The HoverBot C An Electrically Powered Flying Robot

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1 Unpublishd Whit Papr -- Draft Th HovrBot C An Elctrically Powrd Flying Robot by Johann Bornstin Dpartmnt of Mchanical Enginring and Applid Mchanics Th Univrsity of Michigan, Ann Arbor Advancd Tchnologis Lab 1101 Bal Avnu Ann Arbor, MI Ph.: (313) , Fax: (313) johannb@umich.du SUMMARY This papr dscribs th dvlopmnt of a fully autonomous or smi-autonomous hovring platform, capabl of vrtical lift-off and landing without a launchr, and capabl of stationary hovring at on location. Th ida to build such a modl-sizd arial robot is not nw; svral othr rsarch instituts hav bn working on arial robots basd on commrcially availabl, gasolin powrd radio-control modl hlicoptrs. Howvr, th arial robot proposd hr, calld th HovrBot, has two distinguishing faturs: Th HovrBot uss four rotor hads and four lctric motors, making it whispr-quit, asy-to-dploy, and vn suitabl for indoor applications. Spcial applications for th proposd HovrBot ar inspction and survillanc tasks in nuclar powr plants and wast storag facilitis. Without a skilld human pilot at th controls, th formost problms in ralizing a modl hlicoptr-sizd flying robot ar stability and control. It is ncssary to invstigat th stability and control problms, dfin solutions to ovrcom ths problms, and build a prototyp vhicl to dmonstrat th fasibility of th solutions. Th proposd HovrBot will hav ight input snsors for stability and control, and ight output actuators (4 motors and 4 srvos for rotor pitch control). Th rsulting control systm is a vry complx, highly non-linar Multipl-Input Multipl-Output (MIMO) systm, in which practically all input signals affct all output signals. A Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 4

2 surprisingly simpl xprimntal control mthod, calld additiv control, is proposd to control th systm. This mthod was succssfully usd in th currnt xprimntal prototyp of th HovrBot (although with fwr input signals). It is also proposd to invstigat two altrnativ control mthods, adaptiv control and nural ntworks, both of which appar to b spcially suitabl for th Multipl-Input Multipl-Output control problm. If succssful, th projct will rsult not only in a working prototyp of a flying robot, but it will also provid important insight into th functioning of various control mthods for vry complx MIMO systms. 1. INTRODUCTION At first glanc, th thought of arial robots might invok som skpticism. Howvr, a survy of th litratur and talks with othr univrsitis rvald that not only ar arial robots tchnically fasibl, but also that numrous crdibl Univrsitis (such as Gorgia Tch, CMU, U of Southrn California, UT-Arlington) ar alrady conducting srious fforts to dvlop arial robots (s Appndix D, vido tap). Fixd-wing unmannd aircraft ar bing usd routinly for military and mtorological purposs and hav bn in srvic for yars. Typically, ths Adrons@ rquir mobil lounging platforms and rmot opration by traind prsonnl. Th typ of flying robot w addrss in this proposal, howvr, is quit diffrnt. Our aim is th dvlopmnt of a fully autonomous hovring platform, capabl of vrtical lift-off and landing without a loungr, and capabl of stationary hovring at on location. In short: th functional quivalnt of a hlicoptr, only much smallr and, of cours, fully autonomous. With this concpt in mind, it coms as no surpris that most of th ongoing work on arial robots is actually don with commrcially availabl modl hlicoptrs, marktd for th radio-control nthusiast. Th modl hlicoptrs undrgo xtnsiv modifications [Bakr t al., 1992], to mak thm suitabl for autonomous opration and th prformanc of usful tasks. A guidlin of sorts for tasks xpctd from a working arial robot has bn stablishd with th annual Arial Robot Comptition, sponsord by th Association for Unmannd Vhicl Systms (AUVS). Th mor promising arial robots dsignd by th abov Univrsitis ar basd on gasolin powrd, modl-sizd hlicoptrs, and rsarch fforts concntrat on dsigning or down-scaling th autopilots that would stabiliz ths hlicoptrs in flight. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 5

3 Figur 1: Picturs of a Comptition: (following pag) a. Bst prformanc at th 1991 comptition: th ntry from Th Univrsity of Txas. Crashd aftr 6 sconds. b. Modl hlicoptr with human pilot at th Radio Control. Rd disks in gray arna must b pickd up individually and airliftd to anothr ring. (1992 comptition). c. This singl-propllr (not rotor) drivn craft crashd aftr 5 sconds in th air: ngin failur (1992 comptition). d. Larg modl hlicoptr from Gorgia Tch. Crashd aftr 6 sconds. Inrtial navigation systm failur (1992 comptition). Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 6

