Trajectory Planning and Tracking Control of a Differential-Drive Mobile Robot in a Picture Drawing Application

Transcription

1 Acle ajecoy Plag ad ackg Cool of a Dffeeal-Dve Mole Roo a Pcue Dawg Applcao Chg-Log Shh * ad L-Che L Depame of Eleccal Egeeg, aoal awa Uvesy of Scece ad echology, ape 67, awa; M4743@mal.us.edu.w * Coespodece: shhcl@mal.us.edu.w; el.: Receved: Jue 7; Acceped: 7 Augus 7; Pulshed: Augus 7 Asac: hs pape poposes a mehod fo ajecoy plag ad cool of a mole oo fo applcao pcue dawg fom mages. he oo s a accuae dffeeal dve mole oo plafom coolled y a feld-pogaale-gae-aay (FPGA) coolle. By o locag he p of he pe a he mddle ewee wo wheels, we ae ale o cosuc a omdecoal mole plafom, hus mplemeg a smple ad effecve ajecoy cool mehod. he efeece ajecoes ae geeaed ased o le smplfcao ad B-sple appoxmao of dgzed pu cuves oaed fom Cay s edge-deeco algohm o a gay mage. Expemeal esuls fo mage pcue dawg show he advaage of hs poposed mehod. Keywods: dffeeal dve mole oo; ajecoy cool; edge-deeco; le smplfcao; B-sple appoxmao. Ioduco Wheeled mole oos ae ceasgly pese dusal, sevce, ad educaoal oocs, paculaly whe auoomous moo capales ae equed o a smooh goud plae. Fo sace, [] used mage pocessg echques o deec, follow, ad sem-auomacally epa a half-faded lae mak o a asphal oad. Employg a mole oo plafom dawg oo applcaos has he advaages of small sze, lage wok space, poaly, ad low cos. A dawg oo s a oo ha makes use of mage pocessg echques pu a mage ad daws he same mage pcue. A asoal x-y ploe has lms ems of wok space ad ecomes moe expesve fo lage wok szes. Mos poa dawg oos/humaod oos make use of muldegees of feedom fo oo ams [ 5]. Howeve, may e oo cosly o use a oo am dawg a pcue o poa. he asc moo asks fo a mole oo a osacle-fee wok space ae po-o-po moo ad ajecoy followg. ajecoy ackg cool s paculaly useful a dawg applcaos, whch a epeseave physcal po (pe p, fo sace) o he mole oo mus follow a ajecoy he Caesa space sag fom a aay al posue. he ajecoy ackg polem has ee solved y vaous appoaches, such as Lyapuov-ased o-lea feedack cool, dyamc feedack leazao, feed-fowad plus feedack cool, ad ohes [6 8]. I hs wok, we popose a smple ad effecve ajecoy cool mehod fo a pcue dawg oo ha s ased o vese kemacs ad popooal feedack cool dscee me. Omdecoal moo capaly s aohe mpoa faco fe ad pecse moo applcaos. Desgg a mole oo wh soopy kemac chaacescs eques hee acve wheels wh a specal wheel mechasm desg [9]. Kemac soopy meas he Jacoa max s Roocs 7, 6, 7; do:.339/oocs637

