A destination swap scheme for multi-agent system with agent-robots in region search problems

Transcription

1 A destnaton swap scheme for mult-agent system wth agent-robots n regon search problems Zongln Ye, Shuo Yang, Shuo Zhu, Yazhe Tang, Hu Cao, and Yanbn Zhang ABSTRACT As the mult-agent robots can share nformaton and cooperate wth each other, they are appled n the regon search problems lke odor source localzaton. In ths knd of problems, the detecton result of the agent-robot at the current destnaton wll nfluence the locaton of ts next destnaton. So the route plannng of the agent-robots cannot be made n advance. Ths paper proposes a dynamc destnaton allocaton scheme for the agent-robot group to reduce the total movng dstance of the agent-robot group and thus save energy. When the agent-robots start to search the target regon, the scheme calculates the frst destnatons for the agent-robots and allocates the destnatons to the agent group to mnmze ther total movng dstance. Then as the dstances between the agent-robots and ther destnatons are dfferent, the agent-robots wll reach ther target destnatons at dfferent moments. In the followng searchng process, whenever an agent-robot arrves at ts current destnaton and calculates ts next destnaton, the scheme wll then fnd out the best destnaton allocaton plan for the agentgroup to mnmze the total movng dstance of the group. The smulaton s performed wth partcle swarm optmzaton (PSO) on benchmark functons wth agent-robots. The experments verfy the effectveness of the proposed scheme. 1 INTRODUCTION The mult-agent system (MAS) conssts of a number of agents whch can nteract wth each other and react to the envronment. Due to ts superorty n dealng wth complex problems, the noton of MAS has been appled n many aspects lke commercal bargan modellng [1], optmzaton problems [2], wreless sensor network (WSN) [3], and dstrbuted survellance system [4]. In ths knd of applcaton, the agent s a programme sent by the snk node n the WSN or the central computer n the Yazhe Tang s wth the Temasek Laboratores, Natonal Unversty of Sngapore, Sngapore (emal: yztang2008@yahoo.com) Correspondng author. Tel.: ; fax: Emal address: hucao@mal.xjtu.edu.cn Zongln Ye, Shuo Yang, Shuo Zhu, Hu Cao and Yanbn Zhang are wth State Key Laboratory of Electrcal Insulaton and Power Equpment, School of Electrcal Engneerng, Xan Jaotong Unversty, Xan, Shaanx, dstrbuted survellance system when a msson s generated. That s to say, the agents n the applcaton above are vrtual agents, not enttes. They do not occupy any space, wll not be worn, and cost nearly no energy. However, for mult-agent robots, lke robots used for regon search operatons [5] (e.g. odor source localzaton [6]), the stuaton s dfferent. In these two applcatons, agentrobots consume energy whle movng. So the desgner should not only make sure that the problem can be solved, but also reduce the energy consumpton. Decreasng the total movng dstance of the agent-robot group s an effectve approach and s meanngful for all the group-search problems wth agentrobots. There are many works focus on the task allocaton problems of the agent-robot group or the UAV group [7, 8]. However, n these works, the locatons of all the targets are known before the allocaton. As n the regon search problems lke odor source localzaton, the locatons of the targets to be detected are calculated real-tmely wth the nformaton obtaned from the former detecton results, other methods are needed to fnd an optmal allocaton scheme for the regon search problems. Ths paper proposes a dynamc destnaton allocaton scheme for mult-agent system wth agent-robots n the regon search problems to reduce the total movng dstance of the agent-robot group. When the agent-robots start to search the target regon, the scheme frst calculates the frst destnatons under the predefned searchng algorthm for the agentrobots and allocates the destnatons to the agent group to mnmze ther total movng dstance. Then as the dstances between the agent-robots and ther destnatons are dfferent, the agent-robots wll reach ther target destnatons at dfferent moments. In the followng searchng process, whenever an agent-robot arrves at ts current destnaton and calculates ts next destnaton, the scheme wll then fnd out the best destnaton allocaton plan for the agent-group to mnmze the total movng dstance of the group. Generally speakng, the destnaton re-allocaton scheme s trggered whenever an agent-robot reaches calculates ts next destnaton. As partcle swarm optmzaton (PSO) [9] s wdely used n the regon search problems, a smulaton of 2-D PSO benchmark functon optmzaton problem wth agent-robots usng PSO s performed to show the effectveness of the proposed scheme. As the conventonal PSO s a synchronous algorthm and the agent-robots wll reach ts dstance and dfferent moment, an asynchronous verson of PSO s used. In ths asynchronous PSO, the partcles are treated as the real-world robots and 1

