Robotic snow cat. Guttorm Ringstad Opshaug and Per Enge ABSTRACT. Department of Aeronautics and Astronautics, Stanford University

Transcription

1 Robotic snow cat Guttorm Ringstad Opshaug and Pr Eng Dpartmnt of Aronautics and Astronautics, Stanford Univrsit ABSTRACT In rcnt ars, bra-through in GPS-navigation has ld to a whol nw rang of robotic control applications. Th Stanford Univrsit GPS laborator has pionrd rsarch in filds ranging from unmannd arial vhicls, robotic opn-pit mining trucs, and autonomous farm tractors. This sam tchnolog can also find us in grooming th slops of a si ara! With saft paramount, snow grooming is alwas prformd aftr closing tim of a si rsort, i.. vnings and nights. Robotic snow cats hav grat promis for rducing currnt oprating costs of snow grooming, partl du to cost of oprators woring trml odd hours of th da. With a stat-of-th-art navigation sstm, on ma oprat vn in full whitout conditions. Furthrmor, a robotic vhicl could b mor radil usd in avalanch pron aras. From th standpoint of a manufacturr, an autonomous snow cat has no nd for an oprator cabin (w/ chairs, controls, radios/cd-plars tc.). Rmoving that cabin ma wll sav wight as wll as cost of production. Finall, cabin rmoval will opn nw dgrs of frdom in snow cat dsign. A lowr snow cat would b mor stabl, and it could mor asil accss aras undr lifts. As a first stp towards th ultimat goal, a GPS-basd autopilot for a Bombardir MP Plus snow cat has bn implmntd and tstd. This papr givs a gnral sstm ovrviw and prsnts rsults from fild tsts at Alpin Madows Si Rsort. All tsts wr prformd without an attitud sstm, but th rsults still show total sstm rrors in th -cm rang.

2 . Introduction GPS basd robotic sstms ar currntl finding thir wa into th mart plac. GPS has nabld tractors to plow prfctl straight rows in farm filds [], and hug trucs to navigat opn pit mins [2]. Th purpos of this papr is to plor similar tchnologis for robotic grooming of si slops. Thr's mor to using a snow cat than simpl driving it around th si slops. Unli most comparabl hav machinr, snow cats us both front and rar mountd implmnts. Whras a front blad lvls major snow unvnnss, li moguls, a rar tillr rmovs snow lumps and rsidual surfac unvnnss. Both implmnts ar 4-6 dgr of frdom sstms, and th'r controlld through sparat jostics. Finall, snow cats ar strd around ithr using string whls, or 2 "tan li" tracspd control stics. Du to th plthora of controls involvd in handling a snow cat, full mastring such a vhicl is a sill that usuall tas svral sasons to acquir. Not onl must a snow cat oprator guid th vhicl along paths with minimum mutual ovrlap, but th oprator must also ma constant changs to th attitud of th front blad and rar tillr in ordr to nsur bst possibl grooming prformanc. Furthrmor, a groomr must judg th oncoming snow surfac in ordr to cut down all bumps and fill in all ruts, all whil constraind b following natural trrain faturs. Finall, oprators must adapt to a wid spctrum of snow conditions. Still, an prt groomr nds onl on singl pass through a mogul fild to lvl it prfctl. Snow grooming is alwas don aftr closing tim of a si rsort, whn no on is on th hills. Although public saft is maintaind such schduling mans trml odd woring hours for snow groomrs. Night wor during wnds is rathr pnsiv for si rsorts. Furthrmor, som si hills run onl on shift of grooming. This mans th rquir mor $2 snow cats to do th sam job that othr si rsorts do b grooming all night. In th qust to rmain opn to th public, snow cats ar oftn run during whitout conditions. Robotic snow cats with stat-of-thart navigation sstms should gratl improv grooming prformanc during low visibilit conditions as wll as rducing rgular oprating costs. Such robotic vhicls would hav no us for an oprator cabin. Rmoving that cabin should opn nw doors in snow cat dsign,.g. nabling lowr vhicls for as accss undr lifts. Although maing a snow cat full autonomous is th long-trm goal of this projct, sstms for oprator assistanc can b achivd mor radil. Rmoving som of th worload from an oprator should improv grooming and cut down on initial training tim. Thus, a GPS-basd snow cat autopilot was implmntd to tst on possibl tchnolog. 2. Eprimntal st up In this wor w had th grat fortun of borrowing a Bombardir MP Plus snow cat from Alpin Madows si rsort. W mountd a dual-frqunc GPS antnna on th roof of th oprator cabin and a UHF data lin antnna to its right sid-viw mirror. A Trimbl 74 RTK-GPS rcivr, a Pacific Crst Blu Bric UHF data radio, and a 3W powr invrtr wr fastnd to th insid of th oprator cabin. Thn, an Industrial Computr Sourc PC with a DBI "sunlight radabl" LCD displa and a 2V battr wr fit snuggl on th passngr-sid floor. Finall, a Pht 55C microcontrollr was attachd to th top of th PC. S pictur blow for passngr-sid quipmnt. Figur Tchnical quipmnt As GPS rfrnc, anothr 74/Blu Bric pair was put on top of th start towr of th Subwa lift at Alpin Madows. S pictur blow. Figur 2 GPS rfrnc station

