Design of Omnidirectional Mobile Robots with ACROBAT Wheel Mechanisms

Transcription

1 0 IEEE/RSJ Interntionl Conference on Intelligent Robot nd Sytem (IROS) Noember -7, 0. Tokyo, Jpn Deign of Omnidirectionl Mobile Robot with ACROBAT Wheel Mechnim Yuuke Inoue *, Tkhiro Hirm ** nd Myohi Wd **, Member, IEEE * Plnt Engineering Dept., IHI Co. Ltd., Jpn ** Dept. of Mechnicl Sytem Engineering, Tokyo Uni. of Agriculture nd Technology, Jpn Abtrct In thi pper, we tudy the deign of omnidirectionl mobile robot with Actie-Cter RObotic drie with BAll Trnmiion (ACROBAT). ACROBAT ytem h been deeloped by the uthor group which relize mechnicl coordintion of wheel nd teering motion for creting cter behior without computer clcultion. A motion in the pecific direction reltie to robot body i fully depend on the motion of pecific motor. Thi feture gie robot deigner to build n omnidirectionl mobile robot propelled by ctie-cter with no redundnt ctution with imple control. A controller of the robot become imple tht for omni-wheeled robotic be. Nmely DOF of the omnidirectionl robot i controlled by three motor uing imple nd contnt kinemtic. ACROBAT include unique dul-bll trnmiion to trnmit trction power to rotte nd orient drie wheel with ditributing elocity component to wheel nd teering xe in n pproprite rtio. Therefore enor for meuring wheel orienttion nd clcultion for elocity ditribution re totlly remoed from conentionl control ytem. To build n omnidirectionl ehicle by ACROBAT, the ignificnt feture i ome multiple drie hft cn be drien by common motor which relize non-redundnt ctution of the robotic pltform. A kinemtic model of the propoed robot with ACROBAT i nlyzed nd mechnicl condition for relizing non-redundnt ctution i deried. Bed on the kinemtic model nd the mechnicl condition, computer imultion of the mechnim re performed. A prototype two-wheeled robot with two ACROBAT i deigned nd built to erify the ilbility of the propoed ytem. In the experiment, the prototype robot how ucceful omnidirectionl motion with imple nd contnt kinemtic bed control. I. INTRODUCTION The holonomic nd omnidirectionl mobile cpbility gie mny dntge on the wheeled mobile pltform. Flexible nd high mneuerble motion plnning cn be relized by motion plnner of mobile robot ince it i not needed to tke into ccount non-holonomic contrint. Additionlly, the omnidirectionl mobility i lo ery friendly for humn opertor ince they do not he to undertnd the principle of drie mechnim nd it configurtion t ll. A humn drier only commnd the direction nd mgnitude of the deired motion ince holonomic nd omnidirectionl mechnim cn trt to moe in rbitrry direction with n rbitrry mechnicl configurtion uch n orienttion of wheel. In the pt, lot of omnidirectionl drie mechnim he been deeloped, uch Unierl-wheel[](Fig.), Mechnum-wheel[], Orthogonl bll wheel unit[], Vuton crwler[4], Bll-wheel[5], etc. Biclly thi cl of wheel mechnim proide n ctie trction force in pecific direction while it cn be piely moing in the direction perpendiculr to the ctie direction becue of free rolling mechnim. Thee omnidirectionl ehicle re controlled by imple nd contnt robot kinemtic whoe exmple i hown in eq(). By uing thi contnt kinemtic, robot cn be drien by imple control rchitecture hown in Fig.. Thu tep motor with no feedbck or chp DC motor with locl peed feedbck cn be ued to crete DOF motion of the conentionl omnidirectionl mechnim. Thi imple control tructure i cceptble for mny robot reercher nd tudent therefore thi configurtion i widely ued on mobile be uch thoe for occer robot competition, erice robot, wheelchir robot, etc. = 0 d x& d d & φ () Oeriew (b) DOF of the robot Figure :Omnidirectionl robot with three omni-wheel () Yuuke Inoue i with the Plnt Engineering Dept., IHI Co. Ltd., Jpn. Tkhiro Hirm nd Myohi Wd re with the Deprtment of Mechnicl Sytem Engineering, Tokyo Uni. of Agriculture nd Technology, -4-6 Nk-cho Kognei-hi, Tokyo JAPAN (phone: ; fx: ; e-mil: mwd@ cc.tut.c.jp). Figure :Control ytem of three-wheeled omnidirectionl robot //$.00 0 IEEE 485

