Quasi-Static Rolling Control of the Rolling Disk Biped Robot

Transcription

1 Equatn Chapter 1 Sectn IEEE Internatnal Cnference n Rbtcs and Autmatn Pasadena, CA, USA, May 19-23, 2008 Quas-Statc Rllng Cntrl f the Rllng Dsk Bped Rbt Crstan C Phpps, Student Member, IEEE, and Mark A. Mnr, Member, IEEE Abstract Mtvated by the need fr greater speed, adaptablty and effcency n legged rbts, a class f hybrd rbts have been develped whch hybrdze rllng lcmtn wth legged lcmtn. Heren we present a quas-statc rllng cntrl law fr the hybrd clmbng/rllng rbt the Rllng Dsk Bped. We prvde expermental results cmparng speed and energy cnsumptn data fr quas-statc rllng versus walkng. We shw that rllng can sgnfcantly mprve energy effcency ver walkng by as much as a factr f 3.9. I. INTRODUCTION tvated by the need fr greater speed, effcency Mand adaptablty n clmbng and walkng rbts, we have develped a class f rbts whch hybrdze clmbng and walkng wth rllng lcmtn [1-3]. The nnvatve mrphlges f these rbts allw fr rllng lcmtn wthut the need fr addtnal resurces beynd thse requred fr clmbng and walkng. By ncreasng the avalable mdes f lcmtn, the adaptablty f a mble rbt s ncreased because t may select the lcmtn methd best suted fr a partcular peratnal envrnment. Legged lcmtn s excellent fr mvng thrugh rugh and unstructured terran, but s slw and demandng f energy. Rllng s apt t hgher speeds and s mre energy effcent (especally n dwnhll slpes) but requres smther, better structured envrnments. Heren we prve that rllng mdes f lcmtn n such hybrd rbts are capable f greater energy effcences than walkng mdes. The quas-statc rllng lcmtn cntrl we have develped and tested n ths paper s capable f mprvng energy effcency by as much as a factr f 3.9 ver walkng n the Rllng Dsk Bped (RDB) rbt when magnets are used as grppers. The mtrs alne may use 14% less energy fr rllng than the mst effcent walkng gat evaluated here. The RDB s a three degree-f-freedm planar rbt whch serves as a tw dmensnal test-bed fr ur studes n the hybrdzatn f clmbng and rllng and the cntrl theref. Refer t [1, 2] fr detals f ts desgn. Experence wth the RDB wll be appled twards future desgn teratns f the RDB and the sphercal hexapd rbt Hex- Manuscrpt receved September 13, C. C Phpps s wth the Unversty f Utah Department f Mechancal Engneerng, Salt Lake Cty, UT USA (phne: ; fax: ; e-mal: crstanphpps@gmal.cm). M. A. Mnr s wth the Unversty f Utah Department f Mechancal Engneerng, Salt Lake Cty, UT USA (e-mal: mnr@mech.utah.edu). A-Ball (HAB) [3], bth whch are antcpated t extend the capabltes f the current RDB nt E 3. Our quas-statc rllng cntrller (ntrduced n [3]) wrks by slwly mvng the rbt s center f gravty (CG) abut ts gemetrc center thrugh crdnated jnt mvements; f the CG s mved suffcently slwly, the rbt shuld rll t mantan equlbrum. Other rbts have demnstrated the success f smlar CG ffset rllng methds such as thse by Halme [4], Mukherjee [5], Ym [6], Yamawak [7], and Lee [8]. A cntrller such as the ne we present here s best suted fr passve stablzatn at a desred rentatn and fr slwer rllng lcmtn ( rev/s n the RDB) and pstnng where nertal effects are mstly neglgble. Feed-frward jnt paths are calculated fflne usng a statc ptmzatn rutne t fnd jnt angles whse effect s t cause the net rbt CG path t track a reference rbt abut the gemetrc center f the rbt at a specfed radus. Such jnt paths are generated fr rad between 2 and 8 mm and are played back at rates between 10 /s and 30 /s. We cmpare expermental results f these rllng trajectres and evaluate energy effcency and trajectry trackng characterstcs. We