to the fomaton contol of a mult-obot sstem. Secton 4 descbes the smulaton tool and an example of usage. Secton 5 dscusses expemental esults and compaes them to smulaton esults and expeences based on tme-dven contol. Fnall, Secton 6 ends the pape wth conclusons and suggestons of futue woks. 2. Test Platfom Descpton We next descbe the expemental envonment desgned wth low-cost components. Ths ma help eades to buld smla sstems. It can also be scaled up o down to equp bgge o smalle obots, espectvel [19,20] Platfom Achtectue and Components The developed tool s a test platfom fo mult-moble obot sstems. It conssts of two man components: the vson and the communcaton sstems. Dffeent softwae tools exchange nfomaton to tansfom the mages captued b the camea nto postonng data, whch ae sent to the obots va weless communcatons. Fgue 1 shows the block dagam of the achtectue and the components of the platfom, whch ae the followng: 1. A pesonal compute (PC) to calculate and send the poston and oentaton to the obots. 2. A CCD camea (chage-coupled devce) connected to the PC and equpped wth wde angle optcs. The camea s placed n the celng of the oom, as descbed n [21]. 3. A Waspmote Gatewa cad connected to the PC [22]. 4. A goup of LEGO Mndstoms NXT obots wth the HTechnc IR RC Ca confguaton [23,24]. 5. A Waspmote cad connected to each NXT LEGO Mndstoms obot b I 2 C pot [25].

4 Sensos 2013, A contol and communcaton applcaton, developed n LabVIEW, fo each NXT LEGO obot. 7. An applcaton, wtten n C++, fo each Waspmote cad. 8. An applcaton (unnng on the PC), developed n LabVIEW, fo the nteacton wth the camea [21]. 9. A Java applcaton, bult wth Eas Java Smulatons (EJS) [26], fo communcaton between the obots and the PC. 10. A Java XBee API to send and eceve data though the Waspmote Gatewa cad [27]. 11. The JIL seve [28] to lnk LabVIEW wth EJS. Fgue 1. Block dagam of the platfom achtectue Vson Sstem Though LEGO platfoms povde an nteestng goup of sensos such as ultasonc, touch, o lght sensos, thee s no devce fo measung absolute postons. Ths makes expementaton n obot fomaton contol dffcult. One opton to solve the pevous dawback s the use of a GPS as the man localzaton senso as n [29]. Howeve, when the expements ae pefomed ndoos, GPS s mpactcal. Anothe altenatve s to ncopoate a vson sstem to get the obots poses. The ecent appeaance of RGB-D cameas has made possble 3D mappng fom a sngle mage and state estmaton. Howeve, unnng the obot eal-tme state estmaton algothms on boad would eque a poweful compute, whch would ncease the cost of the platfom consdeabl. Thus, a sngle camea on the celng obseves the aena fom an ovehead poston. Each obot can be dstngushed thanks to thee hgh

5 Sensos 2013, bghtness LEDs. These lght spots fom an sosceles tangle wth dffeent aspect ato fo each obot as shown n Fgue 2a. In Fgue 2b, the ponts Pa, Pb, and Pc epesent the LEDs. The oentaton s denoted b θ. The poston of each obot s calculated usng the cente of mass (Xcm; Ycm). Fgue 2. (a) The NXT LEGO obot, (b) Isosceles tangle fomed b the LEDs. (a) (b) The Basle A631fc CCD camea (block 2 of Fgue 1) s confgued n monochome mode fo mage acquston n ode to maxmze the esoluton and shutte speed. Unde these condtons, we obtan mages wth a esoluton of 1,388 1,038 pxels at 18.7 fps. The mages captued b the camea ae pocessed b the LabVIEW Camea App (block 8 of Fgue 1), whch computes the obots poses. The executon of the applcaton mples the followng steps: Bael dstoton coecton: The mage magnfcaton deceases wth dstance fom the optcal axs. The appaent effect means that an mage has been mapped aound a sphee (o bael). Pespectve tansfomaton: Tansfoms the coodnates of the object to the camea coodnates, makng otaton and tanslaton tansfomatons. Calculaton of postons and oentatons: Fom the efeence ponts on the gound, we calculate the poston and oentaton takng nto account the mopholog of the obtaned ponts. Tansfomaton of coodnates: Fom pxels to metes. Calbaton: Gets the pespectve calbaton paametes. The font panel of the LabVIEW Camea App s shown n Fgue 3. The values of the confguaton of the camea (gan, shutte, and fame ate) and the peod (T) ae equed to compute the beangs, and shown on the font panel. The applcaton sends the absolute poston and oentaton to the obots eve 200 mllseconds. Futhe detals about ths applcaton can be found n [21].

