A Novel Multimode Mobile Robot with Adaptable Wheel Geometry for Maneuverability Improvement

Transcription

1 Internatonal Journal of Robotcs, Vol. 4, No. 4, (6) A. Maran, S. Ebrahm, -5 A Novel Multmoe Moble Robot wth Aaptable Wheel Geometry for Maneuverablty Improvement A. Maran a, S. Ebrahm b,* a PhD Stuent, Mechancal Engneerng Department, Yaz Unversty, Yaz, Iran. b Assocate Professor, Mechancal Engneerng Department, Yaz Unversty, Yaz, Iran. A R I C L E I N F O A B S R A C Artcle hstory: Receve: June 3, 6. Receve n revse form: November 7, 6. Accepte: November, 6. Keywors: Aaptable Wheel Geometry Multmoe Moble Robot Maneuverablty Knematc Analyss In ths paper, an nnovatve moble platform s presente whch s equppe by three new wheels. he core of the new ea s to establsh a new esgn of rg crcular structure whch can be mplemente as a wheel by varable raus. he structure of wheel nclues a crcular pattern of a smple two-lnk mechansm assemble to obtan a wheel shape. Each wheel has two egrees of freeom. he frst s to rotate wheel axs an the secon s to change the wheel raus. As the frst step, after efnton of the new moel, ts spatal knematcs an constrants wll be formulate. he well-known Newton-Raphson algorthm s mplemente to fn the current response of the knematc moel. A sem-ynamc formulaton s further utlze to fn the torque of motors for aaptng the requre wheel raus for maneuverablty mprovement on rough surfaces. he prncples of vrtual work wll be use to extract the torque values numercally. he ablty of the propose robot for performng the requre tasks wll fnally be checke by some smulatons.. Introucton In real applcatons of moble robots, mprovement of the maneuverablty on rough surfaces s a challengng task. A great eal of ffcultes arsng n ths topc can effectvely be solve by mplementaton of a proper an nnovatve mechancal esgn. Even a lttle nnovaton n ths regar may effectvely promote the navgaton capablty an mechancal response of moble robots. Substantal amount of esgn efforts have been conucte n ths topc to solve fferent ssues nclung surface sturbance elmnatons [], enhancement of ynamcal stablty [-4], reucng number of actuators, weght an the total cost [5-6], ncreasng the ablty of obstacle clmbng [7-9], promotng the way of connecton between manpulators an the man moble platform [], combnng the platform an manpulator [, ], specal esgn of a moble platform for certan msson [-4], generalzaton of a moble robot to overcome rough surfaces an trouble contons [5-6], an reucng or ncreasng flexblty of platform accorng to the objectve of mssons [7]. In the moble robotcs fel, a we range of such novel esgns can be classfe n the multmoe moble platforms. Wheele moble platforms, havng almost smple esgn, fal n a we range of msson contons. he prmary eas to promote the performance of moble manpulators are to ncrease the number of wheels [7-8] or promoton of the suspenson system. hese efforts lea to the enhancement of maneuverablty an ncrease of the margn of ynamc stablty. * Corresponng author aress: Yaz Unversty, Safayeh, Yaz, Iran. el.: ; fax: , E-mal aress: ebrahm@yaz.ac.r.