2 Roocs 7, 6, 7 of 5 soopc fo all oo poses, whch s oe of he key facos ooc mechasm desg [,]. Kemac soopy makes he es use of cool degees of feedom Caesa moo. he sadad cosuco of a mole dawg oo s ased o a classcal dffeeal dve chasss wh he sgle caso he ack of he oo [,3]. Some oos ae dve y wo seppe moos, whch he moo cool s a ope-loop cool. hus, he oo s poso ad oeao ae compued ased o he pu sep coad fo seppe moos [3]. Fo mos dffeeal-dve mole dawg oos, he daw pe s salled he mddle of he wheels; heefoe, hs cofguao s o omdecoal kemacs, ad a shap cuve s dffcul ad cosumes moe powe o daw. he movao of hs wok s, hus, o exploe he omdecoal moo capaly fo a wo-cool degees of feedom dffeeal-dve mole oo plafom fo applcao fe a dawg. Whe he daw pe does o sall a he mddle of he wheels, a dffeeal-dve mole oo plafom may e omdecoal ad eve soopc he Caesa space y o cosdeg headg cool. Moeove, he mole plafom has less powe cosumpo fo a gve efeece followg pah ad possly ca e used fo shap u moos. Fo he fs sep owad a auoomous a dawg sysem, he auhos popose a egal sysem cossg of a emoe ma coolle ad a dawg mole oo. he emoe ma coolle ca e ehe a pesoal compue (PC) o a smaphoe, whch auomacally geeaes le dawg pcue daa fom a camea eal me. he pcue cuves ae geeaed he sequece of mage edge deeco, seachg ad sog coeced pahs, le smplfcao of mage space cuves, ad le cuve smoohg y cuc B-sple appoxmao. he dawg mole oo s equpped wh a pe ad weless Blueooh coeco; hus, s ale o daw pcues o a pape o-le. he oo s a accuae mole wo-wheel dffeeal dve oo coolled y a feld pogaale gae aay (FPGA) coolle. he oo s dve y wo dc sevo moos. he moo cool s ude closed-loop poso popooal-egal-devave (PID) cool. he couos of hs wok ae as follows: () omdecoal moo fo a dffeeal dve mole oo plafom; () auoomous a dawg sysem ca e ul o keep oh mole oo plafom ad cool algohm as smple as possle; ad (3) sysem egao of a mole pe dawg plafom y mage edge deeco, le smplfcao ad smoohg, ajecoy followg cool, ad FPGA coolle. he es of he pape s ogazed as follows: Seco peses a omdecoal model of a dffeeal-dve mole oo. Seco 3 shows ajecoy ackg cool mehods ad saly aalyss. Seco 4 sudes ajecoy plag fo dawg a coeced dgzed cuve hough le smplfcao ad le smoohg. Seco 5 llusaes seachg ad sog pcue cuves of a gay mage. Seco 6 povdes oh smulao ad expemeal esuls oaed fom a es-ed mole oo. Seco 7 cocludes he pape.. Kemac Model of a Dffeeal-Dve Mole Plafom hs sudy cosdes a smple mole oo plafom wh wo depede dvg wheels ad oe caso fee wheel. A daw pe s salled alog a pepedcula le ewee he mddle of he wo wheels o depc a mage pcue. Le, ) e dvg he wheel agula velocy, s he ( adus of he dvg wheel, L s half of he dsace ewee he wo wheels, ad D s he pepedcula dsace fom he pe poso o he mddle of he wo wheels, as show Fgue. We defe x, y ) as he poso of he mddle of he wo wheels ad ( x, y) as he p poso of ( he pe he wold fame {W}. he og of he oo ase fame {B} s assged o he mddle of wo wheels, ad s he mole oo yaw agle ad s he oeao agle fom ( x, y) pog o x, y ) elave o he x-axs of he wold efeece fame {W}, as show Fgue. (

3 Roocs 7, 6, 7 3 of 5 y pe D L ( x, y ) ( x, y) {B} {W} x Fgue. Coodae fames of he mole oo plafom ad pe sysem: he wold fame {W} ad oo ase fame {B} wh og a he mddle of wo wheels. A daw pe s salled alog a pepedcula le ewee he mddle of he wo wheels. Le v ad e he saaeous lea velocy of he og ad agula velocy of he oo ase fame, especvely. he velocy kemac equao of he mole oo plafom s epeseed y x cos y s v () ad v L L () Coo o all ypes of mole oos wh wo cool degees of feedom, hs kemac s o-omdecoal. Suppose ha he Caesa poso of he pe ( x, y) s he epeseave po of he mole oo plafom, x x cos D (3) y y s ad hece, x cos y s Dsθ v Dcos (4) he mole oo plafom kemacs whou headg cool s ow defed y x J ( ) y (5) whee he Jacoa max s whee ao cos s cos s J ( ) (6) s cos s cos D / L. he deema of he Jacoa max, de( J) /, s a cosa. heefoe, y o locag he pe a he mddle of he wheels,.e.,, he Jacoa max s wellcodoed ad he vese Jacoa max s

