Adaptive PSO Using Random Inertia Weight And Its Application in UAV Path Planning

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1 Adaptve PSO Us Radom Ierta Weht Ad Its Applcato UAV Path Pla Houo Zhu* ab, Chawe Zhe a, Xaohu Hu a, Xa L b a Isttute of Software, Chese Academy of Scece, Bej, Cha, 00090; b Natoal Uversty of Defese Techoloy, Chasha, Hua, Cha,40073 ABSTRACT A ovel partcle swarm optmzato alorthm, called APSO_RW s preseted. Radom erta weht mproves ts lobal optmzato performace ad a adaptve retalze mechasm s used whe the lobal best partcle s detected to be trapped. The ew alorthm s tested o a set of bechmark fuctos ad expermetal results show ts effcecy. APSO_RW s later appled UAV (Umaed Aeral Vehcle) path pla. Keywords: Partcle Swarm Optmzato, Swarm Itellece, UAV, Path Pla. INTRODUCTION Partcle swarm optmzato (PSO) s a ew evolutoary computato techque proposed by Eberhart ad Keedy 995., It has bee motvated by the behavor of orasms lke brd flocks. PSO s characterzed as smple cocept ad computatoally effcet. It has bee wdely used varous optmzato areas, such as ANN optmzato. Path pla s the eerato of a space path betwee a tal locato ad the desred destato that has a optmal or ear-optmal performace uder specfc costrats. UAV path pla shares a lot of smlarty wth moto pla for robots, yet t has more complex search space ad costrats. J. F. Cay has proved that path pla s a NP-hard problem. 3 It has bee the subject of umerous studes the lterature. However, most exsted methods have dsadvataes space represetato, costrats hadl ad computato effcecy. For example, Voroo daram s oly feasble for -D space. 4 PRM eeds a lot of computato tme to update evromet formato. 5 A* alorthm eeds lare memores. 6 MILP requres too much computato tme whle EAs has may complex parameters to set. 7 We troduce a path plaer for UAV based o partcle swarm optmzato here. Ths paper descrbes a varat of partcle swarm optmzato alorthm, amed APSO_RW, whch corporates a radom erta weht ad a adaptve retalze mechasm whe the lobal best partcle s detected to be trapped. Basc PSO, stadard PSO ad APSO_RW are compared o four bechmark fuctos typcally used optmzato research. The results show that the addto of the two stratees has some advataes o certa fuctos. The alorthm s later appled UAV path pla.. APSO_RW Smlar to evolutoary alorthms, PSO coducts searches us a populato of partcles. Each partcle represets a caddate soluto to the problem. Partcles chae ther postos by fly aroud a mult-dmesoal search space accord to ts ow experece ad the experece of ehbor partcles utl a relatvely uchaed posto has bee reached or the computatoal lmtatos are exceeded. Ulke GA ad other heurstc alorthms, PSO has a flexble ad well-balaced mechasm to ehace ad adapt to lobal (va ehbor experece) ad local (va self experece) explorato abltes, whch ehaces the search capablty. Researchers have dscovered that PSO has better performace tha GA some fucto optmzato. The velocty ad posto formulato of the oral PSO are as follows. V ( t + ) = V ( t + ) + C* rad*( P X ( t)) + C* rad *( P X ( t)) () *sophe_hzhu@hotmal.com; phoe ; fax Seveth Iteratoal Symposum o Istrumetato ad Cotrol Techoloy: Measuremet Theory ad Systems ad Aeroautcal Equpmet, Jache Fa, Zhoyu Wa, Eds., Proceeds of SPIE Vol. 78, 784, (008) X/08/$8 do: 0.7/ SPIE Dtal Lbrary -- Subscrber Archve Copy Proc. of SPIE Vol