2 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 o promote the ablty of obstacle overcomng, a specal category of multmoe moble manpulators has been evelope by combnng the leg an wheel structures [9-]. Connectng a wheel to the en pont of the artfcal legs [-6] or mplementng a pattern of wheels [7] leas to the more capable moble platforms. hese efforts focus on the mprovement of locomoton ablty but the exact controllng of a pont of the robot boy has been almost msse. A new esgn satsfyng the locomoton objectves beses controllng a pont on the robot boy has been nvestgate n some researches combnng locomoton an manpulaton as a smplfe platform n D. However, 3D locomoton an manpulaton can be satsfe smultaneously by a novel ea. herefore, n ths paper, a novel ea s propose by focusng on wheels structure, rather than wheels pattern, to aapt the wheel geometry by changng raus. he new platform s a pattern of smple mechansm connecte by means of bene revolute jonts to approxmate wheel shape. hs mechansm s rven by means of a motor to shape the moble robot wheel. Inepenent changng of the wheel raus leas to some new avantages for a three-wheele platform, whch allows manpulatng a pont of the robot boy on a certan trajectory. It leas to have a combne platform whch can be a multmoe structure movng an manpulatng as a unque system on rough surfaces. By some atve nstruments lke accelerometers nstalle on each wheel axs, the conton of sturbance elmnaton wll be prove as t has alreay been one n [] for D. Another avantage wll emerge when the objectve of mechancal structure s whrlng. As the man fference between the newly evelope an ol structures, the whrlng moton can also be obtane by settng the angular velocty of the wheel axs on a constant value an ajustng the wheel raus. In the case of passng over an obstacle, the msson can smply be followe by ncreasng the heght of the robot boy as the result of wheel raus ajustment. As another nterestng case, the robot can move on a ramp, whle ts boy keeps a esre orentaton. As the frst part of the present research, the new system wll be recognze to be obvous as well as possble. Knematc parameters, 3D knematc equatons an mathematcal efnton of the esre path wll be presente, respectvely; hen, the knematc constrants wll be ntrouce. he Newton-Raphson algorthm s use to solve nonlnear system of knematc equatons. Dynamcs wll be further consere to obtan the torques of atve ajustment motors n each wheel n the presence of gravty forces. he smulatons an ervaton of equatons wll be one base on the assumptons such as stckng conton, lumpe mass n, gnorng centrfugal forces an movng on rough surface.. Concept Emboment he goal of ths secton s to efne the new platform whch nclues a moble robot wth three ajustable wheels. he man ea of the new platform s to obtan the ablty of ajustng raus of wheels. he key ea of the new platform esgn s to a a transformable seral pattern of cross mechansms to the axs of motor of the wheels nstea of common crcular wheels. Fgure ( a) shows a part whch connects the new wheel to the motors. As t can be llustrate, the connecton part s a rg boy connecte to motors from one se. Other se of the connecton part s equppe wth prsmatc jont. he prsmatc jont s a groove n Fg. -a. he cross n Fg. -b has two lnks. One of them s restrcte by means of a revolute jont, whle the other s restrcte by means of a prsmatc jont. he angle between two lnks s ajuste by means of the motor whch s locate n a poston shown n Fg. -b. a close-loop seral pattern of the crosses s llustrate n Fg. -. hs seral pattern s connecte to the cross mechansm mentone n Fg. -b. he close-loop mechansm s connecte to the wheel axs by small peces whch are shown on the rght se of the cross lnkage n Fg. -b. It can be seen n Fg. - that when the motor rotates, the close-loop mechansm rotates as a wheel. On the other han, when the restrcte cross n Fg. -b s rven by means of the ajustment motor, the close-loop mechansm raus s change. Because the shape of the close-loop mechansm s not a complete wheel, some atve rubbers have to be ae as Fg. -e llustrates. he effect of rubbers on wheel performance s to complete the crcular shape of the wheel an to soften the collson process wth the surface. Fnally, three complete assemble wheels wll be nstalle on a boy as a threewheele moble robot as llustrate n Fg. -f.

3 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 Fg.. Assemblng process of the new propose platform As t was expresse prevously, the man ea s to esgn a rg an transformable wheel n orer to mprove the maneuverablty on rough surfaces. Fgures. an 3 show the process of raus ajustment an the complete moble robot structure wth aaptable wheel geometry, respectvely. otal raus Fg.. he process of raus ajustment 3

4 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 Fg. 3. he complete moble robot structure wth aaptable wheel geometry 3. Prncple Propertes he man boy of the new platform has sx egrees of freeom, the same as other moble robots. hree egrees of freeom nclung heght of wth respect to the surface, ptch angle an roll angle of the robot boy are restrcte by wheel raus ajustment. It means that the ajustment motors affect these DOFs. he constrants whch control these DOFs as well as the yaw angle of the robot boy are holonomc constrants. wo other constrants for controllng x an y postons are nonholonomc. Smple moble robots only have two nonholonomc constrants (poston x an y on the flat surface) an one holonomc constrant (the yaw angle). he majorty of these moble robots cannot control the heght, roll angle an ptch angle. Inee, the ajustable raus of each wheel as an atve DOF to moble platform. So, new moble platform s equppe by three atve DOFs. he fnal objectve s to control roll, ptch an heght of the boy beses other surface navgaton DOFs (yaw angle, x an y postons) smultaneously, by means of sx control commans. A crucal conceptual queston whch may arse n evelopng the new platform s that how the sgnals of the ajustment motors can be conveye from the robot boy to the rotatng wheel. hs pont shoul be explane to avo any wre cut-off n one complete rotaton of the wheel. he wre cut-off s probable f a se of the wre s fxe n the control an power box an the other se of the wre s connecte to the ajustment motor locate on a rotatng wheel. o solve ths ssue, an atonal part s propose n appenx A. knematc parameters. Parameterw s the length of leg of each cross lnkage etermne n Fg. 4. Parameters x an L y are the length an wth of the robot boy, respectvely. Fg. 4. Geometrc an knematc parameters of boy Other mportant knematc parameters are efne n Fg. 5. Parameter β s the angle between the axs Y of the wheel coornate system an the lne connectng the wheel center an the contact pont of the wheel wth the surface. Parameters R ru,, R ch, an, ru, ch, L R R R are the rubber heght, the close-loop pattern raus an the total raus of wheel, respectvely. he rubber heght R s constant. ru, 4. Knematcs of the New Moel he knematcs of the new structure can be shortene as a conceptual problem. Accorng to Fg. 4, the problem s to fn angle θ for the esre orentaton an poston of the. Parameter θ s the angle of ajustment motor of the th wheel. Fgure 4 shows some geometrc an Fg. 5. Geometrc an knematc parameters of the wheel 4