4 Roocs 7, 6, 7 4 of 5 cos s s cos J ( ) (7) cos s s cos I s clea ha he cool degee he yaw agle s ow asfomed o he cool degee he laeal lea moo. he gge he s, he lage he moly s he laeal moo. Whou cosdeao of he oeao agle, he mole oo plafom ecomes a omdecoal plafom he Caesa space. A eesg example s a ccula shape oo wh a pe salled a he cee poso. he sgula value decomposo of he Jacoa max J ( ) s J U V v v u u whee, v, u cos s ad, v, u s cos he maxmum ad mmum sgula values of he Jacoa max J ( ) ae ad max, especvely; ad he codo ume m max cod ( J). Whe, he codo ume equals oe, ad he colums of m he Jacoa max J ( ) ae ohogoal ad of equal magude fo all oo poses. hus, he mole oo plafom ad pe sysem exh kemac soopy. Each wheel causes he pe s moo o e of equal amou ad ohogoal o ha caused y he ohe wheel. I hs case, makes he es use of he degees of feedom of he wo wheels he Caesa moo. 3. Mole Plafom ajecoy ackg Cool Mehods 3.. ajecoy ackg Cool ad Saly As saed aove, he p poso of he pe ( x, y( )) s he epeseave po of he mole oo plafom, whch mus follow a efeeced Caesa ajecoy ( x, y ),, he pesece of al eo. Sce he Jacoa max J ( ) s well-codoed fo all poses, a smple vese kemacs-ased esolved ae plus popooal cool law s appled o mee he equeme fo he pe ajecoy cool polem. We defe e x x( ) ad e y y( ) as he ajecoy ackg eos. he cool ule of esolved ae plus P cool s as follows x k e J ( ˆ) (8) y k e whee ˆ ( ) s he esmaed oeao agle (), ad k ad k ae posve gas, k, k. Le ˆ, ad he cos s J ( ) J ( ˆ), ad he eo dyamcs ecome a lea mevayg sysem as s cos follows e k cos e k s k s e cos k cos e s s x cos y (9)

5 Roocs 7, 6, 7 5 of 5 he saly ad popees of he aove closed-loop sysem ae dscussed he followg wo cases. Case : Gloal expoeal saly I he case of x y (po-o-po moo whou headg cool), he closed sysem has a gloally expoeally sale equlum a e, e ). I s ased o he use of he ( (, e ) Lyapuov fuco V ( e e )/, e, whose me devave, V e e e e cos ( k e k e ) V, cos m{ k, k }, povdes ha cos cos, k ad k. max Case : Ipu-o-sae saly (ouded-pu ouded-sae saly) Because of he ouded velocy capaly of moos, he ajecoy ackg velocy s lmed. Assume ha he devaves of efeece ajecoy ae lmed, such ha m ad m, whee m s a cosa uppe ouday. Lea 4.6 of Refeece [4] saes ha a ufoced sysem whose val soluo s gloally expoeally sale s pu-o-sae sale (ISS) f sumed o a ouded pu (o peuao). heefoe, he closed sysem Equao 9 s ouded-pu ouded-sae (BIBS) sale. Fuhemoe, he ouds of ajecoy ackg eos ae appoxmaely e k m ad e k m, especvely. he ajecoy followg eos e ad e ae decly popooal o ajecoy speed m, measue eo, ad gas 3.. Dscee-me ajecoy Followg Cool Mehod k ad I s desale o mpleme he aove couous-me ajecoy cool mehod dsceeme fom. Le c e he ajecoy cool updae me, ad ( x, y ) s he efeeced pe ajecoy a dscee me k; heefoe, s lkely o geeae cemeal moo coads ( ad S(, such ha whee ad whee x cos x D y s( y x x( k ) cos ( k ) ( D S( ) y y( k ) s ( k ) ( k ) ( he aove vese kemac equao ca e ewe as x k. y max cos ( k ) cos( ( k ) ( ) x ( D S( ) D () s( k ) s( ( k ) ( ) y x x x( k ) y y y( k ) Hee, s assumed ha x dmax ad y dmax, whch d max s a uppe ouday o how fa o move he pe a sgle updae me. If ( x, y ) s oo dsa fom ( x ( k ), y( k )), he eeds o move he age poso close o he cue pe locao y seg oe o moe emedae pos. Cool ems ( ad S( ca e oaed as follows x s ( k ) y cos ( s D ( k ) ()