2 All of the omnidirectionl ytem mentioned boe re good for lbortory ue. Howeer, thee require pecil kind of wheel, uch lrge wheel with mny free brrel hped roller, phericl wheel, etc. Thee my include difficultie in prcticl ppliction in which rubber or pneumtic tire re required for reducing ibrtion or for enhncing ground contct between the wheel nd the ground. Uully thee mechnim do not preent enough tep climbing cpbilitie becue of the mll rdiu of the free roller or mll clernce between the ground nd the bottom of robotic pltform. To oercome thee difficultie on the conentionl omni-wheel, n ctie-cter ytem [7]-[], which we cll ACRO in thi pper, w propoed. The ACRO i different cl of omnidirectionl mechnim which proide ctie trction force in n rbitrry direction, nmely it h the ctie DOF mobile cpbility on the ground with no free rolling mechnim nor phericl wheel. The ACRO[7] h two ctutor to control wheel rottion nd teering rottion independently to crete DOF plnr motion. To chiee the omnidirectionl motion of ACRO, precie coordintion between the two ctutor re required to oid confliction of motion, becue t let four ctutor re needed to deign robotic pltform moing the plnr urfce with DOF, nmely it h redundncy in the ctution. In thi pper, n omnidirectionl robot with ACROBAT i propoed which include noel dul-bll trnmiion for oiding the problem of the redundnt ctution nd the complicted coordintion control. In the following ection, kinemtic of ACROBAT ytem nd deign condition of omnidirectionl robot with ACROBAT re nlyzed, followed by imultion, the prototype robot deign. Some fundmentl experiment uing the prototype robotic be re performed to erify the propoed omnidirectionl ytem. II. ORIGINAL ACTIVE-CASTER MECHANISM(ACRO) A. Kinemtic Figure how top iew of n originl ctie-cter[8], ACRO. Thi mechnim equip drie wheel which i off-centered from center of the teering xi. ACRO equip with two motor for ctuting the wheel hft for x& w control nd the teering hft for w control (thee elocity ector re hown in Fig.). Thee component ector he to be preciely controlled for correct coordintion not to conflict to other motor moement. To derie the required hft rottion, kinemtic of the wheel mechnim, eq.() i ued. coφ inφ ω 0 w = r x& w = r r Vx () ω y & w inφ coφ V y 0 Note tht V x nd V y re the component of the commnded elocity V long x- nd y-xi of the robot body coordinte ytem. Thi eqution repreent the ACRO kinemtic ued for the wheel nd teering motor coordinted control bed on the orienttion of the wheelφ. Figure. Velocity control of n ctie-cter [7] B. Two-wheeled Robotic Be Figure 4 how chemtic oeriew of n omnidirectionl mobile robot with two ACRO. The robot with pir of ACRO i controlled by four motor which inole one redundnt DOF in ctution. To coordinte the multiple drie wheel, motor on ACRO re controlled bed on the elocity bed robot inere kinemtic which i repreented eq.(). The coordintion control of ctutor uing () nd () enble ech ctie-cter to emulte cter motion which cn be een on the bottom of the hopping crt, conference tble nd chir. The control ytem of robot with ACRO i hown in Fig.5. Thu ACRO ytem relize the omnidirectionl motion with no free rolling mechnicl prt howeer it include ome problem ) the redundnt ctution: robot be need t let four motor to control DOF of the pltform, ) the precie motion control: computer clcultion nd ccurte ero for elocity ditribution. x& 0 W / x& 0 0 = () x& 0 W / & φ 0 0 Figure 4. Oeriew of n omnidirectionl robot with ACRO Figure 5. Control rchitecture of omnidirectionl robot with ACRO 485

