Cooperative perimeter surveillance with a team of mobile robots under communication constraints

Transcription

1 213 IEEE/RSJ Internatonal Conference on Intellgent Robots and Systems (IROS) November 3-7, 213. Toyo, Japan Cooperatve permeter survellance wth a team of moble robots under communcaton constrants J.J. Acevedo, B.C. Arrue, I. Maza and A. Ollero Abstract Ths paper presents the permeter survellance problem usng a set of cooperatve robots wth heterogeneous speed capabltes under communcaton constrants. The problem s solved usng a frequency-based approach. In the proposed path-partton strategy, the robots patrol a segment length related to ther own capabltes and nterchanges nformaton wth ts neghbors perodcally. An effcent decentralzed algorthm s appled to coordnate the robots from local nformaton and decsons. Fnally, smulaton and expermental results are presented to llustrate the convergence and the robustness of the soluton. I. INTRODUCTION Dfferent moton strateges have been appled to optmze a gven crtera whle the robots are patrollng a gven permeter. One crtera may be to optmze the frequency of vstng dfferent locatons along the path (frequencybased approach) as t can be found n [1] or [2]. Other authors address the problem wthout optmzng a frequency crtera. In [3], authors maxmze the probablty of detectng ntruders usng a stochastc approach and assumng potental ntellgent ntruders that could learn a determnstc strategy. Reference [4] proposes a robust soluton to the presented problem usng behavoral control. In [5], a dstrbuted algorthm s presented based on ordered upwnd methods, whch coordnates motons of agents assumng a contnuous opened communcaton and centralzed decsons. In ths paper, the permeter survellance problem wll be faced from a frequency-based approach. In [6], the cyclc and parttonng strateges are appled and compared to solve the mn-dleness problem. Both strateges are also analyzed from a frequency-based crtera n [7]. The cyclc patrollng strategy s better explaned n [8], assumng dentcal robots and a closed path. And a method wth the goal of montorng a set of postons wth dfferent prortes usng homogeneous robots s presented n [9]. In large scenaros, a opened communcaton between all the robots can be no possble. Therefore, a dstrbuted approach would be more approprate n these cases. Also, decentralzed and dstrbuted approaches offer ncreased robustness, adaptablty and scalablty. These methods usually rely on the nterchange of a reduced amount of varables (so called coordnaton varables) requred to obtan a soluton Ths wor has been developed n the framewor of the PANET (INFSO-ICT ) European proect, the CEAR (DPI C2-1) Spansh Natonal Research proect and the proect of excellence of the Junta de Andalucía WSAN-UAV (P9-TEP-512). J.J. Acevedo, B.C. Arrue, I. Maza and A. Ollero are wth Grupo de Robotca, Vsón y Control, Unversdad de Sevlla, Span. E-mals: acevedo@us.es, barrue@us.es, maza@us.es, aollero@cartua.us.es n a cooperatve manner. Ths concept s appled n [1] to ensure cooperaton n a permeter survellance msson usng a team of small homogeneous UAVs. In [11], the authors analyze how consensus s acheved n a mult-robot system wth few teratons usng ths concept. Ths paper apples a smlar decentralzed coordnaton algorthm based on coordnaton varables to solve the permeter survellance problem under communcaton constrants for a team of cooperatve moble robots. It proposes a path parttonng strategy to patrol the permeter n a cooperatve manner from a frequency-based approach (optmzng the refresh tme or elapsed tme between two consecutve vsts to any poston of the permeter). In [12], authors propose a one-to-one method to coordnate a team of homogeneous aeral robots to cooperate n an area survellance msson, assumng communcaton constrants. The same technque s used n [13] to patrol a path n a cooperatve way usng a set of heterogeneous aeral robots. Other research groups propose smlar methods to solve the problem wth a team of vdeo-cameras and asynchronous communcaton between neghbors, as n [2], [14]. The dea s sharng the tass of each par of contactng robots and dvdng the sum between them. As t wll be shown later, ths paper contrbutes wth a dstrbuted algorthm whch converges faster than the proposed ones n prevous wors. Also, t wors wth heterogeneous robots and under communcatons constrants. The paper s