6 Roocs 7, 6, 7 6 of 5 ad S Dcos ( D x cos ( k ) y s( k ) () Moo cemeal poso coads ae he gve y ( k ) S( L( S( L( (3) I s also equed ha ( k ) max ad ( k ) max, whee max s he maxmum cemeal poso coad of each dvg moo. Hee, ( ) ad ( ) ae sued up k ad he used as asolue efeece poso coads of wheel moos, whch ae he se o depede PID poso coolles o close he dc moo sevo cool loops. Fgue shows he sysem lock dagam of he poposed pe ajecoy followg cool mehod. I hs sudy, he ajecoy cool updae me s = mllsecods, ad he poso sevo cool samplg me s s =. mllsecods. c k efeece ajecoy + x y pe p ajecoy c ms _ x y z x( k ) y( k ) u delays x( y( eq. & eq. daw pe eq. 3 S ( k ) eq. 3 z u delay x y ( ) k z z suao + + odomey eqs. 5 & 6 _ s. ms s. ms _ s( ( eq. 4 PID coolle PID coolle z ( k ) ( k ) z mole oo dc moos ad dves dffeece ( k ) ( k ) c ms c ms Fgue. he sysem lock dagam of he pe ajecoy followg cool. he aove ajecoy cool loop eques fomao fom he mole oo s poso ad yaw agle. he compuao of he mole oo s poso ad yaw agle s ased o odomec pedco fom moo ecodes. he odomey updae me s also chose as = mllsecods. he mole oo s cemeal moo chages ae calculaed fom moo ecodes eadg ad whee s( L (4) ( k ) ( k ) he mole oo ase poso ( x, y ) ad oeao agle ae updaed accodg o c x x ( k ) cos ( k ) s( y y ( k ) s ( k ) (5) ad

7 Roocs 7, 6, 7 7 of 5 ( k ) (6) Roo localzao usg he aove odomey, cooly efeed o as dead eckog, s usually accuae eough he asece of wheel slppage ad acklash. 4. Le Smplfcao ad B-Sple Smoohg hs wok epeses each desed pcue cuve y a B-sple appoxmao of a dgzed wodmesoal mage cuve x,, ae used mos ofe. he polem saeme s depced as follows. Gve a dgzed mage cuve of coeced pxels x,, ode o fd a wodmesoal B-sple cuve of degee d, d fo ( + d ) cool pos pos x R. Hee, he B-sple cuves of degee ad degee 3 d y ( p, (7) ), d p,, s es o appoxmae he sequece of pu daa {(, x )} a leas-squaes sese. he fucos of, d ae he B-sple ass fucos, whch ae defed ecusvely as: d ), d ( ), d ( ) (8), d ( d whee,( ), ad s defed. ohewse he B-sple cuve y s he he desed pe dawg efeece ajecoy ( x, y ) a dscee-me he u of ajecoy cool samplg me c. 4.. Le Smplfcao ad Ko Seco he aove B-sple appoxmao polem volves ko seleco ad cool po seleco. o smplfy he soluo seach, ko seleco ad cool po seleco ae foud sepaaely wo phases. Ially, he sa ad ed kos ae se o ad. Fs, he le smplfcao echque s appled o selec kos } d {,, so ha j ad. he leas-squaes eo mehod s he followed o seach ou ew cool pos { p } fo he pupose d of le smoohg. Le smplfcao s a algohm fo educg he ume of pos a cuve ha s appoxmaed y a sees of pos wh a eo of epslo. hee ae may le smplfcao algohms amog hem, he Douglas Peucke algohm s he mos famous le smplfcao algohm [5]. he sag cuve s a odeed se of pos o les ad he dsace dmeso epslo. he algohm ecusvely dvdes he le. I s ally gve all he pos ewee he fs ad las pos. I auomacally maks he fs ad las pos o e kep. I he fds he po ha s fuhes fom he le segme wh he fs ad las pos as ed pos; hs po s ovously fuhes o he cuve fom he appoxmag le segme ewee he ed pos. If he po s close ha epslo o he le segme, he ay pos o cuely maked o e kep ca e dscaded whou he smplfed cuve eg wose ha epslo. Afe he le smplfcao algohm, he seleced kos { },, ae ul fom he dex of le smplfcao pos. kos A lea sple appoxmao of he pu mage cuve ca e oaed ased o he seleced { } ad cool pos lea sple ajecoy y s he: x seleced fom hose he pu daase y x x, x j. he desed, (9)