als cmpare these rllng lcmtn results aganst rudmentary walkng lcmtn data btaned fr the RDB prttype. The cntrller presented here s an mprvement ver the mdel based cntrller f [1, 2] whch was nt capable f reprducng expected results. The cntrller n [1, 2] uses plynmal jnt trajectres t create a net change n the RDB s CG pstn; smulatns are used t manually tune the plynmal parameters such that an entre revlutn f the RDB results. A lkely cause fr the falure f ths cntrller t prduce expected results s dscrepances between mdel parameters used n the smulatns and thse f the actual system especally vscus frctn parameters. It wll be shwn that the quas-statc rllng lcmtn cntrller we have develped s capable f prducng nearly an entre revlutn f the RDB rbt and trackng a rllng angle reference reasnably well. Further, we wll shw that ths rllng methd s capable f ncreasng energy effcency n a dstance bass by as much as a factr f 3.9. We begn ths paper wth a descrptn f the knematc mdel f the RDB n Sectn II. Our quas-statc rllng lcmtn cntrller s detaled n Sectn III. We present and dscuss ur expermental results n Sectn IV. Cnclusns and dscussn f future wrk s cntaned n Sectn V /08/$ IEEE. 1239

2 c T m0 0 m1 1 1 m2 2 2 m3 3 3 m b + T b + T b + T b t fr 0 φ < 60 c T m m1 1+ m m m T b b T b T b t c fr 60 φ < 180 r = c T m0 0 0 m1 1 1 m2 2 m3 3 3 m T b + T b + b + T b t fr 180 φ < 300 c T m m m m 3 3 m T b T b T b b t fr 300 φ < 360 (1) Fg. 1. Knematc mdel f the RDB used fr rllng lcmtn analyses. TABLE 1 VALUES FOR DH AND INERTIAL PARAMETERS USED IN CALCULATIONS AND APPEARING IN FIG. 1 a θ m b (mm) (deg) (g) (mm) Na Na 0 84 * 182 [ ] T * 363 [ ] T * 376 [ ] T 3 84 * 209 [ ] T Na Na where T j s a hmgeneus transfrmatn matrx representng the crdnate transfrmatn frm frame j t, and b s the hmgeneus crdnate f the CG f lnk n frame. The mass f lnk s m, and the ttal mass s mt = m0 + m1+ m2 + m3. Table 1 prvdes numercal values fr the cnstants appearng n the abve equatns and n Fg. 1. Imprtant quanttes used extensvely thrugh the rest f ths paper are the CG Offset Length L L = r + r (2) c 2 c II. ROLLING DISK BIPED KINEMATICS The net CG lcatn f the RDB s determned frm the relatve pstns f ts lnks. The standard Denavt- Hartenberg (DH) cnventn [9] s used fr knematc parameterzatn f the RDB. Fg. 1 dentfes the DH parameters n a knematc drawng f the RDB. Frame c lcates the center f the Rllng Crcle whch s cncdent wth the center f the crcular rllng surface f the grunded lnk and s fxed wth respect t that lnk. Frame g lcates the grund cntact pnt where y g s defned as the nrmal t the rllng surface and z g pnts nt the plane. The Rllng Angle φ s the rtatn f frame c abut z g. The CG lcatn c r expressed n frame c s fund n hmgeneus crdnates usng: and the CG Offset Angle ψ c c ψ = atan2( r2, r1) + 90 (3) where the ceffcents c r 1 and c r 2 are the frst and secnd elements f c r respectvely. III. QUASI-STATIC ROLLING CONTROL Assumng rllng resstances and nertal effects t be neglgble, gravty wll cause the RDB t settle t the rentatn n whch ts CG s drectly abve ts grund cntact pnt, resultng n statc equlbrum. If the CG pstn s slwly perturbed, the RDB wll rll t restre equlbrum. Ths prncple s llustrated n Fg. 2. Our assumptns allw us t further assume that the rentatn the RDB settles t s ndependent f the CG Offset Length L ( L 0 ), and nly dependent n the CG Offset Angle ψ. Hence, ψ = wll prduce a full rtatn f the 1240