5 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 he close-loop pattern raus s obtane from R = wcos( /)cos( /6) () ch, Let the surface equaton be enote wth respect to the fxe coornate as Z f ( x, y) () After etermnaton of the knematc parameters, requre coornate systems are efne n Fg. 6. he frst coornate system X Y Z enotes the global coornate frame. he reference coornate system of the robot boy attache at s enote as. he XY Z pont where the th wheel connects to the man boy s the orgn of the coornate system. X Y Z he coornate frame attache to the th wheel at contact pont wth the surface s enote as. Fnally, the coornate system X sys Zs contact pont n a way that ts X Y Z s attache to the surface at Y s recton s perpencular to the surface. he Y component of the surface coornate frame s algne wth the X sys Zs normal vector to the surface, whch can be expresse as f ( x, y ) f ( x, y ) N( x, y) [,,] x y N( x, y) n N( x, y) (3) Fg. 6. Coornate systems of the knematc problem where n enotes the unt normal vector expresse n the global coornate system X Y Z. he homogenous transformaton matrces [8] between the boy reference an fxe coornate frames are etermne by successve translatons an rotatons as = pos y, y x, x z, z R (4) pos y, y x y z cos( y ) sn( y ) -sn( y ) cos( y ) (4) 5

6 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 x, x z, z Where cos( x ) sn( ) x sn( x ) cos( x ) cos( z ) sn( z ) sn( z ) cos( z ) y, y, x, x an z, z (4) enote the rotaton matrces resultng from the rotaton about the fxe axes Y, X an Z, wth angles, an, respectvely. y x z Furthermore, let the esre poston, [,, ] x y y, be etermne n terms of [ x, y ] whch efne coornates of a pont on the esre path n the current tme smulaton nterval. o o so, we frst conser a pont wth coornates [ x, y, z ] on the ps ps ps 3D surface whch s locate exactly above that pont of the esre path. herefore, one can wrte [ x,, ps yps zps] [ x, y, f ( x, y )] (5) We further efne the stance between ths pont efne by Eq. (5) an the poston by h whch s nee n recton of the normal vector N of Eq. (3). he esre poston can now be calculate as [ x, y, y ] hn ( xps, yps ) [ x, y, z ] ps ps ps (6) In orer to specfcally efne the coornate frames X Y Z at contact ponts, an nex s gven to each wheel specfyng ts relatve poston wth respect to the boy reference coornate frame XY Z. herefore, the nces fr, fl an r are consere to enote the front rght, front left an rear wheels, respectvely. he homogenous transformaton matrx between the fxe coornate frame X Y Z an coornate frame X3 Y3 Z3 for three wheels are etermne as he frst matrx on the rght han se of the above equatons was prevously efne n Eq. (4). he homogenous transformaton matrces ( fr, fl, r) specfy transformaton between frames X Y Z I whch are efne as 33 x y fr I 3 33 x y fl 3 L, L, L, L, XY Z an (8) I33 Lx,, r 3 In orer to algn the Z axs of the coornate frame wth the recton of the wheel axs, a rotaton X Y Z of 9 about ts X axs s performe to obtan the coornate frame X Y Z transformaton matrces (,, ) fr fl r as. hs results n the fr r fr r (9) fl fl Furthermore, the homogeneous transformaton matrces ( fr, fl, r) algn the Y axs of the current frame wth the lne connectng the wheel center an the contact pont of the wheel X Y Z an X3 Y3 Z 3, an are efne as cos( ) sn( ) sn( ) cos( ) () ( fr, fl, r) Fnally, the transformaton matrces (,, ) 3 fr fl r perform requre translatons to reach the orgn of the X Y Z at contact ponts frame R 3 3, ( fr, fl, r) (7) 6

