Multi-Robot Formation Control Based on Leader-Follower Optimized by the IGA

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1 IOSR Journal of Computer Engneerng (IOSR-JCE e-issn: ,p-ISSN: , Volume 19, Issue 1, Ver. III (Jan.-Feb. 2017, PP Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA Tng Huang 1,2, Mngn Yuan 1,2,*, Donghan Lv 1, Y Shen 1 1 (School of Mechancal and Power Engneerng, Jangsu Unversty of Scence and Technology, Zhangjagang, Chna 2 (Servce Center of Zhangjagang Camphor Tree Makerspace, Zhangjagang, Chna Abstract: To mprove the effcency of mult-robot formaton control, a new formaton control algorthm based on leader-follower optmzed by the mmune genetc algorthm (IGA s put forward n ths paper. Frstly, the formaton control s realzed by leader-follower algorthm. Then, the proporton coeffcents k 1, k 2 n leaderfollower s optmzed by the mmune genetc algorthm. Fnally, the optmzed proporton coeffcents k 1 and k 2 s used n the leader-follower algorthm to fnsh the mult-robot formaton control. Compared wth other three formaton control algorthms (.e. GA, smple leader-follower algorthm, behavor algorthm, the epermental results of mult-robot formaton control n two envronments show that the formaton control performance at tme and step fnshng formaton of the proposed formaton control algorthm s obvously mproved, whch verfes the valdty of ths algorthm. Keywords: Multple robots, Formaton control, Leader-follower, Immune genetc algorthm I. Introducton In recent years, the mult-robot system has attracted more and more attenton. The formaton control s one of the key technologes n mult-robot systems. The estng formaton control methods manly nclude the leader-follower algorthm [1], behavor-based control algorthm [2] and vrtual structure algorthm [3]. L et al. [4] put forward a mult-robot formaton control based on dynamc leader and enhance the ablty of mult-robots to deal wth emergences. However, the algorthm has poor adaptablty n comple envronments. Amng at the formaton control of mult-robots, Zhang et al. [5] proposed a quck convergng dstrbuted algorthm for generatng arbtrary shape of mult-robots. However, the leader and followers are relatvely ndependent of each other, and t s dffcult for the proposed algorthm to fnd feasble space when the obstacles are dense. He et al. [6] proposed a dstrbuted formaton control approach to formaton maneuvers. In the control approach, based on vrtual structures, formaton feedback s ncorporated n the formaton control scheme to ncrease the robustness of the formaton. However, because the formaton movement of mult-robots smulates a vrtual structure, the approach s lmted n applcaton range. In order to further mprove the formaton control effcency of the leader-follower algorthm, the mmune genetc algorthm s ntroduced to optmze the proporton coeffcents k 1, k 2 of the leader-follower algorthm n ths paper. The epermental results show that the formaton control effcency of the proposed leader follower algorthm optmzed by IGA s sgnfcantly mproved. II. Formaton Control Based on Leader-Follower The leader-follower method [7] s descrbed as: In a mult-robot team, a leader s set. The rest of the robots are desgnated followers, and follow the movement of the leader. Let l e and φ e be the epected straghtlne dstance and epected ncluded angle between the leader and a follower, respectvely. The purpose of the formaton control s to make the actual detecton dstance l and ncluded angle φ between the leader and a follower equal to the l e and φ e.let ( 0, y 0, θ 0, v 0 and ω 0 be the poston coordnate, drecton angle, velocty and angular velocty of the leader.let (, y and θ be the poston coordnate and drecton angle of the th follower. The th follower can fnsh ts formaton control by calculatng ts forward speed v and angular velocty ω. The knematcs equaton of the th follower can be descrbed: l v cos v0 cos d sn 1 ( v0 sn v sn d cos l0 (1 l where, d s the dstance between the leader pont and the reference pont of the th follower. γ = φ + θ 0 + θ. Accordng to the closed loop characterstcs of the leader-follower formaton control, we can conclude: DOI: / Page