3 φ 0 k φcrt, n 0= θ θnm +Δθk, tanh 180 φ φ smth, n crt, n (6) Fg. 2. Quas-statc rllng prncple. The shaded fgures n the upper-rght f each frame shw sample RDB cnfguratns fr each nstance. RDB f L > 0 fr all ψ. Realstcally hwever, the larger L s, the greater the cntrl authrty and stablty f the rentatn. A. Generatn f Jnt Paths by CG Offset Length Optmzatn Our quas-statc rllng cntrl strategy s t generate jnt paths whch prduce CG Offset Length paths ( L > 0 ) fr CG Offset Angles ψ = The jnt paths are then used as feed-frward cntrl nputs t the jnt servs, played back at varus rates. We treat the generatn f these paths as a sequence f cnstraned ptmzatn prblems where ur bjectve s t fnd jnt angles, θ k, whch maxmze CG Offset Length, L k, at dscreet pnts, φ k, f the Rllng Angle path. The subscrpt k s ntrduced t dente the k th ptmzatn prblem. Matlab s fmncn functn s used t sequentally slve each k ptmzatn prblem where the jnt pstns resultng frm ptmzatn k are used as ntal estmates fr ptmzatn k+1. The ptmzatn cnstrants are detaled belw. Maxmum CG Offset Length: The CG Offset Length L k, calculated usng (2), s cnstraned t sme Maxmum CG Offset Length L max. Ths s accmplshed wth the nequalty cnstrant 0 Lk Lmax (4) CG Offset Angle: Fr any desred Rllng Angleφ k, the CG Offset Angle ψ k, calculated usng (3), must match, resultng n the equalty cnstrant 0 φk ψk = (5) Rllng Surface Cntnuty: Ensurng cntnuty n the RDB s rllng surface requres that the jnt varables be cnstraned t ther nmnal pstns when the Rllng Angle s near the angles crrespndng t the jnt lcatns and the termnal ends f the rbt,.e. φ crt = {0,60,180,300,360 }. The hyperblc-tangent functn s used t cnstran the jnt varables wthn an envelpe accrdng t where θ nm = 120 s the nmnal jnt angle fr all jnts (perfect crcle cnfguratn), Δ θ k, s the devatn frm the nmnal value fr jnt cnstraned t Δθallw Δθk, Δ θallw, where Δ θallw s determned by the physcal angular lmt f the jnts. φ k s the desred Rllng Angle and φsmth = φcrt 30 s the Rllng Angle at whch the envelpe begns t narrw as φ crt s apprached; 30 was chsen because t s the largest value that allws the envelpe t pen t ts maxmum value between φ crt = 0 and 60 (smlarly between φ crt = 300 and 360 ). The value f ndex n s determned by the desred Rllng Angle as < n = < 1 fr 0 φk 30 2 fr 30 φk < fr 120 φk fr 240 φk < fr 330 φk 360 Ft-Aganst-Ft Interference: Fr any desred Rllng Angle, the RDB s lmted t jnt cnfguratns whch d nt result n cllsns between the feet. The magntude f a ft cllsn s quantfed by cmparng the dstances frm the edges f Ft One (O -2 and O -1 ) t Ft Tw (O 3 and O 4 ). A cllsn s determned t have ccurred f x0 d and 0 x d where d j s the nter-rgn vectr frm frame t j expressed n frame 0 fr ={-1,-2} and j={3,4}. Ths prncple s llustrated n Fg. 3. Relevant parameters are lsted n Table 1 and may be used t determne the lcatns f the crdnate frame rgns representng the ft edges. A numercal value descrbng the relatve clseness f the ft surfaces t ne anther may be fund by u x d f 0 x d j 3 j j = x3 dj f 0 x0 dj x0 dj + x3 dj else where negatve values fr u j ndcate n cllsn and pstve values ndcate a cllsn. The resultng nequalty cnstrants are j j (7) (8) (9) 1241

4 Fg. 3. Illustratn f ft cllsn quantfcatn cncept. 