8 Roocs 7, 6, 7 8 of B-Sple Cool Po Seleco hs sudy develops he B-sple wh degee d appoxmao of pu daa dsc kos } x,, wh {,, oaed fom le smplfcao fo le smoohg. Fs, we defe d d ope ege kos { } hee so ha { } {,,,,,,,, }, whee kos ad epea (d + ) mes, ode o guaaee ha he sa ad ed pos of he B-sple cuve ae he fs ad las pu daa x ad x, especvely. he B-sple cuves of degee ad degee 3 ae cosdeed hs sudy. () B-sple of degee (d = ) d he cool pos p ae aaged hee such ha p x ad p x o guaaee ha he sa ad ed pos of he pcue cuve ae uchaged, ad ( ) cool pos { p } ae lef o e deemed. () B-sple of degee 3 (d = 3) d he cool pos p ae aaged hee such ha p p x ad p p x o guaaee zeo ed speeds a he sa po x ad ed po x, ad ( ) cool pos { p } 3 ae lef o e deemed. Cool pos ae seleced y leas-squaes fg of he daa wh a B-sple cuve: E Fo B-sple of degee (d = ), he fg equaos ae: d y x, d p x () x x, d, d, d p x Le X p p p ad 3 B, ad he we have a ovedeemed max equao: whee ( ) ( ) ( ), d 3 A,, ad Fo B-sple of degee 3 (d = 3), he fg equaos ae:, () A ( ) ( X ) ( B ) ( ) () p x ( ) x ( ) x,, d, d, d, d, d 3 Le X p p ad p 3 4 dmesos fo a ove-deemed max equao: whee ( ) ( ) ( ), d 3 (3) B, ad he we also have he same A X B ( ) ( ) ( ) ( ) A,, ad 3. he leas-squaes eo soluo ca he e solved fom he followg omal equao: o oaed fom he pseudo-vese soluo: SX A AX A B (4) X ( A A) A B (5) Sce he omal equao max S A A s a syec ad aded max, s, heefoe, desale o seach fo cool pos hough asc ow elmaos ad he follow wh ackwad d susuo. Oce cool pos p ae foud, he desed B-sple efeece ajecoy y s geeaed hough DeBoo s B-sple ecusve fomulao [6].