structured as follows. Secton II descrbes the problem statement, whereas Sect. III explans the proposed path-parttonng approach followed to solve t. In Secton IV the proposed soluton s presented and some relevant features are analyzed. Sectons V and VI show a set of smulaton and expermentaton results to valdate the proposed approach. Conclusons and future wor close the paper n Sect. VII. II. PROBEM STATEMENT et us consder a set of N moble robots {M 1, M 2,..., M N } that has to patrol a permeter P := { p(x) R 2 : x [,] }, see Fg. 1. s the entre permeter length and x ndcates the dstance along the permeter P from each poston p(x) to a gven ntal poston. Each robot M can move along the permeter P n two drectons d = { 1,1} wth a varable speed n module v so that dx (t) dt = d (t)v (t), = 1,2,...,N, (1) where x (t) [,] s the dstance along the permeter P from the robot M to the ntal poston p() at tme /13/$ IEEE 567

2 Fg. 2. Path-partton strategy appled to the cooperatve permeter survellance problem wth the team of four moble robots depcted n Fg. 1. Fg. 1. A setup wth four robots that llustrates the dfferent varables consdered n the problem statement. t. It s assumed that robots can have dfferent maxmum speeds v max and can reverse drecton nstantaneously. In addton, each robot M can have dfferent communcaton ranges R >. Thus, two robots wll be able to nterchange nformaton, f they are close enough,.e. a dstance lesser than the mnmum of ther communcaton ranges. Hence, the robots are heterogeneous at least n ther maxmum speeds and communcaton ranges. In the context of survellance mssons and assumng that there s no a pror nformaton about the potental locaton of the obects of nterest along the permeter, the man goal s to maxmze the frequency of vsts to any permeter poston. Maxmzng ths frequency s equvalent to mnmzng the refresh tme T r (x,t) (or elapsed tme between two consecutve vsts to any poston of the permeter) as t s defned n [7]. Thus, the problem addressed s a varant of the mn-dleness problem descrbed n [6] appled along the permeter. et us denote the maxmum and the average values of T r (x,t) at tme t as Tr max (t) and T r (t) respectvely. The bounds for these parameters are gven by and Tr max (t) N =1 vmax T r (t) (2) 2, (3) N =1 vmax but, assumng communcaton constrants, a non-closed permeter or robots wth dfferent maxmum speeds, those lmts would not be reached. Otherwse, so as to ncrease the robustness of the system aganst falures, the problem should be solved n a decentralzed manner. As the communcaton range of the robots s lmted, the soluton should guarantee that the robots exchange nformaton perodcally. Then, the computed moton for the robots should allow them to be wthn ther communcaton range perodcally. The nformaton exchange s requred to coordnate the survellance tas and to share the nformaton about the obects of nterest found durng the msson n a fnte tme. III. PATH-PARTITIONING STRATEGY A path-parttonng strategy s proposed for the survellance of the permeter, such as t s stated n the prevous secton. Each robot M should cover a non-overlappng segment P wth a length and the whole permeter should be covered by the team. In order to maxmze the survellance frequency, the robots would move at ther maxmum speed and any robot taes the same tme T to cover ts own segment. Then, the length of the segments s related to the robots maxmum speed accordng to = v max N =1 vmax and the resultng value for T s gven by T = v max =, = 1,...,N, (4) N =1 vmax. (5) Each robot M patrols a length, movng between the endponts of ts allocated segment at ts maxmum speed v max, as t s llustrated n Fg. 2. Each par of neghbor robots meet n the common endpont of ther segments perodcally, ensurng the nformaton propagaton between all the robots. The maxmum refresh tme T r can be calculated as the tme n whch a robot M covers twce ts own segment S whch s T max r (t) 2T. (6) Fgure 3 shows the refresh tme along the segment covered by a robot n the poston x n a steady state and usng the path-parttonng method descrbed above. As all the robots would tae the same tme T to cover ther own segments, the average refresh tme can be computed as the relaton between the area shown n the fgure and the length of the segment. Maxmzng t wth respect to the poston x, the maxmum average refresh tme s obtaned when each robot s located n the mddle of ts own segment (x = /2): T r (t) 3 4 T. (7) Fnally, the maxmum tme T s to share a nformaton wth the rest of the team or latency as t s defned n [7] can be calculated. At worst, a new event s detected by robot n the endpont of a segment. Ths robot taes a maxmum tme of 2T to meet ts neghbor robot and share that nformaton. Now, ths neghbor robot taes a maxmum of T to share t wth ts other neghbor. Ths sequence s followed untl the 568