0 u fr = { 1, 2}, j = {3, 4}. (10) j Sample jnt path generatn results are prtrayed n Fg. 4 whch shws jnt and CG paths fr allwed Max. CG Offset Lengths f 2 and 8 mm. It can clearly be seen that ur jnt path generatn rutne was successful n prducng cntnuus jnt paths whch result n CG Offset Length paths f nearly cnstant value at the desred Max. CG Offset Lengths. The exceptn s at CG Offset Angles near φ crt where the rllng surface cntnuty cnstrant causes the CG Offset Length t dp twards zer. Thugh we neglect nertal effects n the develpment f ur quas-statc cntrl law, we assume that enugh mmentum and gravtatnal effects due t system lag wll be present n expermentatn t carry the rbt past φ crt. The rllng surface cntnuty cnstrant als causes Jnts 1 and 3 t dsplace rapdly near φ crt whch mght ntrduce unwanted dynamc effects. Hwever, by nspectn, ther acceleratns are nearly equal and n ppste drectns whch helps t cancel ut ther net dynamc effect. These rapd jnt dsplacements als place lmts n hw fast the jnt paths may be played back n the rbt whch has a lmted jnt angle rate large gear rats are requred fr clmbng and restrct the amunt f mtr pwer avalable as speed. Ntce als that the jnt paths fr dfferent Max. CG Offset Lengths have very smlar shapes and are nearly scaled versns f each ther, larger Max. CG Offset Lengths requrng larger jnt devatns. A majr mplcatn f ths s that mre energy wll be requred t run larger Max. CG Offset paths, as they requre greater jnt artculatns. IV. RESULTS A. Expermental Setup Walkng and rllng experments are perfrmed usng the RDB rbt and a dspace 1103 cntrller bard s used fr Fg. 4. Results f jnt path generatn fr Maxmum CG Offset Lengths f 2 and 8 mm. Jnt paths and CG Offset Length are shwn as functns f the desred CG Offset Angle. The crrespndng path f the net CG abut the gemetrc center f the rllng crcle s ncluded fr each set f jnt paths. cntrl. PWM mtr cntrl sgnals frm the dspace are amplfed by H-brdges, and bnary grpper cntrl sgnals frm the dspace cntrl dgtal swtches t allw current t the elctr-magnetc grppers. Pwer t the H-brdges and magnets s prvded by a 24V 10A DC pwer supply. Pwer t the RDB s mtrs, magnets and ptentmeters s prvded va a tether, whch als transmts jnt pstn ptentmeter sgnals t the dspace. T mntr mtr and magnet pwer draw, current shunt resstrs are cnnected n seres n the lw sdes f the H- brdge pwer supply and magnets. Dfference amplfers are used t amplfy the vltage drp acrss the resstrs whch s measured and recrded by the dspace. Fr purpses f cmparsn between the dfferent mdes f lcmtn, we chse t express energy cnsumptn n a per meter bass. Fr rllng experments, we assume exactly ne revlutn s cmpleted fr all experments perfrmed. 1242

5 Fg. 5. Stll frames f the RDB rllng ne revlutn (usng the 8 mm Max. CG Offset Length - 30 /s CG Offset Angle Rate trajectry). The cntrller fr the RDB s created usng Smulnk 6.1 and s dwnladed t the dspace bard usng Matlab Real-Tme Wrkshp. The cntrller cnssts f a feedfrward jnt trajectry nput t a prprtnal cntrl serv lp whch cntrls the pstn f the three jnts n the RDB. Cntrl fr the grppers s prvded by feed-frward bnary trajectres. A samplng rate f 1k Hz s used n the mplementatn f the cntrller. User nterface wth and data cllectn frm the dspace 1103 bard are prvded by dspace Cntrl Desk Develper Versn sftware. Data fr jnt errrs and mtr and magnet pwer draw are sampled and recrded at a rate f 100 Hz. Stll frame analyss f vde captures s used t manually measure Rllng Angles at a rate f 12 equally spaced frames per desred revlutn f the RDB, and at the fnal restng Rllng Angle. Analyss f ur Rllng Angle measurement technque prved t t be suffcently precse wth a standard devatn n repeated measurements f 1.2 r less. Rllng experments are perfrmed n ur lab n unpadded ndustral lp-ple carpet surfaces. Walkng experments are perfrmed n ur lab n 3/16 steel plate. B. Level Surface Quas-Statc Rllng Experments Usng Cnstant CG Offset Angle Rate Trajectres Level surface quas-statc rllng experments are evaluated usng Cnstant CG Angle Offset Rate (CCGOAR) trajectres. As