6 Sensos 2013, Fgue 3. Use nteface of the Camea LabVIEW App Communcaton Sstem Afte the pocessng of the obots poses, the ae sent to the obots. Each one eceves ts poston and oentaton, and decdes when to boadcast ths nfomaton to ts neghbos based on the local data, updatng the contol law aftewads. Thus, the contol s dstbuted n the sense that each obot takes b tself the decson of when to tansmt ts state and the contol law s computed locall, n contast to [16], whee the contol law s computed on the cental compute and sent to the obots. Waspmote boads (block 5 of Fgue 1) ae used fo the weless communcatons. Ths cad has a modula achtectue and s based on the Atmel ATMEGA 1281 mcocontolle. The Waspmote also ntegates the Dg XBee RF (ZgBee standad) module fo communcaton n the ISMB bands (Industal Scentfc Medcal Band, RF-868 MHz) [30]. Ths module communcates wth the mcocontolle va nteuptons usng the UART at the speed of 38,400 bps. It allows the defnton of dffeent netwok confguatons (e.g. p2p, tee, o mesh) and uses the potocol wth a fequenc of 2.4 GHz [22]. Fo weless netwok settngs, each cad uses the MAC addess of ts coespondng XBee. Each obot talks to ts neghbos gven b the communcaton gaph (see Sectons 3 and 4.2 fo futhe detals). The powe suppl fo the Waspmote s a lthum batte. The eneg sstem has fou opeatonal modes (on, sleep, deep sleep, and hbenate). In nomal opeatng mode (on), the consumpton s 9 ma. Eve 125 ns the mcocontolle uns a outne of low level (machne language) nstuctons [31,32], whch s fast enough to the tme equements of ou sstem. The I 2 C bus ntefaces the NXT LEGO wth the Waspmote. The NXT LEGO uns as maste and the Waspmote as slave. The Waspmote cad uns an applcaton (block 7 Fgue 1) that allows the LEGO NXT to communcate wth othe obots and the PC. Eve 100 ms the followng tasks ae executed:

7 Sensos 2013, It checks f a packet has been eceved b the XBee ado. Packets can be sent fom the PC o fom anothe obot. If the answe s postve, the eceved data s stoed n a buffe untl the NXT LEGO eques t. 2. It checks f a flag s tue. If the answe s postve, t ndcates that the NXT LEGO eques the sendng of a packet to othe obots (ts neghbos) b Xbee ado. Once the packet s sent the flag s set to false. The NXT LEGO tgges an nteupton outne (whch sets the flag to tue) when a packet must be sent. In event-based contol, the flag s set to tue at the event occuence tme. Each NXT LEGO uns a LabVIEW App (block 6 of Fgue 1) to nteface wth the Waspmote cad b I 2 C (see Secton 2.4 fo futhe detals). Ths applcaton equests data to the Waspmote eve 200 ms. If the eceved packets ae fom the camea applcaton (own poston and oentaton), the poston s compaed to the last boadcasted poston,.e., to the state whch geneated the last event. If the dffeence s geate than a theshold, then the cuent poston s sent to ts neghbos b usng the I 2 C nteface wth the Waspmote. B contast, f the souce s an obot n the neghbohood, the eceved data s then used to update the contol law as explaned late n Secton 3. The communcaton between the PC and the Waspmote s caed out b the Waspmote s Gatewa (block 3 of Fgue 1) connected to the PC though the USB pot. The Waspmote s Gatewa has dves fo Java but not fo LabVIEW. Fo ths eason, t s necessa to use an applcaton developed n Java to send the data to each coespondng obot usng the gatewa. In ths case, the JIL Seve applcaton [28] (block 11 of Fgue 1) s used as nteface between the camea applcaton and the EJS Robots App (block 9 of Fgue 1). Ths latte applcaton sends the poston and oentaton to the obots b usng XBee-Java-API (block 10 of Fgue 1). The data packet sent fom the PC and between the obots has a sze of 16 btes. Ths s the maxmum sze allowed b NXT LEGO Mndstoms fo the communcatons b I 2 C pot [33]. Fgue 4 shows the packet stuctue, whch s as follows: Bte 0 (S): The souce whee the packet comes fom. The value s 0 fo the obot 0, 1 fo obot 1, and so on. Btes 1 4 (X 1 X 4 ): 4 btes coespondng to the X coodnate of the obot poston. Btes 5 8 (Y 1 Y 4 ): 4 btes coespondng to the Y coodnate of the obot poston. Btes 9 12 (T 1 T 4 ): 4 btes coespondng to the obot oentaton (θ). Btes 13 15: Not used n ths platfom. Fgue 4. Data packet stuctue Usng I 2 C n NXT LEGO The LabVIEW toolkt fo LEGO has buffes to wte and ead n each pot, and thee sstem call methods to access to these buffes. The wte opeaton begns wth the coespondng sstem call method, whch consttutes the stat of an asnchonous tansacton between the NXT bck and the