3 Th full sstm ovrviw is shown in th figur blow. Snow Cat 74 UHF DL Ral Tim PC µc Snow Cat Trac Controls Figur 3 Navigation and control sstm ovrviw Th industrial PC ran th Ln ral-tim oprating sstm and communicatd with both th 74 and th microcontrollr through srial intrfacs. A sparat procss on th PC controlld ach srial intrfac, and pips wr usd to pass information to and from a third procss running th ral-tim controllr. Th figur blow shows data flow through th PC. Non-RT RT Non-RT Figur 5 Oprator sat with FNRs Aftr tsting all subsstms, th ntir tst ara at Alpin Madows was accuratl survd. Using that data, paths for th snow cat to follow could radil b mad. During all tsts two popl mannd th snow cat; an primntr and a rprsntativ from Alpin Madows. Kping up a long tradition in fild tsting, this saft officr could indpndntl stop th snow cat if somthing wnt wrong. Thus, ping tsts saf whil nabling th primntr to full concntrat on th tas at hand. Navigation Data Formatting Controllr Path DB Control Output Formatting 3. Vhicl modling Prvious wor controlling tracd vhicls has shown that such vhicls can b modld as uniccls [3]. Th figur blow shows a simpl modl for a snow cat. 2d 74 Srial I/O Pips Figur 4 Ral-tim computr ovrviw uc Srial I/O Bombardir MP Plus snow cats ar strd around using 2 trac-spd control stics, calld FNRs. Ths FNRs contain potntiomtrs, and th on-board computr sts trac spds proportional to th givn voltags across thos pots. Using a microcontrollr with digital-to-analog convrtrs, w b-passd th FNRs altogthr and strd th snow cat from our PC. Th pictur on th nt column shows th oprator sat of a Bombardir MP Plus. θ Iθ.. F M & R F 2 Figur 6 Snow cat modl Gθ &

4 Hr th snow cat bod is modld as a point mass for along-trac motion, and as a slab of inrtia for turning motion. Forcs, F /F 2, btwn snow and th tracs propl th snow cat forward as wll as turn it around. Friction forcs, R and G θ &, rsist linar and turning motion rspctivl. Along-trac quation of motion M & = F F R & Eq. 2 Rotational quation of motion ( F + F ) d I θ & + G θ& = 2 & Eq. 2 Sinc primnts mainl includ lin tracing, w onl considr th rotational quation of motion for our control sstm. W linariz that quation, and put it on stat spac form. & θ& = θ&& z z 2 = V θ + u G N I θ& θ θ& Eq. 3 Eq. 4 In th abov linarizd quations is prpndicular dviation from a curv, θ is hading dviation, θ & hading rat dviation and u is control input. Not that th 74 GPS rcivr onl masurs position and hading (z, z 2 ). Howvr, hading rat bcoms obsrvabl through our sstm modl. Furthrmor, all dviations ar calculatd whn masurmnts ar compard to a pr-programmd path. Th paramtrs of th modl includ vlocit, V, frictional cofficint of rotation, G, momnt of inrtia, I, and control input cofficint, N. 4. Modl paramtr idntification Coars stimats of snow cat modl paramtrs can b found b looing at its wight, ngin siz, garing ratios and gomtric dimnsions. Howvr, som of ths numbrs wr hard to com b, vn rading through th snow cat spcifications. Consquntl, w trid masurmnt basd sstm idntification tchniqus instad. In ssnc, on wants to input into a sstm a nown signal with plnt of spctral contnt in th frqunc rang in qustion. B simultanousl obsrving sstm outputs, on can stimat ffctiv transfr functions of a givn sstm through FFTs. For th vhicl at hand, w dcidd to input chirp signals to th snow cat turning control and log hading data. Chirps ar signals with constant amplitud, but linarl incrasing frqunc. Thus, chirps com out flat in frqunc domain. Th figur blow shows a chirp input and a hading output for on primntal run Input turning command (volts) Hading (dg) Tim (sc) Figur 7 Input-output rlations A total of runs wr prformd at m/s spd; si of which had th snow cat tillr ngagd, and fiv with th tillr disngagd. Th rason for altrnating th tillr was to find its ffct on sstm dnamics. For th givn spd and th givn snow conditions, no substantial diffrncs btwn th two cass wr found. Thus, all runs wr usd to bst dtrmin a singl st of snow cat modl paramtrs.