3 ther speeds to t. Slower robots would not tae part of the soluton. In ths case, when a robot detects an event, t has to get to the stopped robot to exchange nformaton wth t. Then, when the rest of the robots get near to the stopped one, they can be nformed about the new event. Therefore, the maxmum latency can be computed as Fg. 3. Refresh tme n a segment covered by a robot followng the proposed path parttonng strategy. new nformaton reaches the last robot n the other segment endpont. So, the value of T s s gven by the followng expresson: T s 2T +(N 2)T = NT. (8) Cyclc strateges such as [8] are also proposed to solve the same problem, assumng a closed permeter. Then, the robots patrol the whole permeter n the same drecton, wth the same speed and equally spaced. Under these condtons, the system could obtan optmal results smlar to the mnmum lmts defned n expressons (2) and (3). However, these condtons are not always possble. Communcaton constrants are tacled n [8] stoppng a robot to exchange nformaton wth the rest of the team. A falure n the fxed robot would leave the rest of robots wth no communcaton between them, lmtng the system robustness. On other the hand, when all the robots can not move at the same maxmum speed (assumng v1 max v2 max... ), there are two possbltes. The frst one mples than all the robots patrol the entre permeter at ther maxmum speeds. Hence, n the worst case scenaro, the maxmum refresh tme s lmted by the fastest robot M 1 as v max N and T max r v max 1 T r 2v1 max (9). (1) The second one mples that some robots decrease ther speed to accomplsh the condtons assumed n [8]. Thus, a dfferent soluton could be obtaned dependng on the speed, and the mnmal maxmum and average refresh tme usng the cyclc strategy would be and T max r mn T r mn v max 2v max, (11), (12) where = 1,...,N 1 and v1 max v2 max... vn max. The slowest robot M N would stop to share nformaton. Robots wth a maxmum speed greater thanv max could adapt T s v max +( 1) v max. (13) In general, the path-partton method obtans better results accordng to the frequency-based crtera compared to the cyclc strategy when the robots have dfferent speed capabltes. IV. FROM OCA INFORMATION EXCHANGE TO GOBA COORDINATION When the communcaton ranges are short relatve to the sze of the permeter, any robot wll be dsconnected from the rest most of the tme. A dstrbuted coordnaton technque should be used to ensure that the mult-robot system converges to the path partton strategy descrbed n Sect. III. The entre permeter length and the sum of speeds for all the robots wll be used as coordnaton varables. A. Dstrbuted algorthm The proposed dstrbuted and decentralzed method to mplement the strategy descrbed n Sect. III s lsted n Algorthm 1, where x s the permeter poston defned n Secton II. Each robot runs t n an ndependent manner and no dfferent herarchcal levels are consdered among the team members. to patrol ther segments n the mnmum tme, whle they update ts nformaton database nfo. Even f a robot gets the end of ts own segment [a,b ], t contnues on movng untl t communcates wth another one M (and updates ts local nformaton) or arrves to end of the permeter. When robot M communcates wth robot M arrvng on ts rght, M trusts n all the nformaton that M sends The robots M move at ther maxmum speed v max about hs rght sde (for nstance, sum of speeds speed rght and length on ts rght rght ), and M trusts n all the nformaton that M offers about hs left sde. They exchange the requred nformaton to calculate the parameters used to coordnate the team: sum of speeds speed sum and total permeter length. Wth these varables, each robot can compute the segment [a,b ] to cover. If any of the robots s out of ts own segment, they go both to ther common endpont, adustng ther speeds v. Then, each robot moves to ts own other segment endpont. When a moble robot gets the ntalx = or end poston n the permeter x =, t sets up ts nformaton accordng to ts drecton d and turns bac. The algorthm mnmzes the requred nformaton exchange wth or wthout communcaton constrants because robots only has to communcate wth ther neghbors. 569