4 2. STATEMENT OF THE PROBLEM Th formost problm with modl-sizd hlicoptrs is stability. All hlicoptrs (larg ons as wll as modl-sizd ons) ar dynamically instabl bcaus of th lack of damping [Saundrs, 1975]. In th absnc of natural damping (typically found in ground-basd vhicls in th form of friction), a hlicoptr must b stabilizd by th pilot. This task is asir for larg hlicoptrs, bcaus thy hav a largr tim constant. In modl-sizd hlicoptrs th tim-constant is vry small, and stabl hovring is difficult to achiv. For this rason, it taks modl-hlicoptr pilots months and months of xrcis and training to acquir th skill of manual stabl hovring [Tradlius, 1991]. In a robotic modl-sizd hlicoptr, th difficulty of stabilizing th craft falls onto th onboard controllr. Tchnologically, this is quit a challng sinc th smallr tim constants rquir a much fastr rspons tim, which, in turn, rquirs accurat motion snsors and fast computrs. Yt, th modl-sizd hlicoptr is svrly limitd in its payload capacity and can only carry lightwight, lss powrful computrs and lss accurat snsor systms. In our projct w add a furthr dimnsion to th challng by attmpting to dsign an lctrically powrd flying platform. If succssful, an lctrically powrd dvic would hav vry uniqu advantags for crtain applications, bcaus it would b suitabl for indoor applications, asy to dploy, and vry quit. W nvisag applications in hazardous nvironmnts in gnral, and particularly in Nuclar Powr plants, whr a ral nd for a hovring inspction unit xists. Othr potntial applications ar mrgncy rspons, as wll as polic and military applications. Th only accptabl solution for most of ths applications is an lctrically powrd platform. Th disadvantag of lctric powr compard to gasolin powr is th vn furthr rducd payload capacity. W propos to ovrcom both th payload problm and th stability problm by implmnting a uniqu four-rotor dsign. Four-rotor platforms ar not a nw ida C th history of vrtical flight shows svral attmpts at implmnting such dsigns (th arlist dating back to 1922 [Young, 1982]). As much as ths attmpts improvd th ovrall payload capacity, thy all found thmslvs discontinud bcaus of th difficulty in manually controlling th four rotors. W bliv that our proposd approach, will ovrcom th problms of arlir 4-rotor dsigns and bring into xistnc an actually functioning, lctrically powrd, fully autonomous 4-rotor flying platform. Our prliminary xprimntal rsults to dat show that th payload problm, although vr-prsnt in all dsign considrations, is succssfully addrssd by th 4-rotor dsign. Th focus of this proposal is thrfor th qustion of stability. W bliv that th rsults of our rsarch will not only hlp crat a flying robot, but thy will also hav dirct baring on th dsign of larg (popl carrying) 4-rotor rotorcrafts. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 7

5 3. POSSIBLE SOLUTIONS Hr at th Univrsity of Michigan w hav bn working sinc July 1992 on th dsign of an xprimntal prototyp of an arial robot, calld th HovrBot. Our dsign has two distinguishing faturs: Th HovrBot uss four rotor hads and four lctric motors, making it whispr-quit, asyto-dploy, and vn suitabl for indoor applications. Figur 2 shows our artist's dpiction of th HovrBot; rality is rducd to th smallr inst in Fig. 2, showing our actual xprimntal prototyp during stabl 1 hovring. Not that at this tim th motion of th xprimntal prototyp is confind by a stationary fixtur. This fixtur prohibits motion in x and y dirction, but allows pitch, yaw, and roll, as wll as vrtical (z-dirction) motion. In th following Sctions w will discuss th HovrBot dsign in mor dtail. Our aim is to convinc th radr of th fasibility of th concpt, and to xplain th challng of th control and stability problms. 3.1 Elctrically Powrd Rotorcrafts W propos to dvlop an lctrically powrd rotorcraft. To dat, lctrical powr has bn found unsuitabl for rotorcrafts, xcpt for th vry lightst of modl-hlicoptrs. Th rason for this can b xplaind with a fw firstapproximation dsign guidlins for rotorcrafts (S Fig. 3). As a rul of thumb, th powr P rquird to dvlop thrust (i.., lifting capacity) T is givn by P T 3 Figur 3: Powr vs. Wigh chart for lctric rotorcrafts. This function is sktchd in th Powr vs. Wight chart of Fig. 3. Th offst P 0 rprsnts th powr rquird for lifting th motors and structur. Th battry powr vs. battry wight (for a givn maximum flight duration) is plottd as a group of dottd lins, ach for a givn flight duration. Bcaus of th non-linar natur of Eq. (1) lctric hlicoptrs cannot b scald: It is impossibl to simply dsign around a largr motor and largr battry, to gt a largr (rad: strongr rotorcraft). As Fig. 3 shows in principl, thr is only a small rang of fasibl dsigns. Commrcially availabl modl hlicoptrs dmonstrat this principl: only P Rquird powr: P Battry powr: P W P 0 hobo20c.drw, hobo20c.wmf T Fasibl dsign rang t=1min t=5min t=10min t=15min W Battry 1 Mor on this in Sction 4 C Exprimntal Rsults to Dat. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 8