5 5. Path implmntation TF gain stimat Fild tsts Alpin Madows 3/6/ - - Although groomrs frquntl will bac up thir snow cats in ordr to turn around, ths fild tsts lacd an attitud sstm so paths wr mad b conncting straight lins and circular arcs. In this wa, a snow cat could alwas b run in th forward dirction through its path. For straight path sgmnts w stord start position, its lngth, its rfrnc hading, its rfrnc spd, and unit vctors along and prpndicular to th lin. θ -5 TF phas stimat (dg) Frqunc (Hz) l Figur 8 Bod plot for hading rspons Th figur abov shows th Bod plot of th snow cat hading rspons. Whras th llow dottd lins ar stimatd transfr functions for th diffrnt runs, th rd lin shows th mdian valu of thos primnts. Th grn lin signifis th bst fit of modl paramtrs, G/I and N, to th primntal data (rd lin). Although modl and masurmnts fit wll in our rgion of intrst, around. Hz, thr's a significant diffrnc btwn th two at highr frquncis. W blivd that discrpanc stmmd from signal aliasing. Thus, w ran th sam chirp signals from our tsts through our modl. Th blu lin in th figur abov shows th mdian valu of thos simulatd rsponss. Sinc th blu lin (modl) and th rd lin (ral sstm) match up wll, w bliv our sstm modl is valid vn at thos highr frquncis. r r ˆ Figur 9 Straight path sgmnt Th figur abov shows a snow cat along a straight lg. Whras hading dviation, θ, could b found b diffrncing masurd and rfrnc hadings, position dviation,, could asil b found from th quation blow. = r ˆ Eq. 5 ˆ A nw sgmnt was startd if quation 6 hld tru: r ˆ > l Eq. 6

6 For curvd sgmnts w stord cntr position, its radius, its rfrnc spd, its turn dirction, and a unit vctor tangnt to its it dirction. Control Law u Plant θ ^ Estimator Snsor r r Figur Curvd path sgmnt Th figur abov shows a snow cat along a curvd lg. Rfrnc hading, tangnt to an arc, was now calculatd for ach masurmnt point. Howvr, position dviation could asil b found b diffrncing snow cat distanc from th arc cntr and th arc radius (blow). = r Eq. 7 r rf Finall, sgmnts wr switchd if th following quation hld tru: r ˆ > Eq. 8 r rf ˆ Figur DLQG mchanization Th following 3 quations dscrib a currnt Discrt Linar Quadratic Estimator (DLQE), a Discrt Linar Quadratic Rgulator (DLQR) and DLQG stat propagation. ˆ u = [ I L C ] = K ˆ d d = Ad ˆ + d + B d u z + L d z Eq. 9 In th abov quations z is masurmnts, is á priori stat stimats, ˆ is á postriori stat stimats and u is control input. Whras A d, B d and C d ar modl matrics from quations 3 and 4, L d and K d rprsnt DLQE and DLQR cofficints rspctivl. 7. Closd-loop path-following rsults Aftr simulating and tsting svral sts of compnsator cofficints, w finall sttld down on a fairl modrat st. Th following two figurs show 6 full runs of th snow cat autopilot at Alpin Madows on March Fild tsts at Alpin Madows 3/22/ A snow cat compnsator would b providd with data indpndnt of sgmnt tp b formatting paths in th mannr abov. Thus, hand-ovr btwn sgmnts was virtuall samlss. 6. Controllr structur North (m) Rfrnc No tillr Tillr Evn though a classical PID controllr might hav word wll, w dcidd to go with a mor modrn Linar Quadratic Gaussian (LQG) compnsator for th problm at hand [4]. LQG compnsators us Linar Quadratic Estimators (LQE ~ Kalman filtr) to improv stat stimats, and Linar Quadratic Rgulators (LQR) to form control outputs basd on th givn stats. S figur for a discrt mchanization of LQG (DLQG) East (m) Figur 2 Ovrviw of autopilot primntal runs

