Population Density Particle Swarm Optimized Improved Multi-robot Cooperative Localization Algorithm

Transcription

1 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue Populaon Densy Parcle Swarm Opmzed Improved Mul-robo Cooperave Localzaon lgorhm Mengchu TI, Yumng O, Zhmn CHE*, Panlong WU, Cong YUE ( School of uomaon, anjng Unversy of Scence and Technology, anjng 0094, Chna; Chna Saelle Marme Trackng and Conrollng Deparmen, Jangyn, 443, Chna) Emal: @88com bsrac: In lgh of he accuracy of parcle swarm opmzaon-parcle fler (PSO-PF) nadequae for mul-robo cooperave posonng, he paper presens populaon densy parcle swarm opmzaon-parcle fler (PDPSO-PF), whch draws cooperave co- evoluonary algorhm n ecology no parcle swarm opmzaon y akng full accoun of he compeve relaonshp beween he envronmen and parcle swarm, hrough dynamc adjusmen of parcle swarm denses based on Loka-Volerra compeon equaons, PDPSO-PF mproves parcle dverses, speeds up he evoluon of he algorhm and enhances he effecveness of predcon for mul-robo posonng Sudes show ha PDPSO-PF mproves boh he convergence speed and accuracy, hus s suable for mul-robo cooperave posonng Keywords: Parcle swarm opmzaon, parcle fler, mul-robo, populaon densy, cooperave localzaon Inroducon To faclae he pah plannng, navgaon, decson-makng and mplemenaon of asks, he robos are requred o sense he envronmen n advancemen and make accurae selfposonng [] Compared o a sngle robo [], mul-robo cooperave posonng sysem enjoys hgh effcency, hghprecson, hgh faul olerance, and hgh robusness, ec for [3 5] mul-robo cooperave operaons, hus s more suable for a varey of complex asks Deer [6], by applcaon of Markov posonng mehod, proposed ha for deecons beween one robo and anoher, robo moons, suaonal awareness nformaon, and muual observaon models could be aken no accoun for adjusng posons of each robo, so as o acheve mul-robo muual orenaon However as wh no regard o he nerdependence of deecon nformaon, overly opmsc esmaes on posons mgh be resuled Wang Lng [7], by combnaon of parcle fler [8] and exended Kalman fler (EKF), brough up a mul-robo cooperave posonng mehod, whch by akng accoun of he robusness and adapably of parcle fler as well as he hgh effcency and real-me of EKF, makes he robo group members share he overall posonng nformaon, hus effecvely deermnng self-posons n an unknown envronmen n spe of no accuraces Ths paper presens an algorhm of populaon densy parcle swarm opmzaon-parcle fler, whch by akng full advanage of he accurae posonng capacy among he heerogeneous mul-robos and by adopon of populaon denses n o he parcle swarm opmzaon-parcle fler mehod, wh as well as he dynamc adjusmen of parcle denses, can mprove boh he posonng accuracy and speed of robos The remanng par of he paper s organzed as follows: Secon presens he nformaon on relave observaons and Secon 3 provdes an analyss for populaon densy parcle swarm opmzaon-parcle fler Comparave expermens and resuls are shown and dscussed n Secon 4 Fnally, Secon 5 s a concluson of hs research ccess o Informaon on elave Observaons In order o acheve muual posonng of heerogeneous robos, he followng assumpons are aken herewh [9] : () s each robo s equpped wh moon sensors, hus nformaon can be exchanged beween one robo and anoher () Heerogeneous mul-robos conss wh hgh-level robos wh grea ables Such robos are equpped wh exernal sensors ha can measure he relave dsances and drecons of oher robos, whch makes possble for accurae selfposonng; whle low-level robos are confgured wh exernal sensors ha can measure he relave locaons (3) Each robo can deec he oher ones wh accurae denfcaons Observaon daa can be accessed hrough hree sages: frsly, he moons of each robo can be sensed hrough nernal sensors based on her moon models, ncludng movng dsances and drecons; nex, hgh-level robos can drecly oban he relave posons of oher nearby E-ISS: 4-66X 33 Volume 4, 05