9 Roocs 7, 6, 7 9 of 5 5. Pcue Cuves Geeao We ow desce he pocess fom he pu of he mage pcue o he desed pcue cuves geeao. Pcue cuves ae geeaed afe Cay s edge deeco algohm s pefomed o he pu pcue gay mage [7]. he geeao of pcue daw cuves volves seachg ad sog pcue cuves wo sages. he saegy fo seachg ou pcue cuves us hee phases as saed elow: Phase : emove sal pos ad ach pos; Phase : seach coeced pahs; ad Phase 3: seach loop pahs. he pcue po decso s ased o he local fomao of s adjace pxels a 3-y-3 P8 P P5 wdow, P4 pxel P, defed hee. Le he ems 4-coec ad 8-coec of a pxel po e he P7 P3 P6 umes of s 4-coeced pxel equal o ad s 8-coeced pxel equal o, especvely. I phase, sal po ad ach po ae classfed as elow: sal po: 8-coec = ; ad ach po: 4-coec >. I phase, sa po, md-po, ad ed po of a coeced pah ae classfed as elow: sa po: 4-coec = o (4-coec = ad 8-coec = ); md-po: he ode of (P = ) o (P = ) o (P3 = ) o (P4 = ) o (P5 =) o (P6 = ) o (P7 = ) o (P8 = ); ed po: 8-coec =. I phase 3, sal po ad po a loop pah ae classfed as elow: sal po: 8-coec = ; po a loop pah: 8-coec. Fo he sog of fal pcue cuves, a smple geedy mehod of he eaes egho saegy s appled o so pcue cuves ode o sed ou o he oo dawe. he ex cuve o e daw s he oe whee oe of s ed pos s closes o he ed poso of he dawg cuve amog he es of he cuves. Fgue 3 shows pcue cuve seach esuls; he pu gay mage has a sze of 3 35 yes. hee ae 5878 edge pxels afe edge deeco, ad hee ae 36 coeced cuves cuve sog. Afe le smplfcao, hee ae 7 cool pos lef. (a) ogal (a) mage () edge deeco () esuls (c) seached (c) pcue cuves Fgue 3. Image pcue cuves seach esuls: (a) ogal mage; () edge deeco esuls; ad (c) seached pcue cuves.

10 Roocs 7, 6, 7 of 5 6. Smulao ad Expemeal Resuls he expemeal auoomous oo mage fgue dawg sysem cosss of a PC o a smaphoe as a ma coolle ad a dffeeal-dve mole oo plafom as show Fgue 4. he adus of he dvg wheel s = 56.5, ad he dsace of wo dvg wheels s L, whee L =.5. he wheel s acuaed y a dc moo (moo maxmum o-load speed 49 pm) wh a 5: gea educe, ad he moo ecode has a esoluo of 3, ppc. he poposed pe ajecoy followg cool sysem s ul o a Alea DE-ao FPGA developme oad ug a a sysem clock ae of 5 MHz. All cool ad sees coucao modules ae mplemeed usg Velog hadwae descpo laguage (HDL) ad syheszed y a Alea Quaus II EDA ool. he mage pocessg ad coeced cuve geeao pogam ae pogaed Vsual C++ fo PC ad JAVA fo smaphoe. he mole oo eceves eal-me pcue cuves daa, whch ae geeaed fom a PC o a smaphoe hough Blueooh s3 a a Baud-ae of 5, Hz. Fgue 4. A dffeeal-dve mole oo plafom wh a daw pe o geeae a pcue fom a mage. he fs example cosdes a ccula pah o vefy he effec of D/ L. he desed efeece pah ajecoy s epeseed y Rcos( ) ad Rcos( ), /, whee R x = 5, ad he oal ccula legh s f x y d = p. he cool law Equao S (8) wh popooal gas k k s used. Fgue 5 shows he oal dsplaceme f d he jo space wh espec o aay al yaw agle fo seveal dffee pe locao dsaces D o follow he desed ccula pah ajecoy. y f

11 Roocs 7, 6, 7 of 5 3 jo space dsplaceme (ccula pah) 5 ho =. ada 5 ho =.5 Fgue 5. Smulao esuls of he effec of fo a dffeeal-dve mole oo o follow a ccula pah. he secod example cosdes a squae pah of sde legh, ad he oal legh s f x y d = 4. Fgue 6 shows he oal dsplaceme f d he jo S ho = al agle (ada) ho =. ho =.5 space wh espec o al agle yaw fo seveal dffee pe locao dsaces D o follow he desed squae pah ajecoy. As expeced, he jo space dsplaceme deceases as he dsace D ceases. Whe (.e., D = L), he Jacoa max J s soopc fo all mole oo poses; ad hece, s depede o he mole oo al yaw agle ad S /. 3 jo space dsplaceme (squae pah) 5 ada 5 ho =. ho =.5 ho =. ho =.5 ho =. Fgue 6. Smulao esuls of he effec of fo a dffeeal-dve mole oo o follow a squae pah al agle (ada)