ther name mples, these trajectres prduce a CG trajectry abut the gemetrc center f the rllng crcle at sme cnstant CG Offset Angle rate. They were generated usng paths f Maxmum CG Offset Lengths (MCGOL) f 2, 4, 6, and 8 mm (generated as detaled n Sectn III.A), played at Cnstant CG Offset Angle Rates (CCGOAR) f 10, 20, and 30 /s. Trajectres f MCGOL greater than 8 mm cause the rbt jnts t exceed ther lmts and are therefre nt evaluated. Trajectres wth CCGOAR greater than 30 /s requre jnt trajectres whch the current RDB actuatrs cannt suffcently track and are therefre nt evaluated ether. Fve experments were perfrmed fr each trajectry n rder t evaluate success rate (number f experments prducng maxmum Rllng Angles greater than 330 ). Mtr pwer cnsumptn and jnt errr data cllected usng the Cntrl Desk sftware was analyzed fr all f each set f fve experments, and stll frame analyss was used n ne f each set f fve experments. Refer t Fg. 5 fr an example f the RDB rllng usng ur quas-statc cntrl law. The plts n Fg. 6a-d shw the results f the stll frame analyss prvdng measured Rllng Angle trajectres fr MCGOL f 2, 4, 6, and 8 mm respectvely. It s clearly seen that as MCGOL ncreases, trajectry trackng s mprved as a result f the greater cntrl authrty prvded by larger mments. In Table 2 we shw the Rllng Angle Errr RMS data, whch supprt ths bservatn. Als, nte the perfect success rates n Table 3 fr the 8 mm MCGOL trajectres, and the generally pr success rates fr the 2 mm MCGOL trajectres whch further supprt ths bservatn. It s als nterestng t nte n Fg. 6 that many f the trajectres dsplay nn-quas-statc characterstcs; e.g. the 2 mm MCGOL - 30 /s CCGOAR trajectry shws perds f rapd rllng rates frm stll frame 2 t 4 and agan frm stll frame 7 t 9. Such dynamc effects are n fact qute mprtant t the success f ur cntrl law. Ntce n Table 3 that perfect success rates are bserved nly fr the 30 /s CCGOAR trajectres. Because these are the fastest f the CCGOAR trajectres, they are presumably mre dynamc and t s lkely because f these dynamcs that these trajectres are successful whle slwer CCGOAR trajectres are nt. Ths demnstrates the nfluence f dynamcs n ur quas-statc cntrl law and mplcates wrk n dynamc rllng cntrl f the RDB and ther such rbts. Energy cnsumptn results are presented n Table 4 as averages f the fve experments. In general, t s seen that energy usage ncreases wth ncreasng MCGOL and decreasng CCGOAR. Because f the wrm gearng and large gear rat, a large amunt f the mtrs effrt s assumed t g nt vercmng frctn n the gear tran. Therefre the lnger the mtrs are run, and the larger the jnt artculatns (as requred by larger MCGOL trajectres) the mre energy wll be requred, as can be seen n Table 4. Expermental results wrth ntng are the 10 and 20 /s - 8 mm MCGOL trajectres whch have the best Rllng Angle trajectry trackng. Because these trajectres have the largest MCGOL and the slwest CCGOAR f all trajectres examned, ths result s n cncert wth ur expectatns. The larger MCGOL affrd greater cntrl authrty and the slwer CCGOAR make ur quas-statc assumptn mre vable. Anther nterestng result s the pr Rllng Angle trackng and success rates bserved fr the 2 mm MCGOL - 10 and 20 /s CCGOAR jnt trajectres. Inspectn f Table 3 shws that n fact these jnt trajectres are nt at all relable fr rllng. Our quas-statc assumptn wuld requre that these slwer trajectres wrk f the same jnt paths played at a faster rate d. Ths bservatn s an ndcatn f the benefcal rle dynamc effects have n ur quas-statc cntrl law. The nablty f ur cntrller t wrk fr these trajectres may be a result f nadequate 1243