8 Sensos 2013, Waspmote. If the etun value s zeo, the method stats a communcaton tansacton. Afte a wte tansacton s stated t s necessa to use a sstem call functon to check the status of the pot. To ensue the success of the tansmsson, thee s a sstem call functon to check the status pot. The ead opeaton of a devce though I 2 C pot s caed out n two stages. Fst, a wte opeaton must be executed wth the numbe of btes that the slave has to send. If the count of btes avalable n the ead buffe s not zeo, the ead opeaton s executed and the data s obtaned n the extenal buffe. 3. Event-Based Contol and Communcaton n Mult-Agent Sstems 3.1. Mult-Agent Sstems and the Consensus Poblem The smplest model to epesent the communcaton topolog of a mult-agent sstem s a gaph G = {V,E}, whee the nodes V coespond to agents and the edges E epesent communcaton lnks between nodes. Accodng to [3], a smple consensus algothm to each an ageement egadng the state of N sngle ntegatos of the fom x u can be expessed as an nth ode lnea sstem on a gaph: x j x ( t x ) jn The dnamcs of the goup of agents can be wtten as: (1) x Lx( t) (2) whee L s the laplacan of the gaph, and N the set of neghbos of the node [34]. Based on analtcal tools fom algebac gaph theo, t can be shown that f the gaph s connected, then thee s an unque equlbum state fo Equaton (2) of the fom x 1, whee 1 N N 1 x ) (0 and 1 = (1 1) T. Consensus algothms can be extended to fomaton contol f the fomaton s epesented b vectos of elatve postons of neghbong agents. In patcula, let us denote b j the desed nte-vehcle elatve poston vecto. The followng contol law: x x j x j j N elds the goup to acheve the objectve of the fomaton. The consensus poblem has been extendng egadng the agents dnamcs to hghe ode ntegatos [35,36], o lnea sstems [37] Model of Non-Holonomc Moble Robots Sngle o double ntegatos do not descbe popel the dnamcs of most of commecal moble obots, snce these cannot move n an decton nstantaneousl. In obotcs, holonomct efes to the elatonshp between the contollable and total degees of feedom of a gven obot. If the contollable degees of feedom ae less than the total degees of feedom the vehcle s non-holonomc. To avod the non-holonomc constant, Refeence [38] defnes the dnamcs n tems of the font wheels coodnates x, as: eq (3)