4 Algorthm 1 Dstrbuted algorthm proposed to mplement the permeter survellance strategy descrbed n Sect. III. a = b = x speed left = speed rght = left for all t do v = v max f contact(m,m ) then nfo = nfo nfo v = mn(v max f d > then speed rght rght,v max ) = speed rght = rght end f f d < then speed left left end f speed sum = left = left a = speed left b = a +v max f x a then d = 1 end f f x b then d = 1 end f end f f x = then speed left d = 1 end f f x = then speed rght = speed left = speed left + rght speed sum speed sum = left = = rght = = rght = +v max +v max +speed rght d = 1 end f x old = x x = move(x,d,v ) left = max(, left +x x old rght = max(, rght nfo = update(p(x )) end for B. Robustness and fault-tolerance ) x +x old ) +v max A decentralzed and dstrbuted approach should ncrease the robustness and fault-tolerance of the system, snce the msson can be completed f one or more robots are lost. The algorthm s dynamc and allows us to deal wth varatons n parameters such as the amount of robots, ther speeds, the length of the permeter and others, provdng flexblty and fault-tolerance (for nstance, a communcatons fault). Robots contnuously update ther own coordnaton varables and decde ther own tass accordng to the local nformaton, perodcally updated wth the nformaton of other team members. For example, let us assume a system n fully steady state where a set of N robots s coverng a permeter of length. Robot M 1 perodcally receves from M nformaton about the sum of speeds on ts rght gven by speed rght 1 = vmax +speed rght. In a smlar manner, robot M receves perodcally from M +1 the nformaton about sum of speeds on ts rght as speed rght = v+1 max +speedrght +1. At any tme t, M could be lost, and nether M 1 nor M +1 wll contact t. Thus, robot M 1 wll communcate wth M +1 after a whle. Robot M +1 reports to M 1 the nformaton about the sum of speeds on ts rght gven by speed rght 1 = vmax +1 +speedrght Fnally, robot M +1 receves nformaton about the left sde of M 1. Then, both robots can update ther coordnaton varables and calculate correctly the segments to cover. That nformaton s propagated to the rest of robots when they contact wth a robot whch s aware of the new scenaro. In fnte tme, all the robots wll have updated correctly ther coordnaton varables. It should be mentoned that the process would be smlar f the permeter changes for nstance. C. Convergence analyss +1. The use of the Algorthm 1 by each robot maes the whole team behavour converge to the soluton descrbed n Sect. III. All the robots move always nto a fnte permeter wth only two possble drectons. As the robots reverse drecton when they reach endponts, all the neghbors robots have to meet and exchange nformaton. Therefore, they can calculate coherently and share the requred coordnaton varables to solve the problem. Now, the ssue s to analyze tme-complexty of the convergence. et us assume a team of N robots. When the frst robot M 1 communcates wth robot M 2, both robots wll now that at least two robots are present n the team. If M 2 communcates wth M 3, they wll now that at least three robots are avalable. Nevertheless, M 1 could contnue operatng accordng to the scenaro wth two robots. Ths reasonng can be extrapolated to robot M N, and after N 1 nformaton exchanges, M N and M N 1 wll have all the nformaton about the N robots (although the rest could not have t). When robot M N 1 gets bac to communcate wth M N 2, t wll now the whole scenaro and wll compute the ntended soluton. In the same manner, after N 2 new meetngs, nformaton wll have been spread out and wll have reached the frst robot M 1. Therefore, all the robots wll have the necessary nformaton to compute correctly all the requred coordnaton varables. Therefore, each robot wll need at most 2N nformaton exchanges wth ts neghbors to converge to the soluton explaned n Sect. III and the convergence tme-complexty ncreases lnearly wth the number of robots. A smlar path-parttonng strategy was prevously suggested by other authors as a soluton to the problem under dscusson usng dfferent coordnaton technques [14], [13]. In those algorthms only the sum of the segments of both 57