2 ther movements cost tme. As the dstances between the locatons of the partcles and ther destnatons are dfferent and we assume that the veloctes of the partcles are dentcal, the partcles wll arrve at ther destnaton at dfferent moments. Whenever a partcle arrves at ts current destnaton, ts next destnaton s calculated by ts personal best and the current global best. Thus, n ths verson of PSO, the dfferent partcles wll have dfferent update tmes at a specfc moment. The experments verfy the effectveness of the proposed scheme. The nfluence of the number of the agent-robot to the scheme s also analysed. The rest of the paper s organzed as follows. Secton II s the proposed scheme. Secton III s the experment and secton IV gves the concluson. 2 THE PROPOSED SCHEME In regon search problems, the agent-robots need to move n the searchng regon to fnd the problem-related target under the predefned algorthm. No matter what the problem and the algorthm are, the agent-robots are always n the teraton composed of three parts: detectng the destnaton, calculatng the next destnaton, and movng to the next destnaton. The detecton part s accomplshed by the sensors equpped on the agent-robot. Then the agents can exchange the nformaton of the problem, lke the optmal value beng detected and the locatons of the obstacles. When calculatng the next destnaton for every agent, the agent-robots are treated as a group n the sense that the knowledge gathered by all the agent-robots s used. However, when movng to the next destnaton, the agent-robot just moves to the destnaton calculated by tself. In another word, n the movng process, the agent-robots are treated as ndvduals and there s no cooperaton among them. The followng part ntroduces a dynamc destnaton allocaton scheme for the agent-robot group. The destnaton allocaton scheme s based on the fact that the next destnaton of an agent-robot may be closer to another agent-robot. In that stuaton, f the two destnatons are re-allocated between the two agent-robots, the total movng dstance and the energy consumpton of the two agent-robots can be decreased. In the scheme, the parts of detectng the destnaton and calculatng the next destnaton are the same as the conventonal scheme n the regon search problems. Now we show the proposed destnaton allocaton scheme for the process of movng to the next destnaton. Assume that there are m agent-robots r 1, r 2,..., r m n the searchng regon to detect the target whch s at a specfc locaton X. The searchng process s controlled by a specfc algorthm C. The process of the scheme can be descrbed as follows: Step 1: The calculaton of the ntal locatons and the frst destnatons of the agent-robots. The ntal locatons of the agent-robots, donated as x 0 1, x 0 2, x 0 3,..., x 0 m are obtaned by C. The subscrpt s the label of the agent-robot and the superscrpt s the teratons of the agent-robot. For example, x 5 3 s the thrd locaton of the 5th agent-robot. The second locaton of agent-robot, donated as x 1, s also obtaned by C. Step 2: The frst destnaton allocaton process of the agent-robot group. The purpose of ths step s to mnmze the total movng dstance of the robot group. At the begnnng, the agent-robots are at x 0 1, x 0 2, x 0 3,..., x 0 m, and ther destnatons are x 1 1, x 1 2, x 1 3,..., x 1 m. In conventonal algorthms wthout consderng the cooperaton n the movng process, the agent-robots wll move to ther destnaton, respectvely. And the total movng dstance of the robot group s dst(x 1 x0 ), where dst s the Eucldean dstance. The destnaton allocaton process s used to mnmze the total movng dstance. For example, f there are agent-robots, j, and k wth x 1 = p, x 1 j = p j, x 1 k = p k, where p, p j, and p k are the locatons of the destnatons after step 1. Then after Hungaran algorthm gves an allocaton plan, the allocated destnatons may be lke x 1 = p, x 1 j = p k, x 1 k = p j. In ths case, the agent-robots j and k have exchanged ther destnatons to decrease the total movng dstance. Step 3: The agent-robots wth the movng dstance moves to ts current destnaton and gets ts new destnaton. For an agent-robot, after step 2, ts movng dstance wll be dst(x 1 x0 ). For the agent-robot group, there wll be a robot, labeled as, wth the movng dstance. As we assume that the velocty of all the agent-robots are 1, then robot wll frst reach ts destnaton x 1 after t 1 = dst(x 1 x0 ). Here t 1 s the tme nterval between the frst and the second allocaton. Then based on the nformaton obtaned from locaton x 1, the predefned searchng algorthm C calculates the next locaton of the agent-robot, whch s donated as x 2. Step 4: The destnaton allocaton process of the agentrobot group. When the next destnaton of the agent wth the movng dstance, x t +1 s obtaned, another destnaton allocaton for the agent-robot group s performed. The lth destnaton allocaton can be formulated as follows: arg mn( dst(x 1 k j x 0 j)) s.t. where x nj jc =1 k j = 1 =1 k j = 1 j=1 k j = 1 or 0 j = 1, 2, 3,..., m = 1, 2, 3,..., m, j = 1, 2, 3,..., m (1) s the current locaton of agent-robot j when the lth destnaton allocaton happens. n j s the number of tmes that agent-robot j s the frst to reach ts destnaton, whch also can be nterpreted as the tmes that agent-robot j gets ts destnaton by C, not by the allocaton process. Ths s a combnatoral optmzaton problem and can be solved by

3 Hungaran algorthm whch solves the assgnment problem n polynomal tme [10]. The algorthm can gve an allocaton plan to the agent-robot group. x nj jc = xnj j + xnj+1 j x nj+1 j x nj j x nj j xn+1 x n (2) x n c = xn +1 (3) where x n +1 s updated by C. In our scheme, Hungaran algorthm s also used to solve (2) and gves a destnaton re-allocaton plan for the agentrobot group. Step 5: Iterate step 3 and 4, untl algorthm C ends. The followng secton wll llustrate the performance of the proposed scheme on some benchmark functons of PSO algorthm, whch s wdely used n regon search problems. 3 EXPERIMENTS In ths secton, sx test functons (Bohachevsky, Grewank, Mchalewcz, Rastrgn, Rosenbrock, and Schwefel) are used to verfy the effectveness of the proposed scheme. The concept of PSO was frst suggested by Kennedy and Eberhart [9]. The algorthm uses a group of partcles to search the feasble regon and updates the locatons of the partcles by consderng the current locaton of the partcle, the hstory best locaton of the partcle, and the global best locaton of the partcle group. For the th partcle P, let vd t donate the velocty on the dth dmenson at the tth teraton. Smlarly, x t d s ts locaton on the dth dmenson at the tth teraton. Let p t d and pt gd be the partcle best locaton and swarm best locaton tll the tth teraton. Then the velocty of the th partcle on the dth dmenson s updated accordng to the followng equaton [9]: v t d = wv t 1 d + c 1 r 1 (p t d x t d) + c 2 r 2 (p t gd x t d) (4) where d = 1, 2,..., D, and D s the dmenson of the searchng space. c 1 and c 2 are acceleraton factors ndcatng the degree that the partcle s attracted by ts personal best poston and the global best poston. These two constants are set as 2 n order to make the average velocty change coeffcent close to 1 [9]. r 1 and r 2 are unformly generated random numbers wth a scope of [0, 1]. w s the weghtng factor controllng the searchng regon of the partcles. Then the locaton of the th partcle on the dth dmenson s updated as follows: x t+1 d = x t d + v t d (5) For the experments wth real robots, movng from one place to another costs tme. Usually, the agent-robots wll not arrve at ther destnatons at the same tme. Comparng wth the strategy that updatng the new destnatons synchronously when each member of the agent-robot group reaches ts destnaton, we would rather do the destnaton allocaton process whenever an agent-robot reaches the destnaton. Thus, unlke the conventonal PSO, the PSO used n the experment s an asynchronous PSO. The asynchronous PSO s v n = wv n 1 + c 1 r 1 (p n x n ) + c 2 r 2 (p l g x n ) (6) x n+1 d = x n d + v n d (7) The experment uses the asynchronous PSO descrbed above and the asynchronous PSO wth the destnaton allocaton scheme on sx benchmark functons to compare the total movng dstance of the agent-robot group n the entre searchng process. For each functon, the asynchronous PSO algorthm and the asynchronous PSO wth the proposed scheme both run for 100 tmes. The number of the teratons of the algorthm s set to be 1000 before t ends n each run. The average value of the total movng dstance of the agent-robot group n the two methods, the percentage of the dstance decreased by the proposed scheme, and the results of the Wlcoxon rank-sum test are lsted n table 1. From Table 1, t s clear that the proposed scheme can sgnfcantly reduce the