9 Sensos 2013, whee x cos d sn v sn d cos 0 1 x x d cos, d sn. The tple (x,, θ ) denotes the poston and the oentaton of the vehcle (see Fgue 2b, x = Xcm, = Ycm fo each vehcle), and v and ω ae the longtudnal and angula veloctes, espectvel. Let us consde as contol nputs fo each obot u = (v, ω ) Tme Schedule Contol In a dstbuted contol appoach, each agent collects nfomaton fom ts neghbong nodes and updates the contol law accodng to some ules. In a netwoked sstem, collectng nfomaton means to tansmt t though the communcaton channel. The nfomaton can be tansmtted though the netwok n a peodc o an event-based fashon. The fst case nvolves the tadtonal appoach of samplng at pe-specfed tme nstances, usuall sepaated b a specfc samplng peod. Howeve, the selected peod must assue adequate sstem pefomance ove a wde ange of opeatng condtons. Ths can eld to a consevatve choce and esult n sgnfcant ove-povsonng of the communcaton-netwok. Event-tggeng epesents one wa of geneatng spoadc tansmssons acoss netwok channels [39]. The communcaton s nvoked onl when somethng sgnfcant has occued n the sstem. The poblem of mult-agent sstems wth event-based communcatons has been ecentl addessed [40,41]. Wheeas the contolle desgn of [41] s centalzed, [40] pesents a dstbuted appoach, n whch the agents ae modeled b sngle and double ntegatos. The contol law s based on the states that the agents boadcast to the neghbos though the netwok at event tmes. The aveage consensus s eached pesevng convegence popetes and the expemental esults show a sgnfcant educton n the numbe of tansmssons espect to a peodc appoach. Dstbuted event-based contol has been also addessed n [42], whee phscal couplng ma exst between the subsstems. The contol sgnals n each obot ae computed based on the boadcasted nfomaton, whch means that ae not updated contnuousl, not even at each measuement of ts own state eceved b the camea (see Secton 2.2). The ule to detemne when to boadcast s gven b the tgge functon. A tgge functon detemnes the nstants of tme { t k} at whch each agent boadcasts the state to ts neghbos. In geneal, these boadcastng tmes ae not equdstant as n peodc communcatons. Moeove, the poposed tgge functons depend on local nfomaton onl. If we denote the state of an agent as x (t) and xˆ as the boadcasted state of agent to ts neghbos, whch s a pecewse constant functon, an event s tggeed fo an agent when: f ( ), ˆ ( ), ˆ ( ) x t x t x j t 0 (5) jn s fulflled, whee N s the neghbohood of agent. The tgge functons ae sad to depend on local nfomaton because the decson of when to e-compute the contol law depends on the last update values and the neghbos states, and each agent does not have to monto the states of ts neghbos contnuousl n ode to evaluate the tggeng condton, n contast to the tgge ules poposed n [10]. (4)

10 Sensos 2013, Specfc tgge functons based on the eo e ˆ x x ae poposed. Fo example, statc tgge functons have the fom f ( e ) e c, whee c 0 0 s a constant value. The contol law u = (v, ω ) to each the desed fomaton s computed as: whee: v cos sn d sn d cos 1 L 0 0 xˆ x L ˆ T xˆ and ŷ ae the stack vectos of the boadcasted postons,.e. xˆ xˆ,..., xˆ 1 N T ˆ ˆ,..., ˆ. 1 N (6) and x and ae the stack vectos of the desed postons of the agents wth efeence to the cente of the goup. Combnng Equatons (4) and (6) t elds that: x L xˆ x L ˆ (7) 3.4. Stablt Anaalss Note that defnng the contol law gven n Equaton (6), two decoupled equatons ae obtaned and the coespond to the equaton of the event-tggeed consensus poblem of sngle ntegatos studed n [40], but extended to each a fomaton. Thee t was poved that the consensus was eached, so n ths case the agents acheve the desed fomaton tanslated nto the XY plane b a vecto whch s the aveage of the ntal postons (aveage consensus). Hence, the stablt esults sum up n the followng coolla to the Theoem 4 n [40], n whch tme-dependent tgge functons of the fom: f ( 1 t e ) e ( c0 c e ) (8) ae consdeed. Remak 1. In tgge functons gven n Equaton (8) t s assumed that the ntal condtons ae t 0 = 0. Othewse, Equaton (8) can be ewtten as: f ( e ) e ( c 0 c e ( tt 0 ) 1 whee t 0 efes to the ntal tme of the expement. Thus, the theshold deceases exponentall and takes the value c 0 n the lmt when tme goes to nfnt. Coolla 2. If tgge functons gven n Equaton (8) ae defned fo the eos n the x- and - coodnates, such that: e e x,, xˆ ˆ x, the fomaton gven b x, s eached wth an eo that depends on the value of paamete c 0 of the tgge functon, and the cente of the fomaton s the aveage of the ntal postons: ) (9) (10)

