Self-Organized Swarm Robot for Target Search and Trapping Inspired by Bacterial Chemotaxis

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1 Contents lsts avalable at ScenceDrect Robotcs and Autonomous Systems journal homepage: Self-Organzed Swarm Robot for Target Search and Trappng Inspred by Bacteral Chemotaxs Bn Yang a,b,d, Yongsheng Dng a,b *, Yaochu Jn b,c, and Kuangrong Hao a,b a Engneerng Research Center of Dgtzed Textle & Apparel Technology, Mnstry of Educaton, Donghua Unversty, Shangha , P. R. Chna b College of Informaton Scences and Technology, Donghua Unversty, Shangha , P. R. Chna c Department of Computng, Unversty of Surrey, Guldford, GU2 7XH, Unted Kngdom d Department of Mathematcs, Huayn Normal Unversty, Hua an, Jangsu, , P. R. Chna A R T I C L E I N F O A B S T R A C T Artcle hstory: Receved 00 December 00 Receved n revsed form 00 January 00 Accepted 00 February 00 Keywords: swarm robots dstrbuted control target searchng target trappng bactera chemotaxs self-organzaton Target search and trappng usng self-organzed swarm robots have receved ncreasng attenton n recent years but control desgn of these systems remans a challenge. In ths paper, we propose a decentralzed control algorthm of swarm robot for target search and trappng nspred by bactera chemotaxs. Frst, a local coordnate system s establshed accordng to the ntal postons of the robots n the target area. Then the target area s dvded nto Vorono cells. After the ntalzaton, swarm robots start performng target search and trappng mssons drven by the proposed bactera chemotaxs algorthm under the gudance of the gradent nformaton defned by the target. Smulaton results demonstrate the effectveness of the algorthm and ts robustness to unexpected robot falure. Compared wth other commonly used methods for dstrbuted control of swarm robots, our smulaton results ndcate that the bactera chemotaxs algorthm exhbts less vulnerablty to local optmum, and hgh computatonal effcency xxxxxxxx. Hostng by Elsever B.V. All rghts reserved. 1. INTRODUCTION Swarm robots [1], also known as mult-robots systems, nclude a group of smple physcal robots. Swarm robotc systems are beleved to be more relable or effectve n accomplshng tasks than sngle robots. Target search and trappng n a gven area s a frequently encountered task, such as terrorst search, polluton detecton, dsaster area montorng and rescung. Therefore, target search and trappng usng self-organzed swarm robots have receved ncreasng attenton n recent years, although desgn of self-organzed controller of such systems remans a grand challenge. Target search ams to detect targets n a gven area, whch s also known as area coverage. Area coverage problem has been tackled for years usng ether one sngle robot [2][3] or mult-robots/swarm robots [4][5]. It s also ndspensable n smultaneous localzaton and mappng. The dfference between area coverage and mappng s that the former does not need the precse locaton of the targets n the envronment. * Correspondng author. Tel.: ; fax: E-mal address: dhu.edu.cn

2 2 Target trappng s to surround the detected targets usng robots n a certan pattern. Target trappng methods are smlar to pattern formaton usng swarm robots, whch s often concerned wth the formaton of a complex shape. In recent years, much work has been devoted to solvng complex shape formaton usng swarm robots, whch can be dvded nto global shape nformaton [6][7] and local affecton [8][9]. Feng et al. developed a fnte-tme formaton control framework that ncluded global nformaton and local nformaton [6]. Meng et al. proposed a morphogenetc approach to swarm robotc system usng a gene regulatory network (GRN) to form complex shapes. The shape for the GRN s descrbed by Non-Unform Ratonal B-Splnes n ntalzaton [7]. Ghods et al. desgned a control algorthm based on the heat partal dfferental equaton (PDE) and extremum seekng for deployng a group of agents [8]. J et al. used the leader-follower structure wth the neghbor-based rule determned by the topology structure of an nterconnecton graph to solve the formaton control problem [9]. The man challenge n swarm robot target search and trappng s the desgn of a dstrbuted control and coordnaton mechansm. Much research has been conducted on desgnng the dstrbuted algorthms, whch can be roughly classfed nto four categores,.e. vrtual structure algorthms, leader-followng algorthms, artfcal potental feld algorthms, and bo-nspred algorthms. Vrtual structure algorthm