7 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 3fr 3r 3fl I I I 33, fr 3 33, r 3 33, fl 3, R,, R,, R, () N( xy, ) of Eq. (3) at contact ponts, when represente n the coornate system X Y Z 3 3 3, vanshes. hs conton guarantees to obtan a feasble contact between each wheel an surface. he normal vector n the coornate system Fg. (7), X3 Y3 Z3 N( xy, ), can be represente as, see Where R, fr, R, fl an R r, enote the front-rght, frontleft an rear wheel rauses, respectvely, whch have been recently ntrouce n Secton 4. As state before n Secton 3, sx control commans are suppose to control roll, ptch an yaw angles, x an y postons of the esre path, an heght of the boy. hese commans are summarze n a vector as [,,,,, ] x y z h x y. 5. Knematc Constrants he constrants can be classfe nto two man categores, namely contact pont poston constrants an contact surface constrants. All ponts of the wheel whch can be n contact wth a surface are assume to locate on a rm. hs assumpton shrnks a 3D moel of the wheel to a smplfe one. It means that the thckness of the wheel can be neglecte. In ths moel, t s assume that the wheel s wthout thckness capable of ajustng ts raus. hs assumpton proves smpler mathematcal expresson of the wheel n the 3D space. So, the contact pont of the wheel can smply be foun through ths assumpton. For algorthms smulatng contact the reaers are referre to, e.g. [9, 3]. he sx control commans that robot boy has to follow were etermne prevously. he constrants whch wll be explane have to take zero value. he poston constrants are efne as C (3) f ( x, y ), ( fr, fl, r) x 3 (), y () 3 3 () hs equaton mples that the Z components of the contact pont of each wheel enote by (3) 3 (ntrouce n Eq. (7)) an ts assocate pont of the surface are equal. For the contact surface constrants, t s requre that the frst component of the normal vector Fg. 7. Representaton of the normal vector n the coornate X Y Z V ( R ) N( x, y) proj ( fr, fl, r) system x (), y () (3) herefore, the contact surface constrants can be wrtten as CC proj proj [ ] V V () (4) ( fr, fl, r) hese constrants can be combne wth constrant equatons of Eqs. () to obtan the vector of knematc constrants as 7

8 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 C[ C fr, C fl, Cr, CC fr, CC fl, CCr ] (5) he Newton-Raphson algorthm [3] s use n ths paper for solvng the system of nonlnear constrant equatons (5) an obtanng the esre soluton vector q [ fr, fl, r, fr, fl, r ] (6) he constrant Jacoban matrx J s rven by takng the partal ervatves of C wth respect to q as C J q (7) Pror to smulaton, t s esre to choose the numercal values of robot parameters nclung surface equaton (Eq.()), an of the esre path equaton, x y h, orentaton of the robot boy ( x, y, z ) an geometrc parameters w, L x, L y an R ru,. All of these parameters can be efne nepenently but. As t can be unerstoo from the prevous sectons, rotaton angle performe after rotatons z z s the current x an y hs angle s partcularly epenent of the esre path for whch the followng relaton hols y y tan( path) tan( path) (8) x x Where, path x an y are efne n Fg. 6. he angular velocty vector of the esre path enote by ω path yelng ω path s then wrtten by takng the ervatve of Eq. (8) [,, ] path (9) y x x y,, cos ( ) path x We further efne the angular velocty vector of the robot n the boy reference coornate frame XY Z as,, robot x y z. It s then transforme nto the fxe coornate system X Y Z.he orentaton of robot about axs Z s rectly efne by the steerng comman obtane from the path recton n such a way that the robot follows the esre path accurately. herefore, the Z components of R an robot ω have to be the same. path R,, robot robot x y z (). he orentaton of robot about Z axs s rectly efne by the steerng comman obtane from the path recton n such a way that the robot follows the esre path accurately. herefore, the Z components of an ω path have to be the same, yelng robot X, Y, Z X, Y, path Whch by usng Eq. () yels path R (3,: ) x, y z R (3,3) Substtutng z R path robot () () from Eq. (9) nto Eq. () leas to y x x y ( cos ( ) path (3,3) x (3) R (3,: ) x, y ) Equaton (3) enotes that the requre angular velocty about yaw axs of the robot boy whch satsfes the esre commans ( [,,,,, ] x y z h x y ) s erve n terms of the parameters of the esre path as well as the rotaton matrx of the coornate frame. he teratve Newton-Raphson algorthm s ntalze by an estmate for the soluton vector q an s performe n the followng manner tll the convergence s acheve q J C qk ( J C) qk, (4) error norm( C) he computatonal scheme for the knematc analyss of the moble robot movng on a rough surface accorng to the esre path s shown n Fg. 8. It s maybe mportant to notce that n ths algorthm, the commans vector [,,,,, ] x y z h x y t t s a functon of tme an can be upate from the current tme (t ) to the next tme (t +) by substtutng t + nto the tme-base functons whch are nclue n ths vector. 6. Calculaton of Motor orques for Wheel Raus Ajustment In ths secton, the motor torques requre for ajustng the raus of wheels are calculate. For ths purpose, there s no nee to mplement a complete ynamc moelng to fn all motor torques. Instea, a statc 8