2 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue accessble robos and conver hese posons no her own local coordnaes for calculaons of relave observaons; fnally, he hgh-level robos convey he observan nformaon on relave posons o oher robos whch, hrough processng such nformaon, hereby calculae he dsances and drecons of all observan robos and robos naccessble relave o hemselves ssumng a queue of a number of robos ha are engaged n exploraons [0], and here s a leas one robo can oban T accurae localzaons Use = ( xyθ,, ) o represen posons of robos a some pon, and posons of all robos a some pon can be expressed as (,,, ) T The relave posons beween one robo and anoher can be denoed as: d = ( x x ) + ( y y ) () θ () Whereas, y y = arcan θ x x and represen posons of hgh-level and lowly-confgured robos a a gven momen, whle ndcaes he relave dsance from θ s he drecon angle of 3 PDPSO-PF ; o ; θ means he drecon angle of 3 Dynamc djusmen of Populaon Denses Gven a populaon P, he secular equaon beween populaon growh and envronmen as descrbed n ecology goes as he followng [] : K = r d (3) Whereas, K means envronmenal load; r represens ndvdual growh rae for he populaon; ndcaes he populaon sze; K s he logsc coeffcen s can be seen from he formula, logsc coeffcen acs on he varaon of populaon denses, o he effec of populaon denses endng o envronmen load If > K, logsc coeffcen s negave, he populaon densy decreases; whle f < K, hen he logsc coeffcen s posve, hus populaon densy ncreases; n case = K, logsc coeffcen s 0, hen populaon densy remans unchanged d 3 Populaon Densy Parcle Swarm Opmzaonparcle Fler (PDPSO-PF) Gven a group composed wh parcles, and he Parcle s expressed wh an m-dmenson vecor [ 3] of he x ( =,,, ), so s he flyng speeds Parcle whch are noed as v ( =,,, ), hen he updaed formula of PDPSO-PF parcles are as follows: v( + ) = wv() + cr ( p() x()) + cr( p () x()) (4) x ( + ) = x ( ) + v ( + ) (5) g Whereas: p ( ) ( =,,, ) s he opmal locaon ha s accessble currenly for Parcle, whch s expressed as: p( ), f( x( + )) < f( p( )) p ( + ) = x( + ), f( x( + )) f( p( )) (6) pg () s he opmal poson of he whole parcle group, e pg() { p(), p(),, p() f( pg()) = max{ f( p( )), f( p( )),, f( p ( ))}} (7) Whereas, w s nera facor; c and c are non-negave consans; whle r and r are random numbers rangng whn[0,] Gven n parcle swarms P ( =,,, n) wh ( =,,, n), PDPSO-PF undergoes evoluon and j cooperave processes n all eraons Parcle swarm opmzaon algorhm [4] s adoped for evoluon process; whle speces populaon densy equaon shall be appled for calculaons of populaon denses durng cooperave process, and subsequenly szes of each parcle swarm can be adjused based on he calculaed parcle swarm denses, e ( + ) = ( ) +, ( =,,, n) d (8) In case ha he growh rae of parcle swarm d P ( =,,, n) s posve, hen hrough random generaon parcles, parcle swarm P ( =,,, n) s added d of o expand parcle swarms E-ISS: 4-66X 33 Volume 4, 05