was frstly proposed late 1990s [10][11]. Ths method consders a robot as a sngle vrtual rgd structure and adopts tradtonal control algorthms desgned for sngle robots/agents. Leader-followng (vrtual leader) algorthms have attracted huge nterest snce they were proposed [12][13][14][15][16]. Typcally, an algorthm s desgned to control the leader robot, whle others (followers) are located by the relatve postons wth ther neghbors. Artfcal potental feld (APF) algorthms were proposed for real-tme path plannng for robots to solve obstacle avodance problem, and became the most wdely studed dstrbuted control methods. In the APF methods, t s assumed that the robots combne attracton wth the goal, and repulson from obstacles. Much work has been reported to adapt the APF algorthm to controllng swarm robots [17][18]. However, the APF algorthm s known to easly get trapped n a local mnmum. Therefore, many deas for addressng ths problem have been proposed. Bo-nspred algorthms for self-organzed swarm robot to target search and trappng have been proposed n recent years nspred by a varety of bologcal systems, such as flockng behavors n socal nsects. For examples, Garca et al. proposed a smple ant colony optmzaton meta-heurstc (SACOdm) algorthm to solve the path plannng problem of autonomous moble robots [19]. The SACOdm methods determne the robots path based on the dstance from the source to the target nodes, where the ants remember the vsted nodes. Zhu et al. proposed an mproved scout ant algorthm to acheve the optmal statc navgaton path for swarm robots [20]. They also proposed a target ntercepton algorthm called the mult-scout ants cooperaton (MSAC) for robots based on sub-goal forecastng and a scout ant algorthm [21]. The scout ants search randomly the targets wthout the nfluence of pheromone. The MSAC algorthm uses two famles of ants, one searchng the current poston and the other from the target, whch s therefore a bdrectonal search. All the vsted grds by the scout ants of the two famles are stored n a global table to avod repeated search. Ths method has been shown to have greatly mproved the search effcency and can be mplemented for real-tme path plannng. The robotc Darwnan PSO (RDPSO) algorthm, proposed by Coucero et al., s nspred from the natural selecton and socal excluson [22][23][24]. The RDPSO algorthm evaluates the dynamcal parttonng of all the robots and exchanges the nformaton needed to adjust ts parameters based on a number of context-based evaluaton metrcs. Robots are dvded nto multple swarms and the robots n a swarm can communcate wth each other. The man advantage of the RDPSO algorthm s that t can escape from local optmal solutons and reduce the needed nformaton exchange. The bacteral foragng optmzaton (BFO) algorthm was proposed to mmc the E. col bactera foragng behavours n the ntestne [25]. Bactera are one of the smplest speces lvng on the earth. Many bacteral speces are sngle-cells, and are assocated wth each other n ther characterstc patterns. They can, e.g., sense the nutrent nformaton around them and swm to places havng a hgher nutrent concentraton. The BFO algorthm has become very popular [26][27] due to ts strong ablty n escapng from local optma and faster convergence compared wth other heurstc methods. Ideas for mprovng the BFO algorthm have also been suggested. For example, Müller et al. proposed a bacteral chemotaxs (BC) algorthm based on a model of bacteral chemotaxs [28]. Bactera chemotaxs s the phenomenon that bactera drect ther movements by followng the chemcal concentraton gradent around them. For example, bactera can fnd food by swmmng towards area wth a hgher concentraton of nutrton. Bo-nspred algorthms possess the merts of expansblty and flexblty for the self-organzed control of swarm robots. However, some of these algorthms need strct constrants such as absolute ntal postons [19]. In addton, these heurstc algorthms often need to perform large amount of calculaton, ncurrng prohbtve computatonal cost [10][19][22][23]. Therefore, how to mprove the control effcency, such as reducng the convergence tme becomes a prmary concern n these methods. In ths paper, we propose a self-organzaton algorthm for swarm robot target search and trappng nspred by bactera chemotaxs. The advantages of the proposed algorthm are: 1) Robots are less lkely to get trapped n local optmums; 2) The computatonal cost s low; 3) Predefned global coordnate s not needed for accomplshng the tasks.

