31 1 Vol.31, Sup Systems Engineering Theory & Practice Oct., Research on omni directional control of Mecanum wheel mobile robot
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1 ö E à 3 Vol3, up 0 0 ystms Enginring Thory & Practic Oct, (0) TP46 A Mcanum!!"!#!$!%!&!'!(!")#!*)+),!- /, 043 (567897>, 56 Mcanum DMDDODPDQFIFTIUVXFY ZDXFY D IUDV OPQ\^, _Ẁa_bcd^gfhjikjlm (X n Y X^Tg\Mopqrsp ) rtuo PQv^gUVroklm, wxyopqz ~_ O^ƒg OPQ~^g, Ŵ OPQ^g`^Šg Œ ^ gmopq^g`^šgfhi, OPQ^gf Œ^ g UV Mcanum MOPQ š g UV Mcanum sarch on omni dirctional control of Mcanum whl mobil robot Abstract IU i, XU Xiao-ming (usinss chool, Univrsity of hanghai for cinc and Tchnology, hanghai 00093, China) This papr dsigns an mthod to implmnt th control of Mcanum whl mobil robot This mthod can transfr th navigation paramtr stting valu (vlocity in X and Y axis dirction and rvolution angl) to controlling spd stting valu of all whls of robot, simulat th motor and robot modl with th robot simulation modul, and gt th actual position and orintation status of robot Th actual navigation paramtrs can also b analyzd and usd for navigation position and orintation clos-loop control of robot ywords Mcanums whl mobil robot softwar simulation clos loop control Mcanum žÿ ^ ngtilon 973 Ẅ ª «±²³nµẂ ¹ 3 ģ g» ¼½ ¾ À Á½ÃÄ Å ÇÈ ÇÉ Mcanum žžê ^ËgÌÍÎÏÐÒÓÔÕ ŸÕ ØÙÚž ^ËgÌÛÜÝ, ÞßÕ à ģ gá¹, Õ âúž âúãäå 45» 5 ç Mcanum èéê ç ç ëìíîïðòóôõ øïùâ½ãúû, ½ üýþ ÿ, Å ÇÈ ùãúû ã à Øj jãjújû, jå j jãjújû j j, ýjþjÿ jãjä j jãjújû à $ À Á½, Ãúû ¹!Á, "² # Ú± Ø Ãúû à %, "²Å & ' ( )à *j½ + jãújû,, - /Ãúû¹ 0 Ãúûà j ( >73@3A33C (90406) D3E3F3@3G3H3I3J333M33O3P3Q5 ( ) 3T3U3V 3X (98 ), Y, Z33\33^, som liu@hotmailcom
2 $ à $ ž ã 3X, _ ` Mcanum a3b3c3d33f3g3h5i7c3d3j3k3\3 67 j!l m # j jÿ j!- n ö p q r, Å &jãjújûjýjþj jjàj jájâj½jãjä,,j j Ãúû, ² s t u *½, v wùê x y z 6» % Mcanum žãä ~, ƒ, ùãúû Mcanum ž Àg½ÃÄ ø v ˆ Š Œ Ãúû Í ³n7šÀ, þ Ý ž ùãúû Ÿ Mcanum žàgãúû Ãúû¼, Ãúû Í«ªµ¼ Í v ÏjÃúûj ¼ Ãúû ẄÍ ÏÃúû ±, Ÿ, Ãúû¼½ ~ ² ³ Ẃ², µ, ¹ÄÊ, Ãúû ± þ, ± Ãúû» %Á ¼ Ä Å, ½ ¹ Ẃ ¾Ãúûà À Á ±  à ± Óü Ãúû þ, Ãúû ½ ± ¹ Ç Ãúû È», ɲ ʽÃúû¼½ ~, Ë ÌÃúû» %Á ¼ Í, Î ÃúûÁ ¼ Ï Ð Ë Ì Î ± Ì ³, É Ò Ãúû Ó Ô Õ ç 3 3Ø3Ù3Ú3Û3Ü Ý Þ ¹ÄÅ 3 ÇÈ, Ç v ß Mcanum žâ½ãúû À~ 3 ÇÈ ¼½ ~, Ï ½ ƒ p à (Ãúû x g y g È» áãúû (» ) ã â Ÿ, ¹ Ẃ Ãúû 4 žãgã à, Þ ä ßÃúû Ê, åþ ½ ç èã úûá ¼ à, ɲ ¼½ é ~ Ÿ g ê ë èãúû Ê ì í ƒ j áj¼½ ~ ú ƒ 3 Mcanum î ï ð ò óõô g 4 ÇÈ Mcanum ž Àg½ÃÄ ö gâ½ ø, Õ Ẃ±žẂá, $ ±ž á, Ẃ²ž á, ²žẂá, žg Ô ûú üè ý Õ âú þ ž ÿ^ g à ½, ã ž ¹ È ž Ý, Ãúû «ģ»j Àj jáâj½ Mcanum ž å Ãúû Ê ¼½Í ÅgÇÈ, ª F a ž ½ q ý Õ Ç ß â F r Õ ½ ½ q ß ½ (Û F a Ô, ) ω öž¹½ È» p ʽ Ãúû½ ½ F a F a û, Ç þ Y â È», s q Ï X â g È», ŸÓåÀg¼½ ù ú ç 4 Mcanum èïòó3ú!"òï#$