3 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue In case ha he growh rae of parcle swarm d P ( =,,, n) s negave, hen parcle adapables of he parcle swarm s calculaed, followed by sorng based on adapables; he d parcles wh leas adapables are deleed, hus shrnk he parcle swarms s seen from he foregong, f he densy of ceran parcle swarm ncreases, a leas one parcle wll be produced randomly and added no such parcle swarm, whch mproves he dversy of such parcle swarm, hus opmzes he overall layou of parcles o ceran exen In case he densy of parcle swarms decreases, a leas one parcle wh he leas adapably shall be removed Such process no only ndcaes he cooperave compeon among swarms n he evoluon process of parcle swarms, bu also reflecs he muual compeon process among parcles whn he parcle swarm 33 Calculaon seps of PDPSO-PF PDPSO-PF algorhm goes as follows: (a): Deermne he nal parameer values and oban he relave observaons from robos o oher low-confgured robos he pon when k = 0, selec parcles { x,,, } 0 = from mporance funcons a he nal momen, he mporance densy funcon goes lke formula (9): x ~ qx ( x, z) = px ( x ) k k k k k k (9) Gve he objecve funcon as: T f = exp{ sqr[( z z )] ( z z ) / c } (0) pred k pred k represens he measured nose covarance; c3 s Whereas, a consan; z means he observaon nformaon a momen; z pred ndcaes predcve nformaon a momen (b): calculaon of sgnfcan prory w= w pz ( x ) pz ( x) px ( x ) = w = w pz x qx ( x, z) () (c): calculaon of growh rae d d () d K a k k = = r K If 0 n ( ) of parcle swarms >, hen he randomly generaed d are added no he parcle swarm; 3 parcles d If < 0, hen calculae he adapables of parcles whn he swarm and sorng hem accordngly; remove d parcles wh he leas adapables: ( + ) = ( ) + d (d): applcaon of eraon by adopon of parcle swarm opmzaon formula: v ( + ) = wv () + cr( p () x ()) (3) + cr ( p() x()) x ( + ) = x ( ) + v ( + ) (4) ( ), ( ( )) ( ( )) p f x + < f p p ( + ) = x( + ), f( x( + )) f( p( )) p () { p (), p (),, p () f( p ()) (6) g j g = max{ f( p ( )), f( p ( )),, f( p ( ))}} p { p (), p (),, p () f( p ) * n * g g g = g g g (7) (e): In case max{ f( p ( )), f( p ( )),, f( p ( ))} j (5) * p mees eraon ermnaon condons, hen he algorhm ends; oherwse go on wh sep (c) (f): based on he predced parcle concenraon of robos, he relave observaons beween each parcle and oher lowlyconfgured robos, calculae he dfference beween predcve measuremen d and acual observaon θ (g): calculae he prory properes of opmzed parcles and conduc normalzaon a w = + (8) b d θ = / = w w w (h): saus oupu: (9) x= wx (0) = 4 Smulaon Expermen The compuer o do expermens has an 5-400U CPU and 8G memory The sensor daa and he movemen measures are colleced by he robo wh odomeer and sonar sensor To verfy he effecveness of PDPSO-PF n mul-robo E-ISS: 4-66X 333 Volume 4, 05

4 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue posonng by combnaon of relave observaon measuremen, PF, PSO-PF and PDPSO-PF are adoped respecvely n a 5m 5m lab envronmen for expermen observaons Parameers appled n he expermen are: c = 5, c =, w = 07, m = 00 Frsly, use robo and robo and for unform lnear moons wh nal orenaon angle as 0, see Fgure for he acual rajecory and he reference rajecory by applcaon of PDPSO-PF s for he orenaon error of robo, see Fgure 3; wh robos makng unform curve moons, see he acual esmae rajecory and reference rajecory as shown n Fgure Fgure 4 ndcaes he posonng error of In he fgure for rajecores, he Trajecory, and 3 represen he rajecores of, and respecvely MSE/m PF PSO-PF PDPSO-PF Fgure 3 Localzaon -MSE of lnear moon 35 3 True rack Esmaed rack PF PSO-PF PDPSO-PF 5 06 y /m MSE/m Fgure True rack and esmaed rack of lnear moon Fgure 4 Localzaon -MSE of broken lne moon 4 35 True rack Esmaed rack Table comparson of MSE/m for dfferen algorhm moon mode robo PF PSO-PF PDPSO-PF y /m lnear moon Fgure True rack and esmaed rack of broken lne moon broken lne moon E-ISS: 4-66X 334 Volume 4, 05