5 number of robots Fg. 4. Relaton between the convergence tmes usng the algorthm based on one-to-one coordnaton and the algorthm descrbed n ths paper. communcatng agents was shared between them. Informaton about the number and capabltes of other robots, or the total length of the permeter was not requred to be stored. Then, less nformaton storage capabltes are requred, but accordng to [14] the convergence tme-complexty ncreases quadratcally wth the number of robots, whereas n our strategy t only ncreases lnearly. V. SIMUATION RESUTS A large set of 24 smulatons has been executed n MAT- AB to valdate the proposed algorthm and compare t wth other approaches based on the one-to-one coordnaton technque (namely the algorthms presented n [13] or [14]). Dfferent scenaros wth dfferent permeter lengths and dfferent number of aeral robots (wth the same dynamcal model used n [13]) has been launched usng both the presented dstrbuted algorthm based on coordnaton varables and the algorthm proposed n [13]. The ntal robots postons and drectons of moton have been created randomly. Ther maxmum speeds have been chosen usng an unform dstrbuton from.2 to.5 m/s. The communcaton range between robots has been lmted to 4 m. Both algorthms converge to the same path dvson between the robots, but the convergence tmes are dfferent. It s assumed that the system has converged when the dfference between the segment that each aeral robot covers and the one that theoretcally should cover (accordng to expresson (4)) s less than 5 %. Fgure 4 shows the average value for the relaton between the convergence tmes usng the algorthm based on the oneto-one coordnaton technque and usng the one based on the technque presented n ths paper. The smulaton results shows that as the number of robot ncreases t converges more qucly than an algorthm based on the one-to-one coordnaton technque. VI. EXPERIMENTA RESUTS WITH A TEAM OF MOBIE ROBOTS In the expermental setup, a team of Poneer-3AT has to patrol the room permeter shown n Fg. 5. The maxmum speed of the robots s 1 m/s, but for robots 1 (yellow), 2 (red) and 3 (green), t has been artfcally lmted to.6 m/s to test the system theoretcal features for heterogeneous robots. In the experments, t s assumed a sensng range of 2 meters for the robots, whose effect s to decrease the total length to Fg. 5. Intal setup of the frst experment. Grey lne near to the wall ndcates the permeter shape. The ntal and end permeter poston have been establshed n the coordnates (9,). postons nto the permeter (meters) tme (sec) Fg. 6. Permeter postons x of the robots along the permeter n the frst experment. Each color represents a dfferent robot. The dotted lnes ndcate the theoretcally optmal permeter dvson. A vdeo of the experment can be seen n patrol. Each Poneer executes a Player Server [15] that tals to an applcaton runnng the Algorthm 1. Poneers do not need any localzaton system to run the algorthm, they ust use the laser to eep near the permeter (wall). However, a localzaton system s used to lmt the communcaton range to 4 meters va software. Two dfferent types of experments has been developed. In the frst one, the convergence and robustness of the system wth dynamc teams of moble robots were tested. Four moble robots patrolled the whole permeter at the begnnng. At t = 25 seconds, the ffth moble robot starts movng, and at last at t = 42 seconds, a robot leaves the permeter. In Fg. 6 t can be seen that the algorthm converges whle each robot was coverng a length related to ts speed. Fgure 7 shows the maxmum and average values of the refresh tme parameter. Results show an effcent behavor, accordng to the frequency-based crtera, wth values close to the lower bounds defned n (2) and (3). Obvously the results are better wth a larger number of robots. The second type of experment shows how ths approach can adapt to changes n the permeter and how any nformaton s shared between all the robots. A team of four moble robots s patrollng the permeter and at t = 18 seconds, the 571