9 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 analyss s presente base on the equlbrum equatons an vrtual work approach. In ths regar, the effect of gravty on the amount of motor torques s nvestgate. In the absence of slppng, the contact forces cause by gravty are shown n Fg. 9 an are enote by F, F an. fr fl F r In the frst step, the contact forces are obtane from sx equlbrum equatons whch can be wrtten n the global coornate system as Ffl F x fr F x r x Ffl F y fr F y r y Ffl F z fr F z r mg (5) z fr fl r F V F V F V fr fl r he vector V ( fr, fl, r) enotes the vector between the robot boy an contact pont of the th wheel wth surface V (6) 3 3, ( fr, fl, r) Fg. 8. Flowchart for the knematc analyss Fg. 9. Contact forces of the wheels at contact ponts Each contact force nclues three unknown components, resultng n total nne unknowns. Solvng ths uneretermne system of equatons requres mposng some restrctons on the components of contact forces. he frst conton s base on the fact that the normal contact forces exerte to the wheels have to be postve for preservng the contact. hese normal contact forces can smply be obtane n the surface coornate system X sys Zs from the followng relaton 9

10 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 3 P ( R ) ( F. n) n, ( fr, fl, r) (7) hs conton means that the Y component of these normal contact forces takes postve value as P (), ( fr, fl, r) (8) he secon conton s consere to prevent the wheels to slp on the surface. he non-slp stuaton s clearly occurre when the frcton force between each wheel an the surface oes not excee ts maxmum value. he magntue of frcton forces can be obtane by f F - P, ( fr, fl, r) (9) herefore, the secon conton can be presente as f s P, ( fr, fl, r) (3) where s s the coeffcent of statc frcton. For solvng the system of equatons (5) wth constrants (8) an (3), a constrane multobjectve optmzaton proceure has to be use to obtan the contact forces F ( fr, fl, r) whch can fnally be transforme from the global coornate system to the wheel coornate system as 3 F ( R3 ) F, ( fr, fl, r) (3) he prncple of vrtual work s then serve to fn the torques requre for mantanng the robot n statc equlbrum. hese torques are to be apple to keep the wheel n a certan raus. Accorng to the prncple of vrtual work, the total work of the contact force 3 F for changng the wheel raus R, s equal to the work of ajustment motor torque enote by for generatng 3 F () R, ( fr, fl, r), he relaton between (3) R, an can smply be obtane by fferentatng Eq. (), yelng R R =, ch,.5wsn( )cos( ), ( fr, fl, r) 6 Substtutng Eq. (33) nto Eq. (3) results n 3.5 F () wsn( /)cos( /6)= ( fr, fl, r) (33) (34) In orer to be more conservatve, we conser the worst case when the robot moves on a flat surface. In ths conton, the contact forces exerte to each wheel are equal to the one-thr of the robot weght. herefore, we replace 3 F () by mg /3n Eq. (34), leang to the followng relaton for estmatng the motor torques requre for wheel raus ajustment.5 mg wsn( /)cos( /6), 3 (35) ( fr, fl, r) 7. Concept of sensor mplementaton he control process of ths new platform s not consere n ths stuy. However, n the forwar an nverse knematc processes urng locomoton on the surface, the current poston an orentaton ata of the platform man boy have to be etecte. In the vrtual locomoton, these ata can be rea from a couple of accelerometers an gyroscopes locate n the mass center of the boy. he system ajustng the wheels raus receves the poston of the mass center n terms of the absolute poston an orentaton coornates. 8. Smulatons an Results he frst case stuy nvestgate here s the msson of movng the robot on a rough surface whle algnng the axs of ts coornate frame wth the axs Z of the fxe coornate frame by ajustng the angle of raus ajustment motors. In ths msson, the robot has to keep ts center of gravty n a certan absolute heght ( h.5m ) an to follow a prescrbe orentaton pattern whle trackng a esre path (a crcle). hs s nee a surface sturbance elmnaton process whch s to be acheve by fnng the proper motor torques to mpose the requre commans x, y, h, x, y, z. able shows the requre moel specfcatons an also the requre msson commans. he results of ths smulaton are llustrate n Fgs. -. Fgure shows D an 3D vews of trackng a crcle on a rough surface wth sturbance elmnaton. he path shown wth number s the projecton of the requre path on the surface. he path labele wth number s the path tracke by the robot boy center of gravty. As t s seen, the Z