2 l k1( le l k2( e Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA where, k 1 and k 2 are the proportonal control coeffcents. Accordng to Eq.(1 and (2, the velocty v and angular velocty ω of the th follower can be obtaned. cos [ k2l ( e v0 sn l0 psn ] d v p d tan v0cos k1( le l where, p. cos In the mult-robot formaton system, the velocty and angular velocty of each follower robot can be acheved accordng to Eq.(3. Then the mult-robot formaton control can be completed. III. Mult-Robot Formaton Control Optmzed by Immune Genetc Optmzaton 3.1 Immune genetc optmzaton algorthm The genetc algorthm (GA [8] s a knd of global random search algorthm, and s commonly used to generate hgh-qualty solutons to optmzaton and search problems by relyng on bo-nspred operators such as mutaton, crossover and selecton. The mmune genetc algorthm (IGA [9] s a novel optmzaton algorthm based on artfcal mmune theory, and s desgned on the basc framework of genetc algorthm by combng wth mmune operators (such as antbody stmulaton and suppresson, vaccne etracton and noculaton, and so on., whch can effectvely enhance the search effcency and search precson of genetc algorthm. The flow of IGA s shown n Fg.1. (2 (3 Fg. 1 Flow of mmune genetc algorthm 3.2 Immune selecton based on nformaton entropy In order to reflect the dversty of antbodes n the populaton, the nformaton entropy s ntroduced n ths paper. The affnty between the antbody and the antgen, and the affnty between dfferent antbodes are calculated based on the nformaton entropy. The average nformaton entropy of the entre populaton s defned as: DOI: / Page

3 j1 Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA M 1 H ( N H j ( N (4 M 1 H ( N ( p lg p (5 j 0 j j Total number of symbol at jth poston of N antbodes pj (6 N where, M s populaton sze, H j s entropy from jth poston of N antbodes, and p j s probablty whose symbol s from jth poston of N antbodes. Let A j be the smlarty between ndvduals s and s j. j 1 1 H (2 A (7 where H(2 can be obtaned through Equatons (4, (5 and (6 when N = Calculaton of the epected reproducton rate [10] The concentraton of antbody s defned as D 1 N N j Q (8 j Where 1 Aj Qj (9 0 otherwse and γ s the preset threshold value of the smlarty. The affnty between antgen and antbody [8, 9] s defned as: Af Ft( Pra( (10 Where, Ft( s the ftness of antbody. Pra( s the ectaton value of an antbody whch s net to the local or global optmal ponts. The epected reproducton rate (Err of antbody can be descrbed as: Af Err( D ( Optmzaton flow of the proportonal control coeffcents of leader-follower algorthm Step 1 Intalze algorthm parameters: antbody sze M, selecton probablty, crossover probablty, mutaton probablty, threshold value γ, mamal evolutonary generaton k ma, and so on. k 0. Step 2 Generate ntal operaton populaton and memory populaton. Step 3 Calculate the epected reproducton rates Errs of all antbodes n operaton populaton. Step 4 Eecute selecton operaton. Step 5 Eecute crossover operaton. Step 6 Eecute mutaton operaton. Step 7 Calculate the epected reproducton rates Errs of all antbodes n new operaton populaton and memory populaton. Step 8 Select better antbodes to update the operaton populaton and memory populaton. Step 9 Judge whether the termnatng condton s satsfed. If not, k k+1, go to Step 4, otherwse end. The termnaton condton s stated as: The specfed k ma s reached. IV. Immune optmzaton test and result analyss In order to verfy the valdty and superorty of the proposed mult-robot formaton control based on mmune genetc optmzaton, the trangle formaton control smulatons n two envronments are eecuted. The smulaton results are compared wth those of the GA, leader-follower algorthm and behavor algorthm.the proportonal coeffcents k 1 and k 2 n leader-follower algorthm are 0.22 and 0.20 respectvely after optmzaton of IGA. The coeffcents k 1 and k 2 optmzed by GA are 0.20 and 0.20 respectvely. The evolutonary curves of optmal solutons of IGA and GA are shown n Fg. 2. The evolutonary curves of average solutons of IGA and GA are shown n Fg. 3. From Fg.2 and Fg.3, t can be seen that the optmzaton ablty of IGA s stronger than that of IGA. DOI: / Page

4 Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA Fg.2 Evolutonary curves of optmal solutons Fg. 3 Evolutonary curves of average solutons Fg.4 gves the formaton control results of four algorthms (.e. IGA, GA, leader-follower and behavor n an envronment wth three robots. Fg.5 gves the formaton control results of four algorthms n an envronment wth s robots. Form the two fgures, t can be seen that all robots can complete the formaton control successfully through ther respectve algorthms. However, dfferent algorthms have resulted n dfferent control results. (a IGA (b GA (c Leader-follower algorthm (d Behavor algorthm Fg.4 Formaton smulaton of three robots DOI: / Page