12 Roocs 7, 6, 7 of 5 I he followg ajecoy cool expemes, a dawg pe s locaed a a dsace of D = 5. he dscee-me ajecoy followg cool law Equaos () ad () s appled wh ajecoy ad feedack updae me =. s. Fgues 7 ad 8 show he expemeal mole oo s s daw esuls of a ccula pah (adus 5 ) ad a squae pah (sde legh ), especvely. Fo oh cuves, he ajecoy followg eo s wh 3. whou al poso eo. I s show ha he pe p ajecoy has small ajecoy ackg eos shap u coes Fgue 8. 3 ccula ackg eo sa sa me (sec.) hea 4 3 degee (a) me (sec.) () Fgue 7. Expemeal daw esuls of he pe p ajecoy followg cool of a ccula pah wh a adus of 5. (a) desed ad daw ccula pahs; () ackg eo ad oeao agle 6 squae ackg eo me (sec.) hea 4 3 degee sa (a) sa me (sec.) () Fgue 8. Expemeal daw esuls of he pe p ajecoy followg cool of a squae cuve pah wh sde leghs of. (a) desed ad daw squae pahs; () ackg eo ad oeao agle Fgue 9 shows he expemeal daw esuls of awa maps. he og daa has 5 dscee daa pos, ad hee ae 4 cool pos s le smplfcao cuve, ad 44 cool pos he cuc B-sple smoohg cuve. Fgue shows ackg eos of daw awa maps Fgue 9. he dawg sze s 6 8, ackg eos ae wh., ad dawg me s s. Sce he sep sze s small, hee ae few dffeeces Fgue.

13 Roocs 7, 6, 7 3 of 5 6 ogal daa 6 le smplfcao 6 le smoohg (a) () (c) le smplfcao cuc B-sple smoohg (d) (e) Fgue 9. Expemeal daw esuls of awa maps: (a) ogal map; () desed le smplfcao cuve; (c) desed cuc B-sple cuve; (d) daw awa map (fom le smplfcao) ad (e) daw awa map (fom le smoohg)..5 ackg eo : le smplfcao.5 ackg eo : le smoohg hea hea 3 3 degees degees me (secods) (a) ackg eo Fgue 9d me (secods) () ackg eo Fgue 9e Fgue. ackg eos of daw awa maps Fgue 9d ad 9e. Fgue shows he daw esuls of a uldg mage Fgue 3, whch hee ae 36 coeced cuves wh 7 cool pos oal afe pocedues of edge deeco ad le smplfcao. he dawg sze s 5 ad dawg me s aou 9 s.

14 Roocs 7, 6, 7 4 of 5 (a) ogal mage () seached pcue cuves (c) daw pcue (a) () (c) Fgue. Daw esul of a uldg mage compaed o (a) he ogal mage; () seached pcue cuves; ad (c) daw pcue. Fgue shows he mage daw y he expemeal mole oo of a huma poa. he ogal mage s 8 pxels ad has 395 pxels afe edge deeco, ad leaves coeced cuves wh 67 cool pos afe le smplfcao. he daw pcue sze s cm ad s doe aou 6 s. (a) ogal mage () seached pcue cuves (c) daw pcue (a) () (c) Fgue. Image daw y he mole oo s compaed o (a) he ogal mage; () seached pcue cuves; ad (c) daw pcue. 7. Coclusos Wha s ew hs pese eseach s ha y emovg he cool degee yaw agle o a lea laeal moo of a dffeeal-dve mole oo, a omdecoal plafom ca e ul. hus, we ca desg a auoomous a dawg plafom a closed-loop fasho hough a vese kemacs plus popooal cool appoach. Boh smulao ad expemeal esuls show ha he expemeal sysem woks pacce as well as heoy. he lmaos of he cue sysem ae a lack of headg cool ajecoy ackg cool ad slowe moo of he mole sysem. Fuhe woks ca clude egag he vso sysem he FPGA, efg he mole oo odomey fo loge avelg dsace, ad developg fas speed moo coolle.