11 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 algorthm has accomplshe the requre task successfully. he obtane angular splacements an torques of the raus ajustment motors are prove n Fgs. an, respectvely. Accorng to these fgures, the range of angular splacement s between an 7 egree, an the range of torques n the presence of gravty s.4 to 4 Nm. For further valaton of the moel an evaluatng the accuracy of the knematc analyss, we nvestgate the fference between the prescrbe commans an the obtane results. Fgure 3 shows the error of the algorthm n steerng the robot wth the constant heght h.5m as well as algnng the axs of the robot coornate frame wth the axs fxe coornate frame. Accorng to ths fgure, the propose moel can effectvely complete the msson wth acceptable accuracy. able. Moel specfcatons property Descrpton value follow x sn( t), y cos( t), h.5m,,, wll be upate x, y, H, x, y, Commans robot has to z x y z [ w, L, L, R, R, R ] Structural propertes [.3,.6,.6,.,.,.] x y rub fr rub fl rub r f ( x, y) Surface equaton Z sn(.5( x y )) /5 [start tme, nterval, en tme] Smulaton tmes [s,.s, 5s] Error Satsfacton crteron s 5 Coeffcent of frcton (rubber on concrete) m otal mass of the robot Kg Z Z of the Fg.. Msson : trackng a crcle on rough surface wth sturbance elmnaton (D an 3D vews)

12 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 angular splacement of secon motors (egree) front left wheel front rght wheel rear wheel me(s) Fg.. he angular splacements of the raus ajustment motors n msson slope, the man boy can be horzontal permanently. able gves the torques an angles of the raus ajustment motors for ths msson. As t was nvestgate at the frst smulaton, we nvestgate the fference between the prescrbe commans an the obtane results n ths msson to valate the moel accuracy. Fgure 5 confrms that the robot can perform ths task successfully. he torques of the secon motors (N.m) front left wheel front rght wheel rear wheel me (s) Fg.. he torques of the raus ajustment motors n msson he error of the heght of (m) me(s) z(m) - - y(m) - - Fg. 4. Msson : ajustment of the wheels raus for keepng the robot boy n a horzontal level - - x(m) he error of the Z recton 5 x me(s) Fg. 3. he error of the knematc analyss n msson he error of the lenght of (m) 5 x me(s) Another mportant feature of the new multmoe moble robot s the ablty to keep the robot boy n a horzontal level when the robot s movng on a ramp. A locomoton process on the ramp s conucte to show ths ablty. Accorng to ths smulaton, the robot boy s force to be horzontal on a ramp wth slope.. Fgure 4 shows that the robot has passe ths msson successfully. hs smulaton can be extene to other smlar mssons. For example, f the robot moves on a ramp wth uneven he error of the Z recton x me(s) Fg. 5. he error of the knematc analyss n msson

13 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 motor rear front left front rght able.. he torques an angles of the raus ajustment motors for msson torque(nm) angle(egree) Concluson he new moble robot mechancal esgn paragm presente n ths paper was base on compounng of the locomoton an manpulaton n the 3D space by means of a rg ajustable wheel. he artcle has stue a new rg ajustable close-loop mechansm whch s mplemente as the complete wheel n the moble platforms. he man objectves of the new platform whch were mprovement of maneuverablty, 6-DOF controllng of the an obstacle overcomng have been scusse. Exactly, the maneuverablty an 6-DOF locomoton of the have been nvestgate n the smulatons. Beses to track the trajectory, the results emonstrate that the new platform s able to elmnate surface sturbance. he atve ajustment motors have been nvestgate on the torque.. Appenx A.: Atonal Part to Avo Wre Cut-off o solve the problem of wre cut-off, an atonal part s nstalle on the rotatng axs of each wheel as shown n Fg. 6. he atonal part stcks to the wheel axs an keeps the rotor of the rotatng motors n the hole enote by number 7. It causes that the sk enote by number 3 rotates when the wheel starts to rotate. On the other han, part stcks to the motor boy. It means that both motor an part keep ther fxe poston. herefore, part 3 can rotate an part keeps the fxe poston. he torque results are n the acceptable range an the requre angular splacement of these motors s n the range of 4-7 egrees. So t can be recognze that the boy can track each 6-DOF esre comman. he future works whch wll be one to complete the new propose wheel, are to nclue the effect of lttle eformaton of the each part of new wheel an to nclue the effect of frcton between jonts an lnks. Also, the other mportant nvestgaton s to esgn the complete control loop of the new moel nclung ynamc smulaton wth uncertantes of the moel n the presence of frcton an flexbltes, control low n the presence of elays, roun of errors, sensor errors an sturbances. he fnal future work s to propose nterestng motons whch new platform can perform. Fg. 6. he atonal part to convey power an PWM sgnal to the ajustment motor 3