11 Sensos 2013, Poof. Let us denote: a a x x 1 N 1 N N 1 N 1 x x (0) (0). x a 1 x a 1 (11) (12) the dsageement vectos n the x- and -coodnates, espectvel, whee 1 = (1 1) T egenvecto of the laplacan L [3]. Thus, t holds that x,, and t elds: x L x ex L e, x s an (13) whee e x = (e x,1 e x,n ) T and e = (e,1 e,n ) T. Hence, applng the esults of Theoem 4 n [40], t elds the dsageement vectos, convege to the followng egons, espectvel: x L x ( G) 2 L ( G) 2 Nc 0 Nc, whee ( ) s the algebac connectvt of the gaph G (second smallest egenvalue of L). 2 G Remak 2. Note that the convegence of the dsageement vectos x, poves that the goup of obots eaches the fomaton at ( ax1 x, a1 ) wth an eo gven b Equaton (14). Despte the fact that the exstng theo that poves the obustness of the poposed contol stateg and the smulaton esults that show a sgnfcant mpovement as fa as the numbe of tansmssons between agents s concened, thee ae nethe expemental esults on a eal platfom no a smulaton tool to pefom a wde set of expements of fomaton contol of moble obots. The followng secton descbes the developed softwae and all ts capabltes. 4. Smulaton Tool The man contol and sstem confguaton optons needed to smulate a mult-agent sstem demand a gaphcal use nteface (GUI) wth a hgh degee of flexblt. The GUI s ntended to make apd pototpng and smulaton of weless autonomous agents whch execute dstbuted contol algothms and pefom event-based communcatons. Nevetheless, the GUI has been made keepng the nteacton wth the use elatvel smple and ntutve n ode to be used as a pedagogcal tool fo advanced engneeng contol couses. The smulaton tool s avalable on lne at See [43] fo futhe detals Descpton of the Smulato The nteface of the applcaton, shown n Fgue 5, has fve man panels, a menu ba, and a small task ba. The two uppe panels of the nteface povde a quck vew of the mult-agent sstem and a tme plot of the outputs and contol sgnals. The top left panel shows an anmaton of the complete 0 (14)

12 Sensos 2013, mult-agent sstem. Each agent s numbeed and shows a tace of ts fome postons. The lowe left panel, named Agent Paametes, allows uses to set the numbe of agents n the sstem, as well as to add and emove a patcula agent. Fgue 5. Illustatve example of the smulaton tool. A mult-agent sstem wth fou agents s smulated. Note that the contol actons ae constant between two communcaton events. The tme plots on the top ght panel, whch ae gouped n the Sstem Sgnals tab, dspla the elatve dstance to the desed fomaton as well as the contol actons of each agent. Thee ae also plots gouped n the Netwok Sgnals tab, whch povde nfomaton about the measued dela of the sent packets. The lowe panel, named Netwok Paametes, s devoted to settng up the netwok dela and also the netwok packet loss. Uses can choose ths panel to set fxed o andom dela and loss pobablt functons. The lowe ght panel Contol Paametes s used to specf the communcaton stateg whch tgges the sendng of packets fom the agents n ode to update the contol actons. The nteface s completed wth a top task ba that povdes buttons to stat, pause, and eset the smulaton. The components of the nteface descbed eale povde the basc functonalt equed to opeate the applcaton. A menu ba povdes some addtonal featues such as the possblt to specf the dnamc model of the agents and to select a pedefned mult-agent sstem confguaton and the expement to be pefomed. The use can also save a confguaton, mak t as default o load a pevous confguaton A Pactcal Example Ths secton pesents a usage example of the smulato descbed above. Dffeent expements ae pefxed. We select one of them n the top menu, fo example, Expement 2, n whch the communcaton

13 Sensos 2013, topolog fo fou vehcles s gven b the gaph n Fgue 6, and the desed fomaton espect to the cente of the goup s: , x (11) Fgue 6. Communcaton gaph descbng one-dmensonal netwok topolog. The use can fnd n the help menu all the nfomaton about these expements. Random ntal condtons ae geneated, but we ma be nteested n compang the pefomance of dffeent contol stateges (peodc and event-based, fo example) fo a pefxed ntal coodnates. We can do that b ght-clckng n the dawng panel and selectng the opton Settng cuent state as default. Fgue 5 shows the smulaton output when the tgge functon s of the fom 0.2t f ( e ) e e. The use can change the paametes of f whle the smulaton s unnng o swtch to a peodc communcaton and check onlne the effect of these changes n the sstem. 5. Expemental Results 5.1. Compason of Smulaton and Expemental Results Fgue 7a,b shows the second component of the contol sgnals (ω ) and the dstances to the 2 2 fomaton d x x ) (, espectvel, fo the fou agents when the expement descbed (,, ) n Secton 4.2 s pefomed ove the model (sold lnes) and the eal sstem (dashed lnes). Fgue 7. Compaatve of smulaton and expemental esults: (a) Contol sgnal, (b) Dstance to fomaton. (a) (b)