5 Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA (a IGA (b GA (c Leader-follower algorthm (d Behavor algorthm Fg.5 Formaton smulaton of s robots Table 1 gves the performance comparson of formaton control among four algorthms n two envronments. From the table, we can see that, although the tradtonal control algorthms (.e. leader-follower and behavor have completed formaton control, ther control performance (.e. tme and step fnshng formaton are sgnfcantly lower than the ntellgent algorthms (.e. IGA and GA. As for IGA and GA, t can be seen that ther formaton control effect s bascally the same n smple envronment wth only three robots. However, n the envronment wth s robots, we can see that the IGA plays a powerful optmzaton capablty and ts formaton control result s better than that of GA, whch verfes the valdty of the IGA n the formaton control. Table1 performance comparson of formaton control among four algorthms Performance Number of robots IGA GA Leader-follower algorthm Behavor algorthm Tme fnshng formaton Step fnshng formaton V. Conclusons In the tradtonal leader-follower algorthm, the proporton coeffcents k 1, k 2 s obtaned by tral and error. The random coeffcents affect the formaton control effect to a great etent. In order to mprove the formaton control effcency of the smple leader-follower algorthm, the mmune genetc algorthm s ntroduced n ths paper. The proporton coeffcents k 1, k 2 are taken as the antbodes, and optmal solutons are DOI: / Page

6 Mult-Robot Formaton Control Based on Leader-Follower Optmzed by the IGA obtaned through the mmune optmzaton. Fnally the optmzed proporton coeffcents are used n the leaderfollower algorthm. The parameter optmzaton results show that the IGA not only can complete the global optmzaton of k 1 and k 2, but also ts optmzaton ablty s stronger than that of the genetc algorthm. Furthermore, the smulaton results of formaton control n two envronments also show that the formaton control results of IGA are the best, whch further verfes the valdty of the IGA n the parameter optmzaton of leader-follower algorthm. Acknowledgements Ths work s supported by the 2016 College Students Practce Innovaton Tranng Program of Jangsu Provnce, 2016 Entry Project of Servce Center of Zhangjagang Camphor Tree Makerspace, and Specal topc of "Thrteenth Fve - Year Plan" of Educatonal Scence n Jangsu Provnce (No.C-b/2016/01/06. References [1] C.J. Chen, Formaton control based on leader-followers for multple moble robots, doctoral dss., Hangzhou Danz Unversty, Hangzhou, Chna, 2015 [2] Y. Pang, Research on behavor-based formaton control of mult-robot, doctoral dss., Tanjn Unversty, Tanjng, Chna,2012. [3] F. Zhang, Z. Sun, M.J. Lu, Formaton control based on the method of artfcal potental and the leader-follower for multple moble robots, Journal of Shenyang Janzhu Unversty (Natural Scence, 26(4, 2010, [4] B. L, X.F. Wang, Formaton control based on dynamc leader mult-robots, Journal of Changchun Unversty of Technology (Natural Scence Edton, 30(2, 2009, [5] L. Zhang, Y.Q. Qn, D.B. Sun, J. Xao, Behavor-based control for arbtrary formaton of multple robots, Control Engneerng of Chna, 12(2,2005, [6] Z. He, Y.P. Lu, Y.B. Lu, Dstrbuted control of formaton maneuvers based on vrtual structures, Journal of Appled Scences, 25(4,2007, [7] M. Zhao, M.S. Ln, Y.Q. Huang, Leader-followng formaton control of mult-robots based on dynamc value of, Journal of Southwest Unversty of Scence and Technology, 28(4, 2013, [8] N.N. Cha, Y. Shen, Y. Xu, F. Jang, M.X. Yuan, Optmzaton desgn of manpulator based on the mproved mmune genetc algorthm, Journal of Mechancal and Cvl Engneerng, 2015, 12(4: [9] M.X. Yuan, Y.F. Jang, Y. Shen, Z.L. Ye, Q. Wang, Task allocaton of mult-robot systems based on a novel eplosve mmune evolutonary algorthm, Appled Mechancs and Materals, 246, 2013, [10] Y. Shen, Y.F. Bu, M.X. Yuan, Study on wegh-n-moton system based on chaos mmune algorthm and RBF network, Proc IEEE Pacfc-Asa Workshop on Computatonal Intellgence and Industral Applcaton, Wuhan, Chna, 2008, DOI: / Page