3 3 The rest of ths paper s organzed as follows: Secton 2 ntroduces the framework and the basc assumptons used n the BC algorthm. Secton 3 descrbes the proposed BC algorthm for swarm robot target search and trappng. Comparatve smulaton studes are presented n Secton 4. Secton 5 concludes the paper and dscusses future work. 2. The Framework and Basc Assumptons 2.1. The Framework The proposed framework for target search and trappng problem usng swarm robots can be dvded nto the followng steps, as also shown n Fg. 1. Step 1. Establsh a local coordnate system accordng to the robots ntal postons n the target area. Step 2. Dvde the area to be searched nto N (the number of robots) cells usng a Vorono dagram. Step 3. Use the BC algorthm to search the target n each Vorono cell. Step 4. Surround the detected targets usng the BC algorthm. Some defntons n the above steps are elaborated as follows. 1) Constructon of a local coordnate system At frst, we ntalze the poston of the robots usng a local coordnate system constructed based on ther relatve postons [29]. A reference robot s selected frst, whose poston s set to be the orgn of the local coordnate system. Then, the poston of other robots can be determned based on ther relatve dstance to the reference robot. The same can be done to determne the poston of any pont n the area usng the local coordnate system. 2) Vorono dagram Vorono dagram [30] s a mathematcal method to dvde space nto a number of regons. A number of ponts (sometmes called seeds, stes, or generators) are gven at frst. Each pont has a correspondng regon that conssts of all the ponts closer to t than to any others. The regons are called Vorono cells. To mprove the effcency of target search by swarm robots, Vorono dagram s used here to dvde the space nto a number of small regons, termed cells. Each robot detects the target n the -th cell usng the BC algorthm. 3) Movng state We defne robot at tme nstant j as R,j wth two states for area coverage and trappng, respectvely (refer to Fg.1). The two states are: a) Searchng state. After ntalzaton, the robots are all n a searchng state when the area has not been covered. They am to detect targets wthn ts own Vorono cells and then search n others after coverng ther own. The detals about the algorthm for the searchng state usng the BC algorthm wll be presented later on. b) Trappng/Pattern formaton state. The robots wll change nto the trappng/pattern formaton state f the area has been covered. We set a hgh concentraton to the postons for trappng the detected targets. All robots swtch to the trappng/pattern formaton state and trap the targets drven by a gradent. Searchng state Trappng state Fg. 1 The flowchat for target searchng and trappng by swarm robots Assumptons Construct the local coordnate Dvde the area nto Vorono cells Search the targets n the area Has the area been fully covered YES Search the targets n the area Trappng completely YES To develop control algorthms for target search and trappng n a gven area by usng swarm robots, we make the followng assumptons: 1) All targets are detectable The man problem to be solved n ths paper s to detect the targets n a certan area and surround them. Therefore, we assume that the target can be detected f t s wthn the sensng range of the robot. 2) All poston nformaton can be shared among the robots Here we assume that robots are able to self-localze them n the gven area usng on-board equpment, such as blueteeth [31] or WIFI [32]. We also assume that the robots communcaton range can cover the whole area. Thus, the robots can know other robots postons, and do not need the whole feld nformaton. 3) The area s 2-dmensonal and bounded We assume that the edges of the area to be searched are known for develop the control algorthm. In ths paper, we consder solvng the problems n a contnuous 2-dmensonal area of a square-shape. The robot can vst all postons n the area except that the poston s occuped by an obstacle or other robots. 3. A Bactera Chemotaxs Algorthm for Target Search and Trappng The BC algorthm developed n ths work s adapted from the classcal bactera foragng optmzaton (BFO) algorthm proposed by Passno [27][33], whch s used to solve optmzaton problems. The man dea of the BC algorthm s to consder every End NO NO