14 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 Each servo motor has three sgnal wres. he re an black wres (whch are shown respectvely by numbers 4 an 5) conuct the electrcal power an the yellow wre (number 6) sens the PWM sgnal to control the servo motor. hree conuctve crcular paths are etche on the sk 3 an three conuctve brushes convey the sgnal from the wre enote by number to the sk 3. In ths way, the sgnals can be conucte from the man boy to the rotatng wheels wthout any wre cut-off. All conuctve crcular paths (numbers 4, 5 an 6) are connecte to the servo motor. References [] D. Xu, D. Zhao, J. Y an X. an, rajectory trackng control of omnrectonal wheele moble manpulators: robust neural network-base slng moe approach. Systems, Man, an Cybernetcs, Part B: Cybernetcs, IEEE ransactons, Vol. 39(3), (9), []. B. Lauwers, G. A. Kantor an R. L. Holls, A ynamcally stable sngle-wheele moble robot wth nverse mouse-ball rve, Robotcs an Automaton, ICRA Proceengs IEEE Internatonal Conference, (6), [3] S. Ebrahm, A. Maran, Dynamc Moelng an Constructon of a New wo-wheele Moble Manpulator: Self-balancng an Clmbng, Internatonal Journal of Robotcs, heory an Applcatons, Vol. 4(3), (5), -34. [4] S. Ebrahm, A. Marany, Dynamc moelng an constructon of a two-wheele moble manpulator, part I: Self-balancng, Robotcs an Mechatroncs (ICROM), (5), [5] C. Carera, J. S. Da Costa, A low cost moble robot for engneerng eucaton, In Inustral Electroncs Socety, IECON Conference of IEEE, (5), p. 6. [6] A. Stengaar, J. Nelsen, M. Skrver, C. Ln an U. Pagh Schultz, Low-cost moular robotc system for neurologcal rehabltatve tranng, IEEE Internatonal Conference on Inustral echnology (ICI), (6), [7] A. Maran, S. Ebrahm, Dynamc moelng an constructon of a two-wheele moble manpulator, part II: Mofe obstacle clmbng. Robotcs an Mechatroncs (ICROM), (5), [8] C. S. Casarez, R. S. Fearng, Step clmbng cooperaton prmtves for legge robots wth a reversble connecton. IEEE Internatonal Conference on Robotcs an Automaton (ICRA), (6), [9] A. S. Boxerbaum, P. Werk, R. D. Qunn an R. Vayanathan, Desgn of an autonomous amphbous robot for surf zone operaton: part I mechancal esgn for mult-moe moblty. Avance Intellgent Mechatronc Proceengs, IEEE/ASME Internatonal Conference, (5), [] W. McMahan, V. Csencsts, M. Dawson, D. Walker, I. D. Jones an C. D. Rahn, Fel trals an testng of the OctArm contnuum manpulator. Robotcs an Automaton. ICRA Proceengs, IEEE Internatonal Conference, (6), [] P. Ben-zv, A. A. Golenberg an J. W. Zu, Desgn an analyss of a hybr moble robot mechansm wth compoune locomoton an manpulaton capablty, Journal of Mechancal Desgn, Vol. 3(7), (8), 73. [] G. C. Haynes, A. Khrpn, G. Lynch, J.Amory, Sauners, A. Rzz an D. Kotschek, Rap pole clmbng wth a quarupeal robot, Robotcs an Automaton, ICRA'9. IEEE Internatonal Conference, (9), [3] F. Xu, J. Shen, J. Hu, an G. Jang, A rough concrete wall-clmbng robot base on graspng claws Mechancal esgn, analyss an laboratory experments. Internatonal Journal of Avance Robotc Systems, Vol. 3(5), (6), -. [4] M. J. Spenko, G. C. Haynes, J. A. Sauners, M. R. Cutkosky, A. A. Rzz, R. J. Full an D. E. Kotschek, Bologcally nspre clmbng wth a hexapeal robot, Journal of Fel Robotcs, Vol. 5(4), (8), 3-4. [5] M. P. Mann, Z. Shller, Dynamc stablty of a rocker boge vehcle: longtunal moton, Robotcs an Automaton, ICRA Proceengs of IEEE Internatonal Conference, (5), [6] W. M. Shen, M. Krvokon, H. Chu, J. Everst, M. Rubensten an J. Venkatesh, Multmoe locomoton va SuperBot reconfgurable robots. Autonomous Robots, Vol. (), (6), [7] L. Caraccolo, A. Luca an S. Ianntt, trackng control of a four-wheel fferentally rven moble robot, In Robotcs an Automaton, Proceengs of IEEE Internatonal Conference, Vol. 4, (999),