3 š w Ë ` d Z c Å A A 68 %'&'(*)'+', H'-' / ò Mcanum Ä Z \ F H ` a, ^ _ b c d v w x y z X Y t l m ~, 4 ƒ CEDGF Ḧ Ï J F Ḧ M PQT Ü V Ẅ 9 Ẍ Ÿ f g ḧ i j k l m n o p q ` r s t Z Ä, x yv y cs, V ycs, s Z PID s us Z z x v v yv y 5 ˆ Š F H M Œ y 9 5, Z \ ID X š ID ` a ž V ycs, Ÿ z š θ( D F H Œ g ) D A z F H θ PID ª p «w, F H F H ± PID A D F H F H µ ^ _ ² ³ ( _ w ) ¹» Z ED ¼ ½ I Œ À V ycs cs, V ycs, ω s Mcanum ¾ À Á  Z ED ½ Å ED, d Ã Ä ω, ω, ω 3, ω 4 Ç ÈEÉG@ Ê w ` Á Ì Z \ 9 Î Ï Ð, à b c Í 7 Ò Ó n o Î «I Œ À, Ô d ^ _ ¾ Õ «b, ` a Z o «s ž D ^ Ä Ÿ «θ g «, D cv, V ycv Ø Ù «ž ID ID θ, Ÿ x š, y š «ž h ^ _ Ÿ > 7 4 Ú Û Ü Ý Þ ß à Z F H PID A á â ã ω us, T iθ é ¾ ID Y š I Œ ¾ ôõ Î F H Z, θ s å, T dθ å, ω ws, ω ws, ω w3s, ω w4s ö ω us k pθ (θ s θ v ) + θ s θ v Z g, θ v ω us ç è ² ³ ω s ω max, ω us, ω min, T iθ + T dθ ( θ v ) o «Z k Z pθ, ω us > ω max ω min ω us ω max ω us ω min, PID F H I Œ À î \ ID ` a (Ÿ ê ë ì í c ), dïð è X š V ycs, ïò ó F H Z PID A Í ω s Í cs V ycs ω s 4 Å Mcanum ω ws ω ws ω w3s ω ws ω ws ω w3s ω w4s ω ms ω ms ω m3s,, ï ω s ^ _ Ê cs, Y cs, Ëä cs, A d,, ω w4s ω m4s
4 ö Ê ± ò g À d A ' øù úû, ü ý Mcanum þÿ 69 Ê Ë, ω ms ω ms ω m3s Å 4 o «^ _ ω m4s 7 Ò Ó n o ω wv ω wv ω w3v o «ω mv ω mv ω m3v _ Ê, d Î ω w4v ω m4v I Œ À o «Z \ ï é ¾ b D «s x y θ v ž Ÿ v, V yv ^ _ Ù X Y g ž Ÿ v V A 43 Þ Mcanum " ½ D ò ½ Å v V yv cos(θ v ) sin(θ v ) sin(θ v ) cos(θ v ) ç è, A f g i F H M g M Ï Ð Z \ θ v ( X š s ž g cv V ycv ω v ω v θ v ωv, «Z, Ÿ Ÿ cv V ycv I Œ À ¾, Y A,, Z š f g h X, Y ` Z D! ), M Ï Í X cn O c X c Y c X O c X c Y c O ci i V g Y cn X c3 O c3 / Y c3 6 # $ % & y 9 Å 6, Mcanum, α ' ( Ù, ôõ*) Ù α 45, + Ù y α , ) /0 w x O ' Ù Mcanum, ω i, -, ï*3 4 s p X Y ID 9 ID, V g X cn š Y cn š 9 n V yn, ï* d O O c4 Y X c4 n V g cos α, V yn ω i V g sin α ω n n tan α + V yn, n ω Y ocn, V yn V y + ω X ocn ôõ,, V y ID ID X, Y Z Z, ω Ù ôõ X oci, Y oci ö ) i, ) Ù α 45, X oc /, Y oc /, + i, + Ù α 45, X oc /, Y oc /, ) i 3, + Ù α 45, X oc3 /, Y oc3 /, + i 4, ) Ù α 45, Y c4
5 q Í š 3 î g q Œ ƒ n 9 Ø Ã 70 >@@AC@D@E@F@G@H I 3 0 X oc4 /, Y oc4 / d, ¾ I Œ V y ω ω ω ω 3 ω 4 5 JMOPCQ y 9 7, X YV ³ _, Y Z\ ò Ó O P Î Mcanum > X q «h i c,, «Î PID ª z ÕT F H, «F H, É*U ^ _ ² ÕT k PID F H PID 7 ^ _ ` a b c d fš Mcanum 5 ghijkl F H A F H Im no PID 9 n oum p, T i, T d, poq F Hrs F H At y 8 F H V n É*U ôõ w F H U n PID Ay, ω mnv n Å O Ï «, k å T n V n kω mnv n 4 v F H ² ³ A U max, ð U un > U max U n U un, ð U min U un U max U min, ð U un U min xd ÕD É*U, U max, U min F H É*U F H É*U ôõ v, n 4 Ê É*U AY ò ê ó, U un w n Å ( x) + + p + T i T d PID 8 PID ˆ _ z 5 Mcanum ~kl n o Œ y Mcanum > X 9 y 9 9 0, ' 9 D* ƒ D X Y Ï ÐV ` F a X š, Y š F axn, F ayn 3 y 9 ID Î Å ẍ ID ω n ô X Y rs ~ 9 X Y, Ù ƒ s ID F a X š, Y š, ö > X ID ID X, Y > ` a ˆ, y dï 9 ÀŠ À Î ƒ ID ^ _ d Ä X š, Y š ƒ ` a õ* V w õ* Á ( XŒ X ôõ ID ƒ ` ), X š, Y š õ* V ` D X š, Y Ä D ω ^ _, ö w D ω θ v X š, Y š» ED ^ _ Ẍ Ÿ ž ž θ v, Ÿ a x, a y, ^ _ Ä Ä Ÿ
6 D ƒ Î ž Î g Ø s I D ƒ w I øù úû, ü ý Mcanum þÿ 7 x y - - X XY Mass Izz Mcanum z v v cv, V ycv, V y a x, a y x y 9 Mcanum f $ Š D, V y, Ù θ v, ID ID X, Y cv, V ycv A D ¹ ID ID ω š X š Y š ô Â ` 9, ž, I ID X n y, Y, ^ _ 9 À ` «Î 9 3 4,, 53 Mcanum ~kl Ý Þ ß à A X ôeõ Y š F axn F Î V v ax F F ay ayn T wn /, T wn, n 4, F 9 ax F ay X ID*nƒ w 9 F xc Y ID*n 9 ` F yc F xc F yc 9, T c θ v ωv g ž D X Y š ID ω T c /I zz, I zz «Ù V y θ v, T c a x a y c V yc V V V 3 V 4 F ax F ax F ax3 F ax4 F ay F ay F ay3 F ay4 ôõ F ax F ax F ax3 F ax4 a xc a yc F ay F ay F ay3 F ay4 z š ž Ÿ m F xc F yc F a F ax3 F ay3, m Z w «cos(θ v ) sin(θ v ) sin(θ v ) cos(θ v ) a x a y g ž «cos(θ v ) sin(θ v ) sin(θ v ) cos(θ v ) a xc a yc F a3 F ax4 F a4 F ay4 3 4, Ù V y ω ω c V yc, 0 Ÿ F a ω wnv Z š Z ö θ v, ω v ω,
7 ó 0 è o ë 7 >@@AC@D@E@F@G@H I 3 Å «ω wv ω wv ω w3v V V V 3 ω w4v V 4 6 n o Iª n o ïò ó, «q ½± I J A n ors y 7 s ¹ µ\*»¼ ò, ä î \ 768mm Ê ç è t c n o y, ²²³ 0 µ m 0½ v «¾rs Ë Z ± X/ Y/ f X # ÀÂÁ Y # ÀÂÁÄÃ Å Ç È É Ê Ë / Ì 7 8Í ` C I h Z ØÙÚ ÎoÏ F H ` ä n o 0½ v «¾rs Mcanum >, n o î Ð Ò CD*ÓÔ j0 ƒ oõ, _ d ú Û, Ü Ý Þ Mcanum ßþ à á â ã ä å F ç J è é ê ë ì í î, 0(5) Dorofti I, Grosu V, pinu V Dsign and control of an omni-dirctional mobil robotc// ovl Algorithms and Tchniqus in Tlcommunications, Automation and Industrial Elctronics, pringr cinc+usinss Mdia V, Efndi J, alih M, izon M, t al Dsigning omni-dirctional mobil robot with Mcanum whlj Amrican Journal of Applid cincs, 006, 3(5) Digl O, adv A, right G, t al Improvd Mcanum whl dsign for omni-dirctional robotsc// IEEE Intrnational Confrnc on obotics and Automation, Auckland, w Zaland, Gfrrrr A Gomtry and kinmatics of th Mcanum whlj Computr Aidd Gomtric Dsign, 008, 5(9) Hamnr, otrba, t al An autonomous mobil manipulator for assmbly tasksj Autonomous obots, 00, 8() Gurzoni Jr G A On th construction of a obocup small siz lagu tamj Journal of th razilian Computr ocity, 0, 7() 69 8
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