4 4 robot as a bacterum. Then we can use the mechansm of bactera chemotaxs to solve dstrbuted control problems of swarm robots. The bactera am to fnd a poston wth a hgher level of concentraton of nutrent. To ths end, smlar chemotaxs mechansms n the BFO algorthm can be adopted. Durng the search for a hgher concentraton of nutrents, the targets that can be sensed by robots wll be detected. The man deas of the BC algorthm are as follows: 1) Set the concentraton of the targets poston to a large value A, where the grds are colored n black as llustrated n Fg. 2. 2) Calculate the gradent for the robots chemotaxs drecton. 3) Bactera swm along the drecton of to approach the target poston. The nutrent concentraton wll decrease once t s covered by a bacterum. We fnd that ths contrbutes to the BC algorthm s ablty to get out from local optmums because of gradent change caused by the concentraton decrease. Ths has also been demonstrated n our smulatons. Grds L R drecton to the next target usng the method descrbed as follows, referrng to Fg. 4. Fg. 3 Ten robots (black ponts) and ther Vorono cells. The chemotaxs step can be expressed by dn () t b ad (2) dt where N ( t) [ N, x ( t); N, y ( t) ] s the poston of the -th robot s poston, [ ; ] s the drecton, a s the constant coeffcent of x y D, b s the constant coeffcent determned by the robots speed. D [ D, x; D, y ] s the summed nteracton between the -th robot and other robots to avod collson between robots, whch can be calculated by Fg. 2 Grds selecton on the area In the followng, we present the detals of the BC algorthm for target search and trappng, respectvely. 3.1 The BC Algorthm n Searchng State At frst, the poston of the robots and the concentraton of each cell are ntalzed. An example s gven n Fg. 3, where 10 robots are randomly ntalzed n the area, where C A 0 (1) where A 0 s a large constant denotng the ntal concentraton. We set the step length of robot equals to ts real-tme velocty V, 1,2,... n. Then the gven area for target search s parttoned nto 2D grds as llustrated n Fg. 2. Let L R* 2, where L s the length of grds, R s the robots sensng range. Therefore, C s a matrx whose dmensons can be calculated by the sze of the area and the length of the grds. When each robot has reached all of the grds n ts cell, the robot s consdered to have covered the cell. After ntalzaton, robot moves n the drecton to the nearest grd wth the concentraton of A 0. If the robot has more than one nearest cells to search, we calculate the where B m m,x, B m D D (3) m 1 s the number of neghbors for robot, and m D [ D ; D y ] s the nteracton between robot m and robot whch can be gven by D m ( N Nm) (4) N N As the energy consumpton of robots to move straghtforward s less than that for robots to make turns, the robots wll not change ther drectons unless they are trapped n a local optmum. As shown n Fg. 4, to escape from a local optmum, the drectons of the robots are determned as follows: 1, 1 P 0 P X, 0 P X P P X where s denoted as 1 or 0 when the robot moves straghtforward or makes a turn, respectvely. Set arctan( y / x), angle yelds a probablty densty 2 dstrbuton P X, 0 ~ N(, ). Ths means the robot always has a hgher probablty to choose a smaller m (5)

5 5 as shown n Fg. 4. When robots are movng straghtforward, P( 1) 1 P( 0) 0 Fg.4. Drecton settng for robots movement After the drecton was selected, the robots keep movng drven by the BC algorthm for area coverage. Let ( Px, Py ) represents the poston of the -th robot at the, j, j j-th chemotaxs step. In the progress, the concentratons n the area covered by the sensors of the robots are, j, j, j, j (6) C( Px, Py ) C( Px, Py ) / 2 (7) We set the ntal concentraton C n the whole area usng Eq. (1). Once ths ntalzaton has been done, the robots wll swtch nto the searchng state. When the robots are movng n the area, the concentraton of the postons that can be covered by the robot sensors are updated usng Eq. (7). After the robots have been ntalzed and the fled has been dvded nto a number of Vorono cells, the vrtual nutrent matrx of the -th Vorono cell for the -th robot can be descrbed as M n Algorthm 1. Ths means that each robot s movement s guded wth the nutrent concentraton as recorded n M. In ths way, each robot R can detect the targets located n