6 TABLE 2 ROLLING ANGLE ERROR RMS (DEGREES) FOR CCGOAR TRAJECTORIES ON A LEVEL SURFACE. Cnstant Max. CG Offset Lengths (mm) CG Offset Angle Rate ( /s) TABLE 3 SUCCESS RATE OUT OF FIVE EXPERIMENTS FOR CCGOAR TRAJECTORIES ON A LEVEL SURFACE. Cnstant Max. CG Offset Lengths (mm) CG Offset Angle Rate ( /s) Fg. 6. Stll frame analyss results fr level surface rllng shwng measured Rllng Angle trajectres fr Max. CG Offset Lengths f (a) 2 mm, (b) 4 mm, (c) 6 mm, and (d) 8 mm. dynamc nfluence due t slwer rllng and jnt rates cmbned wth smaller MCGOL. C. Walkng Experments Fr cmparsn wth rllng, walkng experments were perfrmed fr smple flppng and nchwrm type gats n a level surface as demnstrated n Fg. 7a and Fg. 7b respectvely. The flppng gat studed here s an extensn t that already develped fr the RDB [2], and the nchwrm gat s cmmn t clmbng rbts wth smlar mrphlges [10-12]. Fr bth gats, the jnt trajectres fr a sngle step cnsst f tw trajectry pnts: the ntal and fnal cnfguratns. Ths s ntended t reduce pwer cnsumptn by elmnatng the need t serv alng the trajectry and t ncrease speed. Electr-magnetc grppers are used t grp the ferrus walkng surface. Ten experments were perfrmed fr each gat type fr averagng purpses. Energy cnsumptn n a per meter bass and average translatnal speed data fr bth walkng trajectres are presented n Table 5 as averages f the ten experments. It can be seen that the nchwrm walkng gat perfrms very prly cmpared t the flppng walkng gat, agan lkely due t the large amunt f frctn n the gear tran. Smply put, the nchwrm gat requres greater jnt artculatns per unt dstance traveled, and therefre mre energy. D. Cmparsn f Lcmtn Mdes Rllng experment data are ncluded alngsde walkng TABLE 4 ENERGY USAGE PER METER TRAVELED (J/M) FOR CCGOAR TRAJECTORIES ON A LEVEL SURFACE. Cnstant Max. CG Offset Lengths (mm) CG Offset Angle Rate ( /s) experment data n Table 5 fr purpses f cmparsn. We have ncluded data frm the experments prducng the greatest energy effcency, greatest translatnal speed, and best rllng trajectry trackng (2.0 mm MCGOL - 30 /s CCGOAR, 2.0 mm MCGOL - 30 /s CCGOAR, and 8.0 mm MCGOL - 10 /s CCGOAR respectvely). It can be seen that quas-statc rllng s nt capable f translatnal speeds as fast as the flppng gat, thugh t prvdes sgnfcant mprvement n energy usage ver bth types f walkng gats. When magnets are used as grppers, the energy requred fr rllng s 26% f that f a flppng walkng gat (the mst effcent f the walkng gats studed here). When grpper energy cnsumptn s neglected, the mtrs alne use 14% less f the energy f a flppng walkng gat fr rllng stll a sgnfcant mprvement. V. CONCLUSIONS AND FUTURE WORK We have shwn that the hybrdzatn f rllng wth walkng s capable f ncreasng the energy effcency f walkng rbts. Tests f ur quas-statc rllng cntrller n the RDB rbt have prven capablty f ncreasng energy effcency by as much as a factr f 3.9 ver walkng usng magnetc grppers. When nly mtr energy cnsumptn s cnsdered, we shw a 14% decrease n energy cnsumptn fr rllng ver walkng. These features allw such hybrd rbts the ablty t better adapt t ther peratnal envrnment by selectng the mde f lcmtn mst 1244