15 Roocs 7, 6, 7 5 of 5 Ackowledgmes: hs wok s suppoed y gas fom awa s Msy of Scece ad echology, MOS 5--E--47 ad 6--E--5. Auho Couos: C. Shh ad L. L coceved ad desged he expemes; L. L pefomed he expemes; C. Shh. ad L. L aalyzed he daa; C. Shh woe he pape. Coflcs of Iees: he auhos declae o coflc of ees. Refeeces. Koa, S.; Yasuom, S.; K, X.; Mo, H.; Shghaa, S.; Masumuo, Y. Image pocessg ad moo cool of a lae mak dawg oo. I Poceedgs of he IEEE/RSJ Ieaoal Cofeece o Iellge Roos ad Sysems, Yokohama, Japa, 6 3 July 993, pp Skaew, A.; Camo, M.; ohup, S.; Pees II, R.A.; Wlkes, M.; Kawamua, K. Humaod dawg oo. I Poceedgs of he IASED Ieaoal Cofeece o Roocs ad Maufacug, Baff, AB, Caada, 6 9 July Lau, M.C.; Bales, J.; Adeso, J.; Duoche, S. A poa dawg oo usg a geomec gaph appoach: Fuhes eghou hea-gaphs. I Poceedgs of he IEEE/ASME Ieaoal Cofeece o Advaced Iellge Mechaocs (AIM), Kachsug, awa, 4 July, pp esse, P.; Leymae, F.F. Poa dawg y Paul he oo. Compu. G. 3, 37, Ja, S.; Gupa, P.; Kuma, V.; Shama, K. A foce-coolled poa dawg oo. I Poceedgs of he IEEE Ieaoal Cofeece o Idusal echology (ICI), Sevlle, Spa, 7 9 Mach 5, pp Kaayama, Y.; Kmua, Y.; Myazak, F.; oguch,. A sale ackg cool mehod fo a auoomous mole oo. I Poceedgs of he IEEE Ieaoal Cofeece o Roocs ad Auomao, Cca, OH, USA, 3 8 May 99, pp Samso, C. Cool of chaed sysems applcao o pah followg ad me-vayg po-salzao of mole oos. IEEE as. Auom. Cool 995, 4, Egesed, M.; Hu, X.; Sosky, A. Cool of mole plafoms usg a vual vehcle appoach. IEEE as. Auom. Cool, 46, Saha, S.K.; Ageles, J.; Dacovch, J. he kemac desg of a 3-DOF soopc mole oo. I Poceedgs of he IEEE Ieaoal Cofeece o Roocs ad Auomao, Alaa, GA, USA, 6 May 993, pp oga, M. A applcao of sgula value decomposo o mapulaly ad sesvy of dusal oos. SIAM J. Algeac Dscee Mehods 986, 7, Mele, J.-P. Jacoa, mapulaly, codo ume ad accuacy of paallel oos. ASME J. Mech. Des. 6, 8, Dua, D.; Peovc, P.; Balogh, R. Rooacka he dawg oo. Aca Mech. Slov.6, , Balogh, R. Paccal kemacs of he dffeeal dve mole oo. Aca Mech. Slov. 7,, Khall, H.K. olea Sysems, 3d ed.; Pece-Hall: Uppe Saddle Rve, J, USA,. 5. Douglas, D.H.; homas, K.; Peucke,.K. Algohms fo he educo of he ume of pos equed o epese a dgzed le o s cacaue. Ca. Caog. 973,,. 6. De Boo, C. A Paccal Gude o Sples, evsed veso; Spge: ew Yok, Y, USA,. 7. Cay, J. A Compuaoal Appoach o Edge Deeco. IEEE as. Pae Aal. Mach. Iell. 986, 8, y he auhos. Lcesee MDPI, Basel, Swzelad. hs acle s a ope access acle dsued ude he ems ad codos of he Ceave Coos Auo (CC BY) lcese (hp://ceavecoos.og/lceses/y/4./).