the area covered by the -th Vorono cell. Once a robot has covered ts own cell and found the targets, t wll swtch nto the leadng state as a leader. When other robots have covered ther own Vorono cells, they move towards the cells where the concentraton equals A 0 outsde ther own cells. The pseudo code of the proposed BC algorthm for swarm robot target search s presented n Algorthm The BC Algorthm n Trappng state The BC algorthm can now be used to solve the target trappng problem by robots n the trappng state. Once a robot detects a target, t communcates and shares the target s poston wth others. Consequently, we can set the concentraton of the target poston to a large constant. When the robots turn to the leadng state, robot fnds ts target T() usng the BC algorthm as descrbed n Algorthm 2. Then the followng robots, whch have detected no target, wll swm to T() accordng to Eq. (2). ALGORITHM 1. BC ALGORITHM FOR TARGET SEARCH 1: Construct a local coordnate system by selectng one reference pont and usng the relatve poston between the robots, defne the range of the area, ntalze concentraton C. Dvde the area nto Vorono cells accordng to the postons of the robots. Get the total number of the grds, S, n the -th cell. C and M represent the grds concentratons and the grds n the -th Vorono cell, respectvely. 2: For the -th robot R n M, chemotaxs loop: j=j+1 3: Set concentraton of each grds G (j) covered by S as C( Px, Py ) C( Px, Py ) / 2, j, j, j, j 4: Fnd the grds G (j) where the nutrent concentraton s the hghest and calculate the possble drecton for next chemotaxs 5: If ( j) δ ( j 1) & P( j 1) P( j) ò& max C A0 ( j 1) ( j) //movng straghtforward 6: Else P X P X, 0, 0 //trapped n a local optmum 7: End 8: dn m b ad dt 9: If max C A0 //the cell s not fully covered Goto Step 2 10: Else M M( Px, Py), where C( Px, Py) A0 //search n other cells 11: End 12: End ALGORITHM 2. BC ALGORITHM FOR TARGET TRAPPING 1: If a robot s n the trappng state and has found nr targets n the area represented by T {T 1, T2... T nr},the dstance from each target to robots s Dt(, k) R Tk, k (1,2,... nr), nr s the number of the targets. 2: Set the concentraton of the ponts (boundary) at a dstance of Rt from each target as C( T ) A. 0 3: In order to mnmze the trajectory and trap the targets evenly, each target wll be trapped by nt ( n / nr) robots. At frst, defne target matrx for robot T ( ) 0, [1, n] Then fnd the nearest target for robot. for l=1:nr // for each target tm mn( Dt( T 0, l), nr) //select the nr nearest robots for the l-th target T( tm) l End 4: The drecton robot can be calculated by ( j 1) grad ( T( ))

6 Re-covered Rate (%) Chemotaxs steps 6 5: 6: dn b ad dt End j 4. Smulaton Results and Analyss To evaluate the proposed BC algorthm for target search and trappng, we have performed some emprcal smulaton studes. Here we ntalze the robots n a square feld, set the coeffcent a=0.025 and the sensng range to Target Search In ths secton, t wll be shown that how swarm robots accomplsh target search based on the proposed BC algorthm. Fg. 5 shows a set of snapshots of the searchng process by 26 swarm robots controlled by the proposed BC algorthm. Fg. 5(a) shows 26 robots randomly located n a square area. The reference robots are selected from the edge of convex regon formed by the swarm robots and a local coordnate system s constructed. Based on the local coordnate system, the ntal poston of robots can be obtaned and establshment of Vorono dagram can be carred out, as llustrated n Fg. 5 (a). Fg. 5 (b) and Fg. 5(c) show the robots coverng the area usng the BC algorthm. Fg.5 (d) ndcates that the swarm robots that have covered the whole area. From the snapshots we can fnd that there are many grey areas, whch ndcate that the concentraton n these areas s stll very hgh. By contrast, the locatons n whte are those that have been searched repeatedly by the robots sensors. Ths ndcates there s a waste of energy and the search s neffcent. Table I lsts the mean and standard devaton of the chemotaxs steps of the swarm robots and the number of re-covered grds. For each case where 10, 20 and 30 swarm robots are used, respectvely, 30 ndependent runs have been conducted. TABLE I AREA COVERAGE PERFORMANCE USING THE BC ALGORITHM No. of robots Chemotaxs steps Re-covered rate (%) (Re-covered / all grds) Chemotaxs steps needed 10 robots 20 robots 30 robots Number of smulaton (a) Chemotaxs steps Re-covered Rate robots 20 robots 30 robots 11 (a) (b) Number of smulaton (b) Recovered rate (%) (c) Fg. 5 Area coverage by 26 robots based on Vorono dagram and the BC algorthm. (d) Fg. 6 Area coverage by swarm robots wth the BC algorthm. From Table I and Fg. 6, we can fnd that when 10, 20, 30 robots are used, they can cover the area n almost 7009, 3839, 2638 steps, respectvely. At the same tme, the re-covered rates of the robots are about 8.1%, 9.0% and