7 North (m) Fild tsts at Alpin Madows 3/22/ Rfrnc No tillr Tillr Position man (cm) Position std. (cm) Hading man (dg.) Hading std. (dg.) Tabl Masurmnt statistics Th tabl abov shows man bias and standard dviation in position and hading masurmnts for all 6 fild tsts on 3/22/ Conclusion East (m) Figur 3 Cntr lg of autopilot primntal runs. In th prvious plots, rd dash dottd lins show dsird snow cat paths. Whras grn lins show rsults from 3 runs with tillr ngagd, blu lins signif runs with that implmnt disngagd. Not onl did w want to larn how disngaging th tillr affctd sstm dnamics, but w also ndd visual quus for vido taping th tsts. Although GPS was th onl mans of navigation for ths primnts, looing at trac mars in th snow gav a qualitativ answr on how wll th sstm prformd. P. rr. (m) H. rr. (dg) H.R. rr. (dg/s) Fild tst at Alpin Madows 3/22/ Control (V) Tim (sc) Figur 4 Sstm stats and control output Th plot abov shows all thr sstm stats for on run and th corrsponding control output. Blu lins ar masurd data whil rd ons ar stimats. Through ths tsts, w implmntd th first nown autopilot for a snow cat; a stp towards an ultimat goal of full autonomous snow grooming. Inspcting th rsults closl, on ma find dviations from th dsird path of up to mtr during turns, and transints of.5 mtrs whn acquiring straight sgmnts. Evn though ths rrors clarl would cd standards for an oprational sstm, comfort can b tan in th fact that virtuall th sam dviations rpat in all runs (Fig. 3). Such consistnc lads us to bliv that a mor "aggrssiv" compnsator has th prospcts of dcrasing rrors. Augmnting th compnsator structur with intgral control stats and fd-forward lmnts ma wll furthr improv prformanc. Howvr, rsults alrad show that sub-dcimtr dviations ar prvalnt onc initial transints di down (Fig. 3). Engaging th snow cat tillr had no noticabl ffct on sstm dnamics in an of our tsts. W bliv that th actuator authorit prsntd b th snow cat's 275-HP ngin plad a larg rol hr. Although w ran primnts on svral occasions, othr snow conditions as wll as diffrnt hill pitch ma affct our currnt findings. GPS was our onl mans of navigation in ths tsts. Although th 74 rcivr providd accptabl navigation accurac, availabilit of GPS provd rathr poor. Mountains and trs at Alpin Madows frquntl blocd SVs so GPS was unavailabl at crtain tims of da or at crtain spots on th tst hill. Still, th dual frqunc natur of th 74 was invaluabl whn it cam to r-acquiring RTK-grad positioning fast. Finall, wor is currntl undrwa looing into options for augmnting GPS and mor robustl navigating such nvironmnts.

8 Acnowldgmnts First of all, w'd li to than Alpin Madows Si Rsort for lnding us a snow cat with crw for our fild tsts. Dav Shtz, Dirctor of Snow Oprations at Alpin Madows, has bn of immns hlp sharing our visions and gtting this projct off th ground. W'd also li to than vron from Alpin involvd in th fild tsts; spciall thos in th mchanics shop that hlpd to rtro-fit th snow cat with our quipmnt, and to th saft officrs that ndurd "ndlss" hours of fild tsts in th oprator sat of th snow cat (Eric Carlson in particular). Bombardir Inc. also dsrvs thans for providing tchnical support whn installing quipmnt in on of thir MP Plus snow cat. Grat thans should go to a good frind and collagu, Bjørnar Vi, who indirctl providd this projct with all its tchnical quipmnt. Finall, th rst of th crw at th Stanford GPS lab has bn of grat hlp in brain storming idas around autonomous snow grooming. Rfrncs. Elaim, G., O'Connor M., Bll T., B.W. Parinson Sstm Idntification and Robust Control of a Farm Vhicl Using Carrir-Phas Diffrntial GPS ION-GPS 97, Kansas Cit, MO. Sptmbr J.M. Ston, J.D. Powll Carrir phas intgr ambiguit rsolution using dual frqunc psudolits ION-GPS-98, Nashvill, TN, Sptmbr 7, Ping Lu and Kou-Chi Lin Nonlinar control of an autonomous tracd vhicl Trans Institut MC, Vol 6, No 4, Franlin, Powll and Worman Digital Control of Dnamic Sstms Fig 6. p 265, Addison & Wsl, 2.nd dition, 992