5 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue The expermenal resuls ndcae ha he posonng accuracy of hgh-level robo s hgher han ha of robo When robo orenaon angle changes, he acual esmaed rajecory would devae from he reference rajecory, hus localzaon esmae error would be ncreased; bu when he orenaon angle keeps unchanged, he acual posons of robos would be mmedaely converged, hus posonng error decreases Compared o PSO-PF and PF, he adopon of robo corporave localzaon can sgnfcanly ncreases he posonng accuracy wh less errors and beer agreemen wh rackng rajecores, hus ndcang ha he algorhm presened n hs paper can be well appled n robo cooperave posonng 5 Conclusons Through an analyss of he defcences of PF and PSO-PF n mul-robo cooperave localzaons, he paper presens a new algorhm populaon densy parcle swarm opmzaon-parcle fler, whch n addon o adopng ndvdual adapably conrol evoluon of parcle swarm, also draws populaon denses no parcle fler, hus mproves he overall opmzaon capables and speeds up he evoluon of algorhm, hereby a hghly-accurae posonng sysem comes no beng The fnal expermenal daa have verfed he effecveness of PDPSO-PF n mulrobo posonng sysem cknowledgemens Ths work s parally suppored by he aonal aural Scence Foundaon of Chna (6505); aonal aural Scence Foundaon of Chna (U33033); aonal aural Scence Foundaon of Chna (647353); aonal aural Scence Foundaon of Chna (64034); aonal aural Scence Foundaon of Chna (60366); Key Defense dvanced esearch Projec of Chna ( ) Thanks for he help eferences [] S Wang, Q Zhu, Z Lu, e al Sudy of enforcemen Learnng based on Mul-agen obo Sysems Journal of Compuaonal Informaon Sysems, 007,3 (5), pp: [] M Das, Zlo, Kalra and Senz Marke-based mul-robo coordnaon: a survey and analyss Proceedngs of he IEEE, 006, 94(7), pp:57-70 [3] T ashd, M Frasca M, l, e al Mul-robo localzaon and orenaon esmaon usng roboc cluser machng algorhm obocs & uonomous Sysems, 05, 63, pp: 08 [4] De Slva, Oscar, G K / Mann, G Gosne n Ulrasonc and Vson-ased elave Posonng Sensor for Mulrobo Localzaon Sensors Journal IEEE 05, 5(3), pp: [5] J Pugh and Marnol Dsrbued adapaon n mul-robo search usng parcle swarm opmzaon The 0h Inernaonal Conference on he Smulaon of dapve ehavor, 008, pp: [6] M nderson, and Papankolopoulos Implc cooperaon sraeges for mul-robo search of unknown areas Journal of Inellgen and oboc Sysems: Theory and pplcaons, 008, 53(4), pp: [7] Deer F, Wolfram, Hannes K, e al probablsc approach o collaborave mul-robo localzaonuonomous obos, 006, 8(3), pp: [8] L Yu, M Wu, Z Ca, e al parcle fler and SVM negraon framework for faul-proneness predcon n robo dead reckonng sysem Wseas Transacons on Sysems, 0, 0(), pp [9] Wang Ln, Shao Jn-xn, Wan Jan-we, e a Dslbued enropy based relave observaon selecon for mul-robo localzaonca Elecronc Snca, 007, 35(), pp: [0] M nderson, and Papankolopoulos Implc cooperaon sraeges for mul-robo search of unknown areas Journal of Inellgen and oboc Sysems: Theory and pplcaons, 008,53(4), pp:38-397, 008 [] P Dasgupa mul agen swarmng sysem for dsrbued auomac arge recognon usng unmanned aeral vehcles IEEE Transacon on Sysems, Man, and Cybernecs-Par : Sysem and Humans, 008, 38(3), pp: [] Z M Chen, Y M o, P L Wu, e al new parcle fler based on organzaonal adjusmen parcle swarm opmzaon ppled Mahemacs & Informaon Scence, 03, 7(), pp: [3] Y J, Wang, Sudy on PSO algorhm n solvng grd ask schedulng Journal on Communcaons, 007,0(8), pp:60-66 E-ISS: 4-66X 335 Volume 4, 05

6 WSES TSCTIOS on CICUITS and SYSTEMS Mengchu Tan, Yumng o Zhmn Chen, Panlong Wu, Cong Yue [4] Y L, a, Y Zhang Improved parcle swarm opmzaon algorhm for fuzzy mul-class SVM Journal of Sysems Engneerng and Elecroncs, 00, (3), pp Ls of abbrevaon posons of robos posons of hgh-level robos posons of lowly-confgured robo d relave dsance θ drecon angle of θ drecon angle of θ drecon angle of K r x v p () pg () w c c z k pred envronmenal load ndvdual growh rae populaon sze poson of parcle flyng speed opmal locaon of parcle opmal poson of he whole parcle group nera facor sudy facor sudy facor measured nose covarance observaon nformaon z predcve nformaon E-ISS: 4-66X 336 Volume 4, 05