6 maxmum elapsed tme (s) average elapsed tme (s) tme (s) tme (s) Fg. 7. Maxmum (above) and average (below) values for the refresh tme. Red dash-dotted lne ndcates the lower bounds defned n expressons (2) and (3), accordng to the robots capabltes along the tme. permeter poston (meters) nfo tme (sec) tme (sec) Fg. 8. The top graph shows the poston of the robots along the permeter n the second experment. The dotted lnes ndcate the theoretcally optmal permeter dvson. In the bottom graph a value of 1 represents that the robot nows the new detected nformaton. Each robot s represented by a dfferent color. A vdeo of the experment s avalable n permeter length s decreased. On the other hand, one of the robots detects an event at t = 275 seconds. Fgure 8 shows as the whole mult-robot system adapts when the permeter length changes. It also shows that any new nformaton s shared between all the robots n a short tme, consstent wth the expresson (8). VII. CONCUSIONS The proposed path partton strategy allows the multrobot system to cooperate n the permeter survellance msson, explotng the dfferent robots capabltes (maxmum speeds). Also, t ensures that any nformaton detected wll be shared between the whole team n a fnte tme, even under communcatons constrants. A dstrbuted and decentralzed algorthm based on the concept of coordnaton varables enables the system to converge to the proposed strategy from local decsons n few teratons (lnearly related to the number of robots). The proposed system s robust n changes to the ntal condtons. Expermental and smulaton results valdate the approach and shows some relevant features. ACKNOWEDGEMENT The experments presented n Sect. VI have been performed usng a robotc testbed of the CONET proect. REFERENCES [1] Y. Elmalach, A. Shlon, and G. A. Kamna, A realstc model of frequency-based mult-robot polylne patrollng, n Proceedngs of the 7th nternatonal ont conference on Autonomous agents and multagent systems - Volume 1, ser. AAMAS 8. Rchland, SC: Internatonal Foundaton for Autonomous Agents and Multagent Systems, 28, pp [Onlne]. Avalable: [2] M. Baseggo, A. Cenedese, P. Merlo, M. Pozz, and. Schenato, Dstrbuted permeter patrollng and tracng for camera networs, n Decson and Control (CDC), 21 49th IEEE Conference on, dec. 21, pp [3] N. Agmon, G. A. Kamna, and S. Kraus, Mult-robot adversaral patrollng: facng a full-nowledge opponent, J. Artf. Int. Res., vol. 42, no. 1, pp , sep 211. [Onlne]. Avalable: [4] A. Marno,. Parer, G. Antonell, and F. Caccavale, Behavoral control for mult-robot permeter patrol: A fnte state automata approach, n Robotcs and Automaton, 29. ICRA 9. IEEE Internatonal Conference on, may 29, pp [5] E. Frew, Combnng area patrol, permeter survellance, and target tracng usng ordered upwnd methods, n Robotcs and Automaton, 29. ICRA 9. IEEE Internatonal Conference on, may 29, pp [6] Y. Chevaleyre, Theoretcal analyss of the mult-agent patrollng problem, n Intellgent Agent Technology, 24. (IAT 24). Proceedngs. IEEE/WIC/ACM Internatonal Conference on, sept. 24, pp [7] F. Pasqualett, A. Franch, and F. Bullo, On cooperatve patrollng: Optmal traectores, complexty analyss, and approxmaton algorthms, Robotcs, IEEE Transactons on, vol. 28, no. 3, pp , une 212. [8] F. Pasqualett, J. Durham, and F. Bullo, Cooperatve patrollng va weghted tours: Performance analyss and dstrbuted algorthms, Robotcs, IEEE Transactons on, vol. 28, no. 5, pp , oct [9] S. Smth and D. Rus, Mult-robot montorng n dynamc envronments wth guaranteed currency of observatons, n Decson and Control (CDC), 21 49th IEEE Conference on, dec. 21, pp [1] D. Kngston, R. Beard, and R. Holt, Decentralzed permeter survellance usng a team of UAVs, Robotcs, IEEE Transactons on, vol. 24, no. 6, pp , dec. 28. [11] X. Geng, Consensus-reachng of multple robots wth fewer nteractons, n Computer Scence and Informaton Engneerng, 29 WRI World Congress on, vol. 5, aprl 2 29, pp [12] J. J. Acevedo, B. C. Arrue, I. Maza, and A. Ollero, Cooperatve large area survellance wth a team of aeral moble robots for long endurance mssons, Journal of Intellgent and Robotc Systems, vol. 7, pp , 213. [Onlne]. Avalable: [13] J. Acevedo, B. Arrue, I. Maza, and A. Ollero, Dstrbuted approach for coverage and patrollng mssons wth a team of heterogeneous aeral robots under communcaton constrants, Internatonal Journal of Advanced Robotc Systems, vol. 1, no. 28, pp. 1 13, January 213. [Onlne]. Avalable: [14] R. Carl, A. Cenedese, and. Schenato, Dstrbuted parttonng strateges for permeter patrollng, n Amercan Control Conference (ACC), 211, uly 1 211, pp [15] R. T. V. Bran Gerey and A. Howard, The player/stage proect: Tools for mult-robot and dstrbuted sensor systems, n Proceedngs of the 11th Internatonal Conference on Advanced Robotcs (ICAR 23), Combra, Portugal, June 23, pp