movng dstance of the agent-robot group for all the benchmark problems. For all the functons, the proposed scheme helps to decrease the total movng dstance of the agent-robot group by nearly one quarter except one functon. The maxmum reducton happens on the Rastrgn functon, whch s 24.2 %. Wth a sgnfcance level of 5%, the p-value also ndcates that the superorty of the proposed scheme does not happen by chance. And the superorty also holds over Bohachevsky functon. Another experment s performed to nvestgate the relatonshp between the number of the robots and ts effect on the proposed scheme. For Grewank functon, the experment s performed for 100 tmes wth the number of the robots ncreasng from 6 to 12. The average values of the total movng dstance of the two schemes n 100 experments of Grewank functon wth the number of the robots rangng from 6 to 12 are n Table 2. From ths table, t can be found that the total movng dstance of the two schemes change wth the number of the robots. The total movng dstance of the proposed scheme s always smaller than that of the conventonal PSO. The percentage of dstance decreased vares, rangng from 5.7% to 47.4%. It can be seen that the number of the robots s not the only element that affects the total movng dstance. More experments are needed to dscover the other elements. 4 CONCLUSIONS Ths paper proposes a dynamc destnaton allocaton scheme for the agent-robot group to reduce the total movng dstance of the agent-robot group and thus save energy. As PSO s wdely used n regon search problems, experments

4 Benchmark functons Asynchronous PSO wth proposed scheme Asynchronous PSO Decreased percentage (%) P-value Bohachevsky E E E-04 Grewank E E E-16 Mchalewcz E-18 Rastrgn E E E-20 Rosenbrock E E E-19 Schwefel E E E-15 Table 1: The average of the total movng dstance on sx benchmark functons of the two schemes The number of the robots The proposed scheme (1E+03) Asynchronous PSO (1E+03) Decreased percentage (%) Table 2: The total movng dstance wth the changng of the number of the robots for the two schemes are performed on the benchmark functons to verfy the effectveness of the proposed scheme. From our research, several conclusons can be obtaned. Frst, the proposed scheme can sgnfcantly reduce the total movng dstance of the agentrobot group. Second, lke the conventonal PSO, the asynchronous PSO can fnd the optmal value of the regon search problem. Fnally, the asynchronous PSO wth the proposed scheme can reduce the total movng dstance of the agentrobot group compared to the asynchronous PSO tself. In the future, the smulatons and experments on practcal regon search problems lke odor source localzaton need to be mplemented. More propertes of the asynchronous PSO also deserve further analyss. ACKNOWLEDGEMENTS Ths work s supported by the Natonal Natural Scence Foundaton of Chna under Grant , the Program for New Century Excellent Talents n Unversty under Grant NCET , the Natural Scence Foundaton of Shaanx Provnce of Chna under Grant 2014JQ8365, State Key Laboratory of Electrcal Insulaton and Power Equpment EIPE16313 and the Fundamental Research Funds for the Central Unversty. REFERENCES [1] M.H. Chen and L. Wang. Impact of ndvdual response strategy on the spatal publc goods game wthn moble agents. Appled Mathematcs and Computaton, 251: , [2] X.F. Xe and J.M. Lu. Multagent optmzaton system for solvng the travelng salesman problem (tsp). IEEE Transactons on Systems Man And Cybernetcs Part B, 39(2): , [3] D.Y. Ye, M.J. Zhang, and D. Sutanto. Self-organzaton n an agent network: A mechansm and a potental applcaton. Decson Support Systems, 53(3): , [4] J.M. Gascuena and F.C. Antono. On the use of agent technology n ntellgent, multsensory and dstrbuted survellance. The Knowledge Engneerng Revew, 26(2): , [5] D.W.Gong and C.L. Q. Modfed partcle swarm optmzaton for odor source localzaton of mult-robot. In IEEE Congress on Evolutonary Computaton (CEC), [6] A.T. Hayes, A. Martnol, and R.M. Goodman. Swarm robotc odor localzaton: Off-lne optmzaton and valdaton wth real robots. Robotca, 21(4): , [7] M. Alghanbar, Y. Kuwata, and J.P. How. Coordnaton and control of multple uavs wth tmng constrants and loterng. In Proceedng of the IEEE Amercan Control Conference, [8] S. Rathnam and R. Sengupta. Lower and upper bounds for a multple depot uav routng problem. In Proceedng of the IEEE Amercan Control Conference, [9] J. Kennedy and R. Eberhart. Partcle swarm optmzaton. In IEEE Internatonal Conference on Neural Networks, 1995.

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