3 III. DUAL-BALL TRANSMISSION ON ACROBAT A. Configurtion of ACROBAT To oercome the problem on the ACRO ytem, we he propoed new ctie-cter mechnim which include dul-bll trnmiion, we cll thi mechnim ACROBAT(Actie-Cter RObotic drie with BAll Trnmiion)[]. A dul-bll trnmiion i introduced for relizing elocity ditribution which repreented in eq.() by mechnicl moement not by coordinted motor control. For the purpoe, we deign mechnim to decompoe elocity ector into two component for wheel nd teering drie. Figure 6 how chemtic oeriew of ACROBAT. Two bll re locted in the mid prt of drie trin between ctutor nd the wheel. The propoed trnmiion deign include two bll which i imilr to robotic pltform with bll wheel. In contrt to the conentionl bll wheel robot, bll in ACROBAT do not touch to the ground directly nd contct preure between two bll cn be controlled to mintin n pproprite lue. Therefore, we cn pecify the trnmittble trction power in the deign proce. Actutor A Bll B Smll roller c Drie Belt Smll roller X X Y V wx Y Bll A Figure 6 The configurtion of ACROBAT ACROBAT i compoed of two prt, A nd B. The prt A include lrge bll A nd two ctutor for drie the bll A i mll roller contcting to the bll A. A the mll roller rotte bout the horizontl xe, the bll A rotte bout horizontl xi while it rottion bout the erticl xi i retricted. The prt B include nother lrge bll B whoe trction force i ditributed to nother pir of mll roller. One of the roller i connected to wheel xi the other i connected to teering xi for driing thee xe. The bll A nd B mke point contct to trnmit trction force from prt A to prt B, hown in Fig.7. In norml deign, prt A might be fixed to robot body. The prt B cn be rotted bout the erticl xi ince prt A nd prt B i connected by bll bering. r V wy Prt A Actutor B Smll roller b Prt B Beel ger Steering ger Smll roller d Wheel ω c Bll A ω c Figure 7 A dul-bll trnmiion B. Kinemtic of bll-roller drie ytem Now, we conider the kinemtic of fundmentl bll-roller drie ytem. Figure 8 how the top nd ide iew of the bll-roller ytem in which the coordinte frme i ttched to locte it origin t the center of the bll nd the XY plne lie horizontlly. The roller nd b contct with the bll urfce t ngle α nd β from X xi repectiely. Since the xe of the roller re long the horizontl direction, the bll rottion bout the erticl xi i retricted by the roller. A the roller rotte in ω nd ω b imultneouly, the bll rotte in ngler elocity Ω bout horizontl xi which direct θ from the X xi. Then following eqution cn be deried. R = R in( θ α) (4) R = R in( θ β ) b where R i rdiu of the bll while R nd R b re the rdiu of the contct circle, thoe re contct point trjectorie of the roller nd b on the bll urfce. We define circumferentil elocity V i t the bottom point of the bll which i repreented, V = R Ω i = R Ω = R Ω b b where nd b re the repectie contct point elocitie between the bll nd the roller. From eq.(4) nd (5), we get = V coα + V inα x y (6) = V co β + V in β b x V x nd V y re the elocity component of the circumferentil elocity V i long the X-xi nd Y-xi repectiely. y V Bll B Figure 8 A bll contcting with two roller b ω b ω d d (5) 4854

4 Now we get bll-roller kinemtic which repreent the reltionhip between ω, ω b nd V x, V y, coα inα ω r r V x = (7) ωb co β in β V y r r b b By inerting eq.(7), we derie V x r in β r inα ω b = (8) V y in( α β ) r co β r coα b ω b Additionlly following prmeter cn be clculted, r ω in β r ω inα θ = tn b b (9) r ω co β r ω coα b b Ω = r ω + r ω r ω rω co b b b b R in ( α β ) ( α β ) (0) From eq.