7 7 9.9%. Ths ndcates that f we use more robots to cover the area, a smaller number of chemotaxs steps wll be needed. These results show the BC algorthm can effcently cover the area wthn certan steps and re-cover the grds. In other words, the more robots are used, the qucker t s to cover the area. However, the re-covered area wll ncrease at the same tme. In the followng descrpton, the ablty of the swarm robot systems to avod obstacles s llustrated. To ths end, we consder a scenaro wth sx statonary obstacles and 26 robots n the area. Fg. 7 shows a number of snapshots observed n ths smulaton. From Fg. 7, especally n the area marked wth around rectangle, we can see that when a robot detects an obstacle, t can keep away from the obstacle to avod collson. Fg. 8 (a) llustrates a stuaton where the robot could have got trapped n a local mnmum. The force dagram for the robot s llustrated n the Fg. 9. FO represents the nfluence of the obstacle on the robot and F BC s the force for drvng the robot. Ths means that f the control algorthm s based on the artfcal potental fled [18], then only F s drvng the robot. As a result, the robot O can no longer move away from ths locaton and thus gets trapped. By contrast, f the proposed BC algorthm s used for control the swarm robots, FBC 0, and the robot wll be able to move out of the local mnmum and contnue searchng the area. The above example demonstrates that the BC algorthm has a better capablty of escapng from local optmums than a potental feld based algorthm. (a) (b) (a) (b) (c) Fg. 7 Sx statonary obstacles that can be avoded by 26 robots. It s descrbed n fg.(a) and fg.(b) that the robot marked n the rounded rectangle detects an obstacle and the edge of the cell. In fg.(c) and fg.(d), the robot moves n the drecton of avodng the obstacle under the controllng of BC algorthm. In order to further evaluate obstacle avodance capablty of the proposed BC algorthm, we consder another scenaro n whch an obstacle s movng across the area, as shown n Fg. 8. In the area marked wth a red rectangle at the rght bottom n Fg. 8, we can fnd that the robot can avod the obstacle f t detects the obstacle. In the smulaton, the robot moves very close to the obstacle and a collson wth the obstacle could have happened for physcal robots. Ths s because the robot and the obstacle are movng n opposte drectons. Therefore, the robot has moved backward for avodng a collson wth the obstacle. (d) (c) Fg. 8 Collson avodance wth a movng obstacle by 26 robots. The purple crcle represents the movng obstacle and the smaller one represents a robot. Obstacle (d) Fg. 9 The force dagram for the trapped robot Mult-Target Trappng FBC Robot Mult-target trappng by swarm robots s nvestgated here to further assess the performance of the proposed algorthm. We consder a scenaro where 48 robots are used to trap four targets usng the BC algorthm. In ths Fo

8 8 smulaton, robots detect the targets and trap each target usng the same number of robots. The results for mult-target trappng by swarm robots are llustrated n Fg. 10. We can fnd that each target s trapped by 12 robots and the dstance between the neghbourng robots can be tuned automatcally by usng Algorthm 2. When the robots turn nto leadng state, as shown n Fg. 10 (a), they separate nto dfferent groups for detectng the movng targets, as shown n Fg. 10(b). The robots wll then swtch nto the trappng state once they detect targets, whch are llustrated n Fg. 10 (c). Fnally, the postons of the robots are tuned so that they dstrbute evenly, as shown n Fg. 10(d) Interacton Analyss to the Robots From Fg. 10 and Fg. 12, we fnd that robots can trap the targets drven by the BC algorthm. However, the