7 apprprate. Fnally we ntend t utlze ur experence wth the RDB n the mre versatle sphercal HAB rbt and future desgn teratns f the RDB. (a) (b) Fg. 7. Demnstratn f (a) flppng and (b) nchwrm type walkng gats. apprprate: walkng lcmtn affrds the benefts f beng able t walk r clmb ver bstacles and scalng vertcal surfaces, whle quas-statc rllng lcmtn s capable f greater energy effcency and lcmtn n surfaces whch the rbt cannt grp. Because the RDB s prmarly ntended as a clmber, mtr and gearng selectns were based heavly n the requrements f clmbng. Specfcally, the mtrs and gearng were selected t allw fr jnt mtn when n the full cantlever pstn. Ths hgh jnt trque requrement fr clmbng s n cnflct wth the desre fr greater jnt speed fr rllng whch wuld facltate faster and mre dynamc mdes f rllng. The large gear reductn s als a detrment t all frms f lcmtn because f nherent neffcency n the gear tran. Future wrk wll nclude reevaluatn/ptmzatn f the mtr and gearng selectn wth the ntent t ncrease jnt speeds, decrease gearng neffcency, and stll allw fr clmbng n vertcal surfaces. Thugh ur quas-statc rllng cntrller has nt demnstrated the ablty t prvde translatnal speeds greater than walkng, ur future wrk s t nclude develpment f cntrl fr mre dynamc methds f rllng. These methds culd nclude: usng the legs t kck ff the grund, jnt artculatns t pump mmentum nt the system, and usng CG ffsets t sustan large trques. We ntend t mplement feedback cntrl whch wll requre the develpment f a sensr sute fr state estmatn and perhaps terran characterzatn. The tether and ff-bard cntrller wll be replaced wth an embedded cntrller. We wll study transtns between lcmtn mdes and terran characterzatn t enable selectn f the mde mst REFERENCES [1] B. Shres and M. Mnr, "Desgn, Knematc Analyss, and Quas- Steady Cntrl f a Mrphc Rllng Dsk Bped Clmbng Rbt," presented at IEEE Int'l Cnf. n Rb. and Autm (ICRA 05), Barcelna, Span, [2] B. E. Shres, "Hybrd lcmtn fr enhanced mblty n rbtc systems," n Mechancal Engneerng. Salt Lake Cty: Unversty f Utah, 2005, pp [3] C. C. Phpps and M. A. Mnr, "Intrducng the Hex-A-Ball, a Hybrd Lcmtn Terran Adaptve Walkng and Rllng Rbt," presented at CLAWAR 2005, Lndn, U.K., [4] A. Halme, T. Schnberg, and Y. Wang, "Mtn cntrl f a sphercal mble rbt," presented at Prceedngs f the th Internatnal Wrkshp n Advanced Mtn Cntrl, AMC'96. Part 1 (f 2), Mar , Tsu, Jpn, [5] R. Mukherjee and T. Das, "Feedback stablzatn f a sphercal mble rbt," presented at IROS 2002: IEEE/RSJ Internatnal Cnference n Intellgent Rbts and Systems, Lausanne, Swtzerland, [6] M. Ym, "New lcmtn gats," presented at Prceedngs f the 1994 IEEE Internatnal Cnference n Rbtcs and Autmatn, 8-13 May 1994, San Deg, CA, USA, [7] T. Yamawak, O. Mr, and T. Omata, "Nnhlnmc dynamc rllng cntrl f recnfgurable 5R clsed knematc chan rbt wth passve jnts," presented at IEEE Internatnal Cnference n Rbtcs and Autmatn. IEEE ICRA 2003 Cnference Prceedngs, Sept. 2003, Tape, Tawan, [8] W. H. Lee and A. C. Sandersn, "Dynamc rllng lcmtn and cntrl f mdular rbts," IEEE Transactns n Rbtcs and Autmatn, vl. 18, pp , [9] J. Denavt, and Hartenberg, R.S., "A knematc ntatn fr lwer par mechansms based n matrces," J. Appled Mechancs, vl. 22, pp , [10] M. Mnr, H. Dulmarta, G. Dangh, R. Mukherjee, R. L. Tummala, and D. Aslam, "Desgn, mplementatn, and evaluatn f an underactuated mnature bped clmbng rbt," presented at 2000 IEEE/RSJ Internatnal Cnference n Intellgent Rbts and Systems, Oct 31- Nv , Takamatsu, [11] M. A. Mnr and R. Mukherjee, "Under-actuated knematc structures fr mnature clmbng rbts," Jurnal f Mechancal Desgn, Transactns f the ASME, vl. 125, pp , [12] S. P. Krsur and M. A. Mnr, "Desgn, mdelng, cntrl, and evaluatn f a hybrd hp jnt mnature clmbng rbt," Internatnal Jurnal f Rbtcs Research, vl. 24, pp , TABLE 5 COMPARISON OF LOCOMOTION MODES, MOST FAVORABLE VALUES ARE HIGHLIGHTED IN BOLD. Flppng Inchwrm Effcent Rllng Fast rllng Best Trackng Rllng Mtrs Energy Cnsumptn Magnets NA NA NA (J/m) TOTAL Average Translatnal Speed (m/s)