(8), we derie the circumferentil elocity V i t the bottom of the bll. Note tht thi V i ector doe not conform the ordinl grphicl lw, nmely the prllelogrm lw. Fig. 9() nd (b) how grphicl reltionhip of V i nd, b. Figure 9() how tht the two roller contcting the bll with reltie ngle greter thn 90deg nd (b) how the other ce in which the ngle i mller thn 90deg. () Ce (β α) > 90deg (b) Ce (β α) < 90deg Figure 9 Vector um on phericl urfce In Fig.9, the roller nd b rotte to proide contct elocitie nd b on the bll urfce. Let u define the X-xi to interect with the contct point of roller. Conidering tht the ech contct elocity ector i trnlted to the bottom of the bll long the phericl urfce, thee ector cn be een rrow hown in Fig.9. Uully, reultnt elocity ector cn be deried from the prllelogrm lw in the norml ector um method. Howeer in thi ce, the reultnt circumferentil elocity V i i grphiclly repreented Fig.9, nmely the end point of the V i i defined n interection of two perpendiculr t the endpoint of the component ector, nd b. Only if thee roller contct with the bll to be right ngle to ech other, the reultnt ector would be identicl to the reult of the prllelogrm lw. When β-α=π/, eq.(8) cn be implified, V x r 0 ω = () V y 0 rb ωb In ACROBAT ytem, roller in prt B he to contct with the bll B to be right ngle. The right ngle configurtion in prt B relize the pproprite elocity ditribution which i repreented by the ACRO kinemtic, eq.(). When the roller in prt A contct with the bll A to be right ngle well, the oerll kinemtic of ACROBAT i repreented, x& ω x = R () ω y where pco θ + qin θ ( p q) coθ inθ R = ( p q) coθ inθ pin θ qco θ p nd q: contnt determined by the ger rtio in the drie trin nd ome mechnicl prmeter. By chooing mechnicl condition of deign prmeter, p=q cn be tified. Then eq.() i gretly implified, x& K 0 ω x = () 0 K ω y where K nd K re contnt. Detil for deriing the eq() nd () re preented in the reference []. Thu ACROBAT kinemtic i not function of the wheel orienttion θ, therefore the motion of ACROBAT cn be controlled by clculting the contnt kinemtic, eq.(). Thi feture implifie control ytem nd robot hrdwre, mentioned in the introduction ection. C. Omnidirectionl robot with ACROBAT In the preiou ection, we deried kinemtic model of the bll-roller ytem. In generl, roller do not he to tke right ngle configurtion in the prt A. Depending on the number of motor nd the lyout of wheel on the robotic frme, the ngle of the roller cn be ried from the tndrd right ngle configurtion. By the tudy in the preiou ection, it i clrified tht elocity component long line, which connect the center of the bll nd the contct point of the roller, would completely depend on the pecified roller rottion but doe not get ny effect from the other roller loction or rottion peed t ll. In Fig.9, the orienttion nd the mgnitude of the reultnt ector V i re ried by the loction of roller b(the ngle β α), the elocity component long the x-xi i mintined to be t ll time. Therefore ome roller in plurlity of ACROBAT, tht proide elocitie long n identicl direction to robot body, cn be drien by common ctutor. For intnce, roller in Fig.9() nd (b) gie identicl rottion, nmely long x-xi, thee roller cn be drien by common motor, lthough roller b mke contct to the bll in different ngle. The fundmentl olution to tify the condition i two-wheeled robot in which pir of roller re drien by common motor nd indiidul two motor drie the bll from different direction hown in Fig.0(). By extend thi ide, n omnidirectionl robot with three-acrobat in which three pir of roller re drien by three common motor could be one of the poible configurtion, whoe chemtic i hown in Fig.0(b). Thi tringle configurtion cn be conidered combintion of three pir of common drie hown in Fig.. Note here tht tringle i not necery to be n equilterl tringle. 4855

