Ant Algorithm for Navigation of Multi-Robot Movement in Unknown Environment
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- Βλάσιος Παπαγεωργίου
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1 ISSN , CODEN UXUEW E-al: Journal of Sofware, Vol7, No9, Sepeber 006, pp hp://wwwosorgcn DOI: 0360/os7890 Tel/Fa: by Journal of Sofware All rghs reserved + (, 0097 An Algorh for Navgaon of Mul-obo Moveen n Unnown Envronen ZHU Qng-Bao + (Deparen of Copuer Scence, Nanng Noral Unversy, Nanng 0097, Chna + Correspondng auhor: hn: , Fa: , E-al: qbzhu@ealnnueducn Zhu QB An algorh for navgaon of ul-robo oveen n unnown envronen Journal of Sofware, 006,7(9: hp://wwwosorgcn/ /7/890h Absrac: The navgaon proble of ul-robo oveen n a cople and unnown envronen s suded n he paper A new algorh, ans navgaon algorh, s presened A he sar he ehod aps he global arges ono he area near he border of he robo s eyesho, and aes he as he local arges Then wo groups of ans wll be cooperang o coplee he search for he local opal pah n he robo s eyesho Based on hese confguraons, he algorh can predc possble collson wh oher robos and eecue subsequen avodance plans The local search wll be eecued by he algorh repevely whenever he robo progresses a sep So, he pah of he robo wll be alered dynacally, whch aes he robo ove on he global opal pah o he endng node The sulaon resuls ndcae ha he opal pah, whch he robo oves on, can lead he robo o reach he end safely even n coplcaed geographcal envronen The effec s very sasfacory Key words: : ul-robo navgaon pah plannng unnown envronen an algorh,,,,,,,,,, : : T4 : A (, [ 4],, N-Hard,, Suppored by he Naonal Scence Foundaon of Jangsu rovnce of Chna under Gran NoBK0068 ( eceved Acceped
2 : 89, [5], [],, [6], [7],, (, (,,,,,, q ob (=,,,q, ob v, δ AS obs, Sb,Sb,,Sb n g begn, g end, ob r, ob Vew, >r, Vew AS Σ 0, AS 0, X, Y, AS X,Y a y a δ X,Y, N = a /δ N y =y a /δ g AS,A AS g, OS={o,o,,o } A( n, Sb OS g A Σ 0 (,y, g(,y,=row,y=col, :row g col g C={,,3,,M},g(,,g(,,,g(, N +,, Fg elaon beween rang coordnae and seral nubers,g A (,y C, ( :,n,od =(( od N +, y =(n(( /N + ( ob AS, Σ 0 (,y, ( (( y ((,,
3 89 Journal of Sofware Vol7, No9, Sepeber 006 ob Vew g sub, ob (,g sub, ob,,,,, an ={,,,,,} (=,, an,, ( g,g g A,g OS, g, FS g A,g OS, g, NFS 3, Σ 0 (,y, ( (,y (, (, g (,y, g, ~g 4, d(g,g h d(, h,,h C, (, d(g,g,, C, = =N,(g,g AS e,,d(g,g, d l d ( g, g h = ( h + ( y yh ( 5 B (g (,y ={g g A,d(g,g S}, C g g,s={, },S= 6 g,w (g (,y ={g g B (g (,y,g O S, C} B abu = {( 0,(,,( } 0 < < <, 0, +, ( + W ( + abu, ( + +, Z, Z < W abu ( g sub, ah( (,g sub, ah( (,g sub, L, (3 e L = dl, dl = d( g, g h, g, g h Os,, h C l= 7 η ( g D d( g, g, η ( g = D d( g, g, η g, η ( g = sub ( (3 g g,d,g 8 an, an, g, g sub n,,, d(, S,, S 5, : Sep g begn g end, Sep g end ob Vew g sub ( g sub g end,, Sep 3 Sep 3 ob (, Sb, (~g, Sep 4 ob Sb,=,,,n, F ( 3 ah(p,p b,,p b ~g sub,p ~ ( Sep 5 ob, Sep 7, ob ( 4 : ob, Sep 7, ob ob Sep 4 F g sub ob, C O Sep 6 C O ( 4, C O,,
4 : 893 LFS Sep 7 g sub Sep 8 Sep,ob Vew( (, d( (,y,g end ( e,y e =r+δ, g sub =g end,, g sub g end, d( (,y,g sub (,y =r+δ n d(g sub (,y,g end ( e,y e (4,r δ g sub,g end,, g sub g end (4 g end g sub,y, g sub Vew( ( Vew g sub, g sub Vew, g sub Vew ( δ, Vew Barrer d= g sub g end Fg Local navgaon pah 3,,, : Sep g abu (=,,, (0= 0 ( 0 n=0, MAX,, 4 Sep, g FS, g, g W (g, g abu, : Case g B (g, g (, W g g g W ( g, Case g B (g, (5 (6 g W (g, g abu arg a{[ ( n] ( g } f q q0 = η S else [ ( n] η ( g p ( n = [ q ( n] [ ηq ( g ] q Z abu,,=,,,,, : C, g, S (6 q (0<q q,q 0 η (g 7 e (n p n,, C abu Sep 3, (7 ( n + = ( ρ ( n + ρ (5 (6 (7