14 Sensos 2013, We obseve that the majo dscepances ae at the begnnng of the expement. Note that the contol sgnals ae constant pecewse functons and change the value onl at event tmes, whle Equaton (6) eads that the change contnuousl wth the oentaton θ even though x ˆ x and ˆ eman constant n the nte-event tmes. The eason fo ths s the constant mposed b the hadwae n the eal sstem. Because one agent cannot monto ts state contnuousl (the camea sends measuements eve 200 ms, whch s the mnmum peod allowed b the Waspmote cads), and the slow vaaton of the angle, the computaton equed to mplement the contnuous contol law gven n Equaton (6) s not woth. Thus, the angle s consdeed to eman constant between events. Moeove, the selected tgge functons decease wth tme. Ths means that the theshold to detect an event s geate fo small values of tme, and fewe events ae geneated consequentl. When the sstem appoaches to the desed fomaton, the theshold deceases and makes the eo abta small. Note that d takes the same value fo all = 1,,4 and the fnal state onl depends on the ntal condtons, as pedcted b the consensus poblem theo (see Secton 3). Howeve, the fnal state fo the eal expement dffes slghtl fom the esult gven b the model. The eason fo that mght be sensng eos, dead-zone n the actuato and/o tansmsson delas. Fnall, Fgue 8 shows the vew of the expement at t = 0, 6, 12, and 24 s. Fgue 8. Vew of the eal expement at t = 0, 6, 12, and 24 s Event-Tgge Vesus Tme-Tgge Fgue 9 compaes the esults obtaned fom event-tgge and tme-tgge expements. In the last case, each agent eceves data fom the camea eve 200 ms, t pocesses the nfomaton, boadcasts ts state to ts neghbos, and computes the contol law eve two samples (400 ms). In the lowe gaph of Fgue 9 the boadcasts n both cases ae depcted fo each agent (labeled fom 1 to 4). Fo the peodc case, the numbe of packets sent though the netwok dung the expement should be 50s 4agents / Howeve, fo the event-based contol ths numbe s b fa lowe: 83 events n total.

15 Sensos 2013, Fgue 9. Compason of the esults obtaned fo event-tgge and tme-tgge expements. In the uppe gaph of Fgue 9 the dstance to the fomaton s shown. Note that even though the desed fomaton and the ntal condtons ae the same, the fnal state (whch depends on the aveage of the ntal postons) s dffeent. As emaked befoe, these dffeences come out because t s dffcult n expementaton to exactl epoduce the same condtons. Fo nstance, netwok delas cannot be contolled, o sensng eos ma occu moe fequentl n one case than n the othe. Howeve, obseve that the tme at whch the fomaton s acheved (the statona) s ve smla fo both tme-tgge and event-tgge. 6. Conclusons We have descbed an expemental envonment fo moble obots. The hadwae platfom was developed usng dffeent components and softwae to ovecome the lmtatons of the LEGO Mndstoms NXT obots. A dstbuted contol appoach has been used n fomaton contol. Each obot communcates to ts neghbohood n an event-tggeng fashon fo netwok savng puposes. A smulaton tool wth hgh degee of flexblt has been pesented. An example has demonstated ts usablt, and smulated and expemental esults have been pesented showng how the mult-agent sstem eaches the desed fomaton wth few communcatons meanwhle the sstem pefomance s peseved. Futue woks wll nclude the mplementaton of collson and obstacle avodance contol and fomaton contol wth specfed paths. Explong self-tggeng technques [44] to pedct the next event occuence n ode to optmze the communcaton between the camea and the obots s also a futue lne of eseach. Acknowledgments Ths wok was suppoted n pat b the Spansh Mnst of Econom and Compettveness unde Pojects DPI and DPI C Conflct of Inteest The authos declae no conflct of nteest.

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