5 () -wheel configurtion (b) -wheel configurtion Figure 0 Poible omnidirectionl robotic be uing ACROBAT Figure Concept of -wheel robot (three pir of common drie unit) The robot kinemtic for the robot in Fig.0() i deried, 0 0 x& = 0 (4) & φ 0 W W And tht for the robot in Fig.0(b) i lo deried, x& = 0 & φ d d d IV. ANALYSIS OF ACTUATION INDEX (5) One of the criteri of utomted mchine i Actutor Index which repreent n ctutor uge efficiency. The bic concept of the efficiency w propoed in [] in which Actution Index η p i defined, η Poible Output Power p Sum of Intlled Actutor Power (6) To mximize thi Actution Index i the one of the direction of robot deign to minimize the um of the ctutor power on robot, which directly ffect on the weight nd the ize of ctutor. In[], the deign concept of coupled ctution or coupled drie w introduced which relize pecific robot motion by ctuting multiple ctutor imultneouly. Thi i type of prllel coupled drie to mximize the Actution Index. In thi ection, we inetigte Actution Index on the propoed omnidirectionl robot with ACROBAT. Since thi mechnim relize not only non-redundnt drie but n efficient drie from the iew point of Actution Index. Let u conider the two-wheeled omnidirectionl robot hown in Fig.0(). Conidering the robot motion long the x-xi, only motor h to be ctuted while motor, nd mut top during the pecific motion. Therefore, power of motor cn contribute to the robot motion in X-direction. The mximum Actution Index in the direction would be deried from, Rted Power of Motor η p ( x direction) (7) ( Rted Motor Power) = n When the robot moe in the direction 45deg from the X-xi, the three motor he to drie the bll urfce t the me peed tht reult in proiding the trnltionl elocity nd trction force both of tht re time thn the motion long X-xi. Therefore proided power become twice of tht for the motion in X-direction which reche 00% of the um of equipped motor power. Thu Actution Index of the trnltion motion of the -wheeled robot cn be deried. Fig. how Actution Index in ll direction. Here we uppoe tht the motor h doubled cpcity thn the motor or ince motor drie two bll imultneouly. Figure Actution Index for contct ngle π/ Thi Actution Index profile cn be ried by the contct ngle of the independent roller drien by the motor nd. If contct ngle re et to /π rd from x-xi hown in the mid of Fig., profile of Actution Index become irregulr nd line of ymmetry pper in /π rd. Figure Actution Index for contct ngle /π 00% Line Actution Index 00% Line Actution Index From the iewpoint of omnidirectionl robot ppliction, ymmetricity of the mobile cpbility i not pproprite. Therefore we chooe the -wheel configurtion hown in Fig. for the prototype deign where the front of the robot to be et t 45deg from the X-xi, nmely two drie wheel re locted t digonl poition on robot frme. 4856

6 V. ROBOT SIMULATIONS To erify the mobile cpbility of the propoed omnidirectionl robot with ACROBAT, computer imultion re performed. Uing robot kinemtic deried in the preiou ection nd wheel kinemtic which detil dicued in [], typicl motion i nlyzed. The robot i expected to how omnidirectionl motion with cter motion in ACROBAT mechnim with no enor nor coordinted motor control. To erify thi performnce, we tet behior of the robot in which DOF re imultneouly generted, nmely trnltion motion in x nd y direction nd rottion of the robot body. Figure 4 how one of the imultion reult. The ngle of drie wheel on ACROBAT re et 0deg t initil condition. The robot i commnded to moe long line with contnt rottion. The elocity reference in ech DOF i x& = 0.m /, = 0.9m / nd & φ = 0.5rd, repectiely. / Motor A Beel ger Roller Steering ger Roller d Beel ger Roller b Figure 5 Prototype deign of the ctie-cter Roller c Drie wheel Motor B Steerin g Spring (Horizontl) Bll B Figure 4 Simultion of n omnidirectionl robot with two ACROBAT A. Prototype mechnim VI. PROTOTYPING To confirm the propoed mechnim working in the rel world, we deigned prototype omnidirectionl robot with two ACROBAT. Specifiction of ACROBAT for the prototype deign re hown in Tble. Figure 5 nd 6 how D deign nd n oeriew of the ACROBAT prototype. Two tinle teel bll for bll bering ue re ued for the lrge bll in prt A nd B. In prt A, mll roller re contct with the lrge