5 894 Journal of Sofware Vol7, No9, Sepeber 006 Q, = l b 0, e l b = w l= ( n + <, ( n + = n,q ρ n w l b Sep 4,=,,,,, 8, : Sep 5, Sep, Sep 5 8, (3 L L n L d, L n <L d, L n L d, Sep 6, (8 : new = n old = ( α + α = Q, f global - bes - our = L n 0, oherwse,q,α,l n, global-bes-our Sep 7 n, MAX,, n=max 4 ob Xb Vew( (, Xb Vew( ( OS, ob, ( (, y (, ((y(,, ( + y ( +, (9, (0 ob Vew d, v = d( ( ( + y( +, ( ( y( /, = ( y( + y( /( ( + (, c = y( ( /( ( + ( l y=+c (0 ob ob,,, :, y, ob ob, ob ( δ V ah(p,p b, v g sub, =δ/v, ={, +, v }, Γ((,( v,γ((,( v ah(p,p b,ob ob v (0 (0 ob (( + y( +,=,,,h B I ={(,( + ( +,( v } ob,b Vew ob ob,ob : B Γ( (,( v =φ, d(( ( ε,,,ε ob ob d( ( ( ε,,, B Γ( (,( v =φ, d( ( ( < ε, =,, (8 (9
6 : 895 d ( ( 3 B Γ( (,( v =φ, d ( ( d( ( 4 B Γ( (,( v =φ, d( ( 4 (9 (0 V, v ( ε, ( < ε, ( ε, ( < ε,,,,+ =, 3, 3,,3+ 4 =, 4 4,Γ :ob ob,ob ob ob,ob n w,,, d ob η,ρ n =η( /+ d /V, w =ρ(n + d / v d 3:ob ( ob,, 4 ob ob 3 4,, C o, C o, 3,ob 3 9 T={ 0, e }, e > 0, e, FS, f:t Vew, f( 0 = 0,f( e = e, f Vew,f( 0,f( e f 0 0, e FS,FS 0 e F f F,, [ 0, n ], = +, d((,( =n{d((,, Vew L((, e <L((, e, f ( =( e,, e ~g sub e ~g ( α ρ ρ e, n a,, a a + =,, = a( ρ, α ρ ρ ( α ρ α + : f o, (5~ (8, 3 : ( e, (7 n ( ( ρ 0,, 0, = n ( n ( = ( e, e f o,, (7 a ( = ( ρ 0 + = ( ρ, = ρ,, a ( ρ (3 e e f o,, (7 (8 a a ( α ρ + ρ [( α + ],, ( = ( ρ ( α 0 + ( ρ ( α (3 = ρ ( α ρ + α, = a( ρ, α 3 : e, n a 9 f, 0<q 0 <,, : 9 f,, f F y r, r, q q 0, (5, (6,, p 5 p 6 ( y y q q 0 q>q 0, p 6 q q 0 q>q 0, p 5
7 896 Journal of Sofware Vol7, No9, Sepeber 006 y y = q0 p5 + ( q0 p6 r = q0 p5 + ( q0 p5 y 7 (5, =0, =, > n >0 7,η n >0, (6 f p 5 p 5 nη n p n > 0 η + η a a h ( Z > 0 y p6, p > 6 0, >0,r>0 = :(= ε n n ( ( r y,,( (4, 0<q 0 <,,,,, ( 9 f, s, an, an (,=,,, s,, :, / y/, / y/ (4,y,, 0,ob Vew((, d( p (, p ( > r,, 0,, ob ob,,, ob, 4, Vew n n 6 Vew 3, (4 ((n+ //,, q 0 085, n=9,=5, (5 0, (4, p( 0999, 4, 9 9,, 3,, 4, 5 ob, 5,,, 6 3,, ob 6(a~ 6(d ob 6,,, 6(b, 6(c 6,ob,,,,, 5,
8 : 897,,, ob,, Fg3 Global opal pah s Fg4 Global pah s fro Fg5 Opal pah s fro fro our algorh rollng algorh forecased collson (a Frs local pah (b Second local pah (c Thrd local pah (d Sh local pah (a (b (c 3 (d 6 Fg6 Local pah resolvng drawng 6,,,,,,,,,,,,,,, eferences: [] Zhang CG, X YG Moble robo pah plannng based on rollng wndows n he unnown envronen Scence n Chna (Seres E, 00,3(:5 58 (n Chnese wh Englsh absrac [] Zhang CG, X YG obo rollng pah plannng based on locally deeced nforaon ACTA Auoaca Snca, 003,9(:38 44 [3] Bruce J, Veloso M eal-te randozed pah plannng for robo navgaon In: roc of he Inellgen obos and Syse, 00 IEEE/SJ In l Conf, Vol [4] Sun SD, Ln M ah plannng of ul-oble robos usng genec algorhs ACTA Auoaca Snca, 000,6(5: (n Chnese wh Englsh absrac [5] Dorgo M, D Caro G An colony opzaon: A new ea-heursc In: Evoluonary Copuaon, 999 (CEC 99 roc of he 999 Congress, Vol Washngon: IEEE ress,
9 898 Journal of Sofware Vol7, No9, Sepeber 006 [6] Fan X, Luo X, Y S, Yang SY, Zhang H Opal pah plannng for oble robos based on nensfed an colony opzaon algorh In: roc of he In l Conf on obocs, Inellgen Syses and Sgnal rocessng 003 IEEE, [7] Dng YY, He Y, Jang J Mul-obo cooperaon ehod based on he an algorh In: roc of he Swar Inellgence Syposu, 003 (SIS 003 IEEE, : [], (E,00,3(:5 58 [4],,000,6(5: (955,,,, 0 (CODATA 0 CODATA CODATA Shuch Iwaa CODATA IA CODATA CODATA ICSU 006 CODATA CODATA ICSU Jane Lubchenco Tony Hey 0 0 CODATA e-scence egy IY hp://wwwcodaacn/ 006/ndehl
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