15 Internatonal Journal of Robotcs, Vol. 4, No. 4, A. Maran, S. Ebrahm, -5 [8]. Ester, Y. Crausaz, B. Mermno, M. Laura, R. Pguet an R. Segwart, An nnovatve space rover wth extene clmbng abltes, LSA-CONF, (), -3. [9] H. Aach, N. Koyach,. Ara, A. Shmza an Y. Nogam, Mechansm an control of a leg-wheel hybr moble robot, Intellgent Robots an Systems, Proceengs of IEEE/RSJ Internatonal Conference, IROS'99, Vol. 3, (999), [] H. appener, S. Skaff,. Szabo an R. Holls, Remote haptc feeback from a ynamc runnng machne, Robotcs an Automaton, IEEE Internatonal Conference, ICRA'9, (9), [] A. Halme, I. Leppänen, S. Salm an S. Ylönen, Hybr locomoton of a wheel-legge machne, Conference on Clmbng an Walkng Robots, CLAWAR, (). [] B. H. Wlcox,. Ltwn, J. Besaeck, J. Matthews, M. Heverly, J. Morrson an B. Cooper, AHLEE: A cargo hanlng an manpulaton robot for the moon, Journal of Fel Robotcs, Vol. 4(5), (7), [3] B. H. Wlcox, AHLEE: A cargo an habtat transporter for the moon. Aerospace conference, (9), -7. [4] C. Gran, F. Benamar, F. Plumet an P. Bau, Stablty an tracton optmzaton of a reconfgurable wheel-legge robot, he Internatonal Journal of Robotcs Research, Vol. 3(-), (4), [5] V. SunSpral, D. Chavez-Clemente, M. Broxton, L. Keely, P. Mhelch, D. Mttman an C. Collns, FootFall: A groun base operatons toolset enablng walkng for the AHLEE rover. Proceengs of AIAA Space Conference, (8), - 4. [6] G. Eno, S. Hrose, Stuy on roller-walker: mult-moe steerng control an self-contane locomoton, Robotcs an Automaton Proceengs ICRA', IEEE Internatonal Conference, Vol. 3, (), [7] M. M. Dalvan, M. Moghaam, Desgn an moelng of a star clmber smart moble robot (MSRox), ICAR, Proceengs of the th Internatonal Conference on Avance Robotcs, (3), [8] M. W. Spong, M. Vyasagar, Robot ynamcs an control, John Wley & Sons, (8). [9] S. Ebrahm, P. Eberhar, Contact of Planar Flexble Multboy Systems Usng a Lnear Complementarty Formulaton, PAMM Proceengs n Apple Mathematcs an Mechancs, Vol. 5(), (5), [3] S. Ebrahm, A Contrbuton to Computatonal Contact Proceures n Flexble Multboy Systems. PhD's hess, Rehe: Schrften aus em Insttut für echnsche un Numersche Mechank er Unverstät Stuttgart, Ban 8, Shaker Verlag, Germany, (7). [3] A. A. Shabana, Computatonal ynamcs, John Wley & Sons, )9(. Bography Arman Maran s currently a PhD stuent n the Department of Mechancal Engneerng at Yaz Unversty. He receve hs BSc n Mechancal Engneerng n from Yaz Unversty an hs MSc n Mechatronc Engneerng n 4 from Shahroo Unversty. Hs research nterests nclue robotcs, structural esgn of robots an multboy smulatons relate to multmoe an moble robots. Saee Ebrahm s currently an assocate professor of Mechancal Engneerng at Yaz Unversty, Iran. He has receve hs PhD n Mechancal Engneerng from Stuttgart Unversty, Germany, n 7. He has also complete hs postoctoral fellowshp at the Center for Intellgent Machnes (CIM), McGll Unversty n 8. Hs current research nterest nclues Dynamc Moellng of Multboy Systems, Robotcs, Mechansms Desgn an Vbraton Analyss of Mechancal Systems. 5