bll t the right ngle ech of tht i drien by n independent motor. The lrge bll i pring loded horizontlly to contct with both roller firmly. Two phericl bering re intlled t the top of the upper bll nd the bottom of the lower bll to upport the dul-bll trnmiion. Another et of pring proide pproprite lod between the bll long the erticl direction i the phericl bering t the top. Two ACROBAT re mounted on n Aluminum plte which i 0.6x0.6 qure with 0mm thickne. The power of motor(x-motor) i trnmitted to two ACROBAT i beel ger nd drie belt hown in Fig.7. ACROBAT re eprted with ditnce of 0.5m, ech of the mechnim i locted t the corner of the robot frme therefore the front ide of the robot i 45deg from the x-xi of the ACROBAT coordinte. The oeriew of the prototype robot i hown in Fig.8. Sphericl bering Wheel Drie belt Figure 6. Oeriew of ACROBAT prototype Tble. Specifiction of prototype robot with ACROBAT Rdiu of mll roller r.5 mm Ger rtio G t, 4 (roller to wheel) G p 4 (roller to teering) Wheel rdiu R 50 mm Cter offet 50 mm Lrge bll dimeter 50.8mm ( ) Wheel ditnce W 0.5 m Robot frme dimenion 0.6 x 0.6 m Motor cpcity 00W(motor), 50W(motor,) Figure 7 A Three-motor rrngement on the prototype robot 4857

7 () Top iew (b) Side iew Figure 8 Holonomic omnidirectionl mobile robot with two ACROBAT B. A Control ytem for prototype robot Since ACROBAT i ble to coordinte wheel nd teering motion by the bll trnmiion mechnim, the robot controller my jut end elocity reference to motor with uing imple robot kinemtic, which tructure i hown in Fig.9. Thi controller rchitecture i quite imple compred with controller deign for conentionl ACRO robot which exmple i hown in Fig.5. Ech motor i controlled by imple elocity controller, which i often clled motor drier or motor mp by pplying pproprite oltge to motor by power circuit. ending elocity commnd to three motor with imple elocity control, the reultnt robot motion re detected nd recorded by the cmer ytem. Figure0()-(c) how one of the implet experimentl reult. Figure0() how trnltion motion of the robot long X-direction in which only motor w commnded to rotte while the motor nd were commnded to top. In the figure, line on the left ide repreent pth of ACROBAT nd the one on the right repreent tht of ACROBAT, while the center one how the midpoint of the two wheel. It i found tht pprox. 0mm error occurred in Y-direction during the 50mm treling long the X-direction. The robot motion long the Y-direction i hown in Figure0(b). For relizing thi motion, the motor nd re commnded to rotte t n identicl peed in the me direction. Error in X-direction re found well, which i pprox. 0mm during 700mm treling. Next, pure rottion motion (piot turn) w performed by the prototype. Figure0(c) how the pth of the robot in rottion. An oer 60deg rottion were teted in which ech ACROBAT could not be bck to the initil poition. Approx.50mm error re found on both ACROBAT between the initil poition nd tht fter 60deg rottion. It i etimted tht the error re cued by difference in the elocity control of motor drier. Dynmic lod chnge reult in the moement of the center of the robot body becue the elocitie of the drie wheel cn not be mintined to be identicl t ll time. Figure0(d) how the mximum elocity of the robot in 8 direction. By rotting pecific motor() in the rted peed, reultnt robot elocitie in the direction re meured from 0deg to 60deg with 45deg increment. It i found tht mximum elocitie in 45, 5, 5, 5 direction re.4 ( ) time of the elocitie in 0, 90, 80 direction. Thi reult gree with the nlyi of the Actution Index in chpter IV. Though ome motion error re found on ACROBAT, the fundmentl omnidirectionl mobility h been erified by the erie of the experiment. Figure 9 Control block digrm for the omnidirectionl robot prototype VII. EXPERIMENTS To tet the omnidirectionl mobility of the propoed