dstance between the target and the robots, the radus of the (a) (b) (a) (b) (c) (d) Fg.11. Area coverage after a robot s falure. The robot n the red rounded rectangle s defect and the other robots contnue to cover the area. (c) (d) Fg. 10 Four targets trappng usng 48 robots Target Searchng and Trappng n the Presence of Robot Falure Fnally, we evaluate the robustness of the system f some robots become defect durng accomplshng the task. For ths purpose, we assume one robot s defect durng the search (the one marked wth red rectangle n Fg. 11). From Fg.11 (a), we can see that all robots work properly for target searchng. Then, we assume the robot marked by a red rectangle breaks down. The consequent reactons of the swarm robotc system controlled by the BC algorthm are shown n Fg. 11 (b)-(d). We can see that other robots are able to autonomously take over the area orgnally covered by the defected robot, because the concentraton n ths area wll reman hgh. Moreover, the robots are able to adjust ther poston so that an even dstrbuton of the robots can be mantaned. (a) (c) (b) (d) Fg.12. Target trappng after a robot s falure by 16 robots.

9 9 crcle formed by the robots s larger than we set. The reason s that each robot s nfluenced by ts neghbors as well as the target. As the total number of robots n the system changes, the dstance between the robots wll also be adjusted autonomously. From Fg. 12, we can see that the robot marked n red n Fg. 12(a) was mssng n Fg. 12(b) after the trappng msson was completed. Then the other robots wll move autonomously under the control of the BC algorthm to locate evenly, as evdent from Fg. 12(c) to Fg. 12(d). In Fg. 13, the red crcles represent the robots marked by R 1, R 2 and R 3, and the blue crcle stands for the target marked by T 0. R r s the radus of crcle formed by the robots, R s ntalzed radus. F, 1 F and 3 F are forces TR of R2 from ts neghbourng robots R, R 1 3 and the target T. The desred dstance from the target to the robots s 0 Rs and the real dstance s R r. Here, F F F 13 F 1 TR 0 0 Rr Rs 3 0 Eq. (11) explans why the radus crcle s longer than the set radus R. Rr Fg.13. Robots stress analyss when convergence. T0 Rs R1 s R2 FTR R3 F3 F1 (11) R r of the formed F13 F R (8) T R To hold the stablty of the trappng robots, we can get: S F F (9) TR where F 13 s the resultant force of F 1 and F 3. When we gnore the nteractons between the robots: F F 0 F 0 F TR robot R2 wll trap the target at the dstance of the forces F1 and 3 3 (10) Rs wthout F. However, the robots nteract wth ther neghbors to avod collsons followng Eq. (2) and (3). So we have 4.5. Comparson wth other Algorthms We compare the proposed BC algorthm wth some other ones, such as the SACOdm [19], the MSAC[20][21], and the RDPSO [22] for target search. The comparatve results are presented n Fg.14. In the comparson, the feld sze s set to, M=10,20,,50, and the number of obstacles s 2M. The SACOdm algorthm exhbts a good performance n search for small areas wth, however, however, an ncreased tme as the sze of the areas ncreases.. The comparson, 50 ants are used, and evaporaton s set to 0.3, 1, 7. The SACOdm algorthm always searches for the shortest path n the area so the robot moves very fast when the feld sze s small (M=10 or M=20). By contrast, the tme consumed by RDPSO, MSAC and the BC algorthm remans smlar when the area sze changes. These algorthms are decentralzed methods, so the smulaton tme corresponds to the local nformaton around the robots and the path to the target s formed by the local optmal solutons. In addton, RDPSO needs more tme to complete the msson than MSAC and the BC algorthm. RDPSO does not assume global communcaton TABLE II SUMMARY OF SWARM ALGORITHMS FOR SEARCH TASKS SACODM [19] MSAC [20][21] RDPSO [22][23][24] The Proposed BC Computatonal complexty O( Nt ) O(2 Nt ) O(2 Ns ) O( Nt) Memory complexty Or ( ) O( Nt ) Or ( ) O( Nt) Intal envronment Known Unknown Unknown Unknown Intal deployment Fxed Random EST approach Random Avod local mnma Low-level control Punsh-reward method Local penalty Local penalty based on natural functons functons selecton Obstacle avodance Low-level control Low-level control Artfcal repulson Artfcal repulson PS: r stands for truncaton of the fractonal order seres [24].