2 X ( t + ) = X ( t) + V ( t + ) () V (t) ad X (t) are the velocty vector ad posto vector for the partcle at eerato t. P s the best posto ts past experece ad P s the best posto amo all partcles the populato whle rad ad rad are two radom fuctos wth rae [0, ]. C ad C are cotve ad socal parameter respectvely. Sce ts troducto PSO has attracted a hh level of terest. 8,9,0 May researchers have worked o mprov ts performace varous ways, thereby derv may terest varats. Oe of the varats troduces a parameter called erta weht to the oral PSO alorthms as follows. V ( t + ) = W * V ( t + ) + C* rad* ( P X ( t)) + C * rad * ( P X ( t)) (3) The erta weht W s employed to cotrol the mpact of the prevous hstory of veloctes o the curret velocty. A learly decreas erta weht over the course of search was proposed by Sh ad Eberhart, whch s called stadard PSO. By aalyz the coverece behavor of PSO, a PSO varat wth a costrcto factor was troduced by Clerc ad Keedy. Costrcto factor uaratees the coverece ad mproves the coverece velocty. As a ew tellet alorthm, PSO stll has the problem of premature coverece. Varous approaches have bee proposed to solve ths problem.oe way s to mprove the populato dversty.we preset a modfed PSO based o ths dea. As metoed above, the erta weht W keeps balace betwee lobal ad local search ablty. A lare erta weht facltates lobal explorato whle a small oe ehaces the local search ablty. Expermets show that a dyamc W performs better tha a statc oe. We try a radom erta weht, whch chae the velocty updat equato to: V ( t + ) = rad * V ( t + ) + C* rad*( P X ( t)) + C* rad *( P X ( t)) (4) Besdes, a adaptve retalze mechasm s troduced wheever the lobal best partcle s detected to be trapped. Ths s derved from the atural pheomea that a swarm wll splt whe the swarm s too crowded or the dvdual s too smlar to evolve. Our APSO_RW s descrbed as follows. ) Italze the populato of partcles, clud posto, velocty, persoal best ad lobal best partcles. Set fla = 0 ; ) For t = to maxe do step3 to step8; 3) Set fla = fla +, evaluate partcles us ftess fucto; 4) Update persoal best ad lobal best partcles; 5) If lobal best partcle s updated, fla = 0 ; 6) Update the velocty ad posto of partcle us equato (4) ad (); 7) If fla = max tme, retalze part of the partcles; 8) If stopp crtera s satsfed o to step9, else o to step. 9) Output the optmzato results. 3. EXPERIMENTAL RESULTS Four umerc optmzato tasks were used to compare the relatve performace of our hybrd PSO to oral PSO ad stadard PSO. See Table. These are stadard test fuctos from pror evolutoary optmzato studes. The frst fucto s umodal whle the secod s multmodal cota a sfcat umber of local optma. All are desed to have mma at or ear the or. Table shows the mea ftess value of the best pot foud by the ed of the tral for the 50 trals the expermet. The results showed the mea best pot foud by APSO_RW to be statstcally Proc. of SPIE Vol

3 sfcatly better at all vector wdths for all fuctos except F4. For fucto F4, o statstcally sfcat dfferece was foud. Expermet results have demostrated that our APSO_RW performs better o some bechmark fuctos. Name Fucto Dmeso XMAX Sphere 0 (-0,0) F = x = Rastr 0 (-0,0) DeJo s f Bra [ x 0cos( x ) + 0] F = π = Table.. Bechmark fuctos F3 = 00( x x ) + ( x) 5. 5 F = ( x x + x 6) + 0( )cos x 4π π 8π (-0,0) (-0,0) Table.. Expermetal results Fucto Oral PSO Stadard PSO APSO_RW F e e-007 F F e e-007 F APPLICATION IN UAV PATH PLANNING Path pla problem ca be formulated as a 5-elemets array as follows. { ξ, ρ, ψ, σ, ϕ} P = (5) where ξ s the space represetato whch s the decso space of the optmzato problem, ρ s path cod whch represets the optmzato soluto, ψ s the cost fucto whch evaluates the optmzato soluto whle σ s the costrats expresso ad ϕ s the pla method used. I ths paper we use real-value cod of path waypots. See F. where ( 0, y0, z0 ) ( x y, z ) x s the start pot ad, s the oal pot. The other (-) pots are the optmzato varables. Ths kd of path cod has the follow advataes: ) the umber of the pots offers a trade-off betwee computato ad path qualty ad ) the decomposto of the path provdes possblty of parallel or dstrbuted mplemetato. xoyo zo F.. Path cod The cost fucto of a caddate path tak accout of three factors ca be defed as follows. C = = ( w l + wh + w3 f ) (6) TA Proc. of SPIE Vol