ytem, fundmentl motion re performed. Since rottion nd orienttion of drie wheel on ACROBAT cn not be detected, we meure the robot motion by uing tereo cmer poitioning ytem. In Fig.8, it i een tht two mrker re mounted on the top of the robot frme, which i ued for the cmer ytem. The robot motion re creted by VIII. CONCLUSION A new omnidirectionl robot with ACROBAT nd it deign method were preented in thi pper. The ACROBAT mechnim include dul-bll trnmiion which trnmit trction force from motor to wheel nd teering xe i bll to bll contct. The bll rottion ditribute elocity component in pproprite rtio which relize the cter motion of the mechnim. Thi feture implifie robot control ytem ince the dnced ero control bed on the orienttion of the drie wheel cn be remoed from the control rchitecture. Firt, the kinemtic of the propoed ACROBAT mechnim nd robot with ACROBAT were deried. Next, bed on the kinemtic, we nlyzed the roller lyout condition for building the omnidirectionl robot with ctuted by three motor, nmely with no-redundncy. 4858

8 After Actution index nlyi, we determined the two-wheel robot configurtion nd the drie wheel lyout to be locted t digonl poition of the robot frme for mximizing the power production in front direction of the robot. The prototype of ACROBAT nd the robot with two ACROBAT re deigned nd built. Some fundmentl motion nd mobile cpbilitie were teted by the erie of experiment. Expected omnidirectionl motion were performed by the prototype with imple control ytem with imple robot kinemtic nd locl elocity controller. REFERENCES [] J.Grbowiecki, Vehicle-wheel, US Ptent No.,05,55. June 99. [] B.E.Ilon: Directionlly Stble Self Propelled Vehicle, US Ptent No.,746,. July 97. [] F.G.Pin nd S.M.Killough : A New Fmily of Omni-directionl nd Holonomic Wheeled Pltform for Mobile Robot, IEEE Trnction on Robotic nd Automtion, Vol.0, No4, pp , 994. [4] S.Hiroe nd S.Amno : The VUTON : High Pylod High Efficiency Holonomic Omni-Directionl Vehicle, 6th Int. Symp. on Robotic Reerch, October, 99. [5] M.Wd nd H. H. Ad,"Deign nd Control of Vrible Footprint Mechnim for Holonomic nd Omnidirectionl Vehicle nd it Appliction to Wheelchir," IEEE Trn on Robotic nd Automtion, Vol.5, No.6, pp , 999. [6] M.Wet nd H.Ad: Deign of Holonomic Omnidirectionl Vehicle, Proceeding of the 99 IEEE Interntionl Conference on Robotic nd Automtion, pp97-0, My.99. [7] M.Wd nd S.Mori," Holonomic nd Omnidirectionl Vehicle with Conentionl Tire," Proceeding of the 996 IEEE Interntionl Conference on Robotic nd Automtion, pp67-676, 996. [8] M.Wd, A.Tkgi nd S.Mori, "Cter Drie Mechnim for Holonomic nd Omnidirectionl Mobile Pltform with no Oer Contrint," Proceeding of the 000 IEEE Interntionl Conference on Robotic nd Automtion, pp5-58, 000. [9] R. Holmberg nd O. Khtib. Deelopment nd control of holonomic mobile robot for mobile mnipultion tk, Intl. J. Robotic Reerch, 9():pp , 000. [0] Y.Li, T.Zielinky, M.H. Ang Jr. nd Wei Lin : Vehicle Dynmic of Redundnt Mobile Robot with Powered Cter Wheel, Proceedimg of the 6th CISM_IFToMM Sympoium, pp-8, 006 [] Woojin Chung, Chng-be Moon, Chngbe Jung nd Jiyong Jin: Deign of the Dul Offet Actie Cter Wheel for Holonomic Omni-directionl Mobile Robot, INTECH Interntionl Journl of Adnced Robotic Sytem, Vol.7, 00. [] M.Wd, Y.Inoue nd T.Hirm, A New Actie-cter Drie Sytem with Dul-bll Trnmiion for Omnidirectionl Mobile Robot, Proceeding of the 0 IEEE Interntionl Conference on Intelligent Robot nd Sytem, pp.55-5, 0. [] S.Hiroe nd K.Arikw, "Coupled nd Decoupled Actution of Robotic Mechnim," Proceeding of the 000 IEEE Interntionl Conference on Robotic nd Automtion, pp.-9, 000. () Trnltion (X_xi) (b) Trnltion (Y_xi) Robot front Tril Tril 00% 4% (c) Piot turn (d) Mximum elocitie in 8-direction of the prototype robot Figure 0. Experimentl reult of the prototype omnidirectionl robot with ACROBAT 4859