10 t(s) t(s) 10 and as a result, the robots move n a random drecton to search targets.. From Fg. 14, we can also fnd that the tme consumpton of MSAC and the BC algorthm s almost the same. However, the MSAC algorthm needs the target s nformaton for bdrectonal search and the computatonal complexty s hgher, as shown n Table II Feld sze Fg.14. Comparson of robot swarms controlled by four bo-nspred algorthms. Then we compared the BC algorthm wth the GRN algorthm[34] to llustrate the effcency of trappng one target. The feld sze s set to and the ntal postons for the robots and target are randomly ntalzed n the feld. We performed 30 ndependent runs for each smulaton for the BC and GRN algorthms, respectvely. The results are shown n Fg. 15. We can fnd that the tme cost for the BC algorthm s less than that of the GRN algorthm. The reason s that the GRN based algorthm controls the robots for two steps medated by two proten concentratons whle the BC algorthm uses just the gradent to gude the movements. The tme consumpton n dfferent runs changes a lot for both the BC and GRN algorthms dependng on the randomly ntalzed postons of the swarm robots and the target SACOdm MSAC RDPSO BC BC GRN runs Fg.15. Trappng comparson for the BC and GRN algorthms. Whle the proposed algorthm can perform both trappng and search, tradtonal algorthms lke vrtual structure and leader-followng algorthms can accomplsh trappng tasks only. In addton, the BC algorthm s more flexble than the leader-followng algorthm because n the BC algorthm, each robot does not need to follow a fxed leader or relatve leader. Due to the above dfferences, drecton performance comparson s not lkely.. 5. Conclusons and Future Work In ths paper, we present a dstrbuted control algorthm of swarm robot for target search and trappng nspred by bactera chemotaxs. Extensve smulatons have been performed to assess the performance, robustness and computatonal complexty of the algorthm. Our results have demonstrated the effectveness and robustness of the BC algorthm compared wth several state-of-the-art methods for dstrbuted control of swarm robots. For the future work, we wll further study the robustness of the proposed algorthm n the presence of varous dsturbances n swarm robots. In addton, we wll examne performance change f some of the assumptons, for example, the global communcaton can only be partally satsfed. Fnally, we wll mplement the BC algorthm on physcal robots to verfy the performance. ACKNOWLEDGMENTS Ths work was supported n part by the Key Project of the Natonal Nature Scence Foundaton of Chna (No ), the Natonal Nature Scence Foundaton of Chna (No ), Cooperatve research funds of the Natonal Natural Scence Funds Overseas and Hong Kong and Macao scholars (No ), Program for Changjang Scholars from the Mnstry of Educaton, Specalzed Research Fund for Shangha Leadng Talents, Project of the Shangha Commttee of Scence and Technology (Nos. 13JC ), and Innovaton Program of Shangha Muncpal Educaton Commsson (No. 14ZZ067). References [1] V. Trann and S. Nolf, "Self-organzng sync n a robotc swarm: a dynamcal system vew," Ieee Transactons on Evolutonary Computaton, vol. 13, pp , Aug [2] B. Kupers and B. YungTa, "A robot exploraton and mappng strategy based on a semantc herarchy of spatal representatons," Robotcs and Autonomous Systems, vol. 8, pp , Nov [3] Y. Gabrely and E. Rmon, "Spannng-tree based coverage of contnuous areas by a moble robot," Annals of Mathematcs and Artfcal Intellgence, vol. 31, pp , [4] P. Dasgupta, T. Whpple, and C. Ke, "Effects of mult-robot team formatons on dstrbuted area

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