4 The frst term l s the leth of the th semet, whch pealzes the leth of the path to prevet the arcraft from wader too far away. The secod term h s the averae alttude above the sea level of the th semet, whch mmzes the arcraft s alttude to utlze the terra mask effect as much as possble. The thrd term f TA pealzes the paths that pass too close to the kow roud threat stes. f s calculated as follows. TA f TA N = ste j= 4 K /( R ) (7) Where K s a scale whch reflects the testy of jth kow threat. R s the arcraft s slat rae to the threat ste. j sj N ste s the umber of threat stes. The weht coeffcets w, w ad w cotrol the leth, stealth ad safety qualtes of a 3 caddate path. The eerated routes must satsfy the physcal lmtatos of the UAV, clud mmum route le leth, maxmum route dstace, mmum fly heht, maxmum tur ale ad maxmum clmb/dv ale. The path plaer was mplemeted a Vsual C proramm evromet o a Petum IV PC ru Wdow XP. The expermets were coducted us a DTED wth a resoluto of 00m 00m ad a set of sythetc threat data were tested. I the expermets, the parameters of the alorthm are set as follows: ) Populato sze s set to be 30 wth a dmeso of 8. ) C = C =. 0, maxe=00, fla = 8. 3) The coeffcets w, w ad w the cost fucto are.0,.0, ad Some of the results are show F. ad F.3. j sj F.. -D vew of the result path F D vew of the result path The flled crcles at the edpot of the route represet the start ad oal postos. The larer crcles represet the areas of threats. I eeral, 00 eeratos are suffcet to obta a ear-optmal route. ACKNOWLEDGMENTS Ths work s supported by Natoal Natural Scece Fud of Cha uder rat # Proc. of SPIE Vol

5 REFERENCES. R. Eberhart ad J. Keedy, A ew optmzer us partcle swarm theory, Proc. 6th It. Symp. Mcromache Huma Sc., Naoya, Japa, 39 43(995).. J. Keedy ad R. Eberhart, Partcle swarm optmzato, Proc. IEEE It. Cof. Neural Networks, , (995). 3. J. F. Cay, The complexty of robot moto pla, MIT press, Cambrde, R. W. Beard et al., Coordated taret assmet ad tercept for umaed ar vehcles, IEEE Tras o Robotcs ad Automato, 8(6), 9-9(00). 5. D. Hsu et al., Radomzed kodyamc moto pla wth mov obstacles, Workshop o the Alorthmc Foudatos of Robotcs, R. J.Szczerba et al., Robust alorthm for alorthm for real-tme route pla, IEEE Tras o Aerospace ad Electroc System, 36(5), (000). 7. I. K. Nkolos et al., UAV Path Pla Us Evolutoary Alorthms, Studes Computato Itellece, 70, 77-(007). 8. Y. Sh ad R. C. Eberhart, A modfed partcle swarm optmzer, Proc. IEEE Cor. Evol. Comput., 69 73(998). 9. A. Rataweera et al., Self-oraz herarchcal partcle swarm optmzer wth tme vary accelerat coeffcets, IEEE Tras. Evol. Comput., 8, 40 55(004). 0. Wa Hu et al., A Smpler ad More Effectve Partcle Swarm Optmzato Alorthm, Joural of Software, 8(4), (007). Y. Sh ad R. C. Eberhart, Partcle swarm optmzato wth fuzzy adaptve erta weht, Proc. Workshop Partcle Swarm Optmzato, Idaapols, 0 06(00).. M. Clerc ad J. Keedy, The partcle swarm-exploso, stablty, ad coverece a multdmesoal complex space, IEEE Tras. Evol.Comput., 6(), 58 73, 00 Proc. of SPIE Vol