6 xtrmly lightwight (2-3 lb) modls with 5-6 minuts flight duration ar availabl. Ths modls us ultra-light building matrials and control lmnts. A robotic rotor-craft would nd an onboard computr and snsors, in addition to th convntional radio-control componnts. For this rason, w conclud that it is unfasibl to build a robotic rotorcraft basd on currnt lctric powr modl hlicoptr tchnology. To ovrcom this smingly inhrnt limitation, w propos to dsign a multipl rotor platform, calld th HovrBot. In principal, th Hovrbot can b considrd as four individual lctric modl hlicoptrs, linkd togthr at thir tails. Whil this dsign slightly incrass th wight of th structur, its advantag is that crtain componnts ndd in vry convntional modl hlicoptr (such as gyros and th rcivr and its powr sourc) can b shard among th four units, and so can spcial componnts for autonomous opration (such as a computr board, mor gyros, and othr snsors). In prliminary xprimntal battry nduranc tsts, w achivd 3-minut flights with our prototyp HovrBot and convntional NiCad battry packs. Th tsts wr somwhat flawd by infrior charging quipmnt that wouldn't allow optimal charging of th clls. Rotor blad loading, powr transmission, and motors wr also far from optimal in our arly xprimnts. W xpct that by th nd of a thr-yar projct, w will hav improvd on ths factors to achiv flight tims of 4-5 minuts with standard NiCad battris. Mor important, nw battry tchnologis promis additional two- to thrfold improvmnts in wight-to-charg ratios. Drivn by th rapidly xpanding markt of notbook computrs, mor powrful nickl-hydrat battris ar alrady in us, which provid tims highr nrgy dnsitis, and rcntly Byt magazin [Byt, 1993, March, p. 24) rportd on th dvlopmnt of nw lithium-iron battris that promis 3 tims longr opration than Alkalin battris of th sam siz Four-Rotor Dsign In th arlir days of vrtical flight xprimntation (bfor th dvlopmnt of th ingnious cyclic/collctiv pitch concpt C which is now usd by all modrn hlicoptrs) dvloprs lookd at th intuitivly asy control functionality of 4-rotor dsigns. Whil som of ths prototyps did indd fly, non vr mad it into production. Th rason most oftn quotd was th fact that th 4-rotor machins wr difficult to control and stabiliz: With manual controls, th pilot would hav to coordinat at last four control paramtrs (for xampl, th pitch of th rotor blads), which wr rathr countr-intuitiv (s principl of opration, blow). Anothr rason to considr multipl rotors is to achiv largr pay-load capacitis thn what is possibl with singl rotor dsigns. Th rason for this is th fact that th thrust of a rotary wing is proportional to th squar root of th ara swpt through by th rotor. This ara is also calld th rotor 2 Ultimatly, of cours, w ar intrstd in wight-to-nrgy ratios. Yt, th litratur quotd sizto-nrgy ratios (rlativ to xisting products). W quot ths xampls hr to show th fasibility of lctric powr, whil th focus of th proposal is on th stability and control problm. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 9

7 disk. I othr words, th largr th rotor disk, th mor thrust is dvlopd. Obviously, thr ar tchnical limitations to th maximal siz of th rotor disk. Multipl rotors multiply th ffctiv rotor disk ara, although thr ar, of cours, losss. Most notably ar losss causd by th additional wight of th structur and losss du to turbulnt intraction of th air undrnath th disks. Nonthlss, tandm rotor dsigns ar clarly suprior to singl rotor hlicoptrs in trms of pay-load capacity [Lightbody and Poyr, 1990]. 3.3 Control of th HovrBot Th control systm of th HovrBot is dsignd to allow ithr fully autonomous opration or rmot opration by an unskilld oprator. To ithr, th HovrBot will appar as an omnidirctional vhicl with 4 dgrs of frdom: (1) up/down (2) sidways, (3) forward/backward, and (4) horizontal rotation. High powr Low powr Mov sidways Low powr Thrust Rotors Sid viw Thrust Up/down motion is asily controlld by collctivly incrasing or dcrasing th powr to all 4 motors. Control ovr (2) can b achivd as xplaind in Fig 4a: For xampl, incrasing th powr to th two lft rotors lifts th lft sid up and gnrats a thrust componnt to th lft. Consquntly, th HovrBot movs to th right. By th sam principl, adding powr to th two rar Rotat right High powr Inducd momnt du to rotor drag, works in opposit dirction of rotor turning. Rotat lft Figur 4: Controlling th HovrBot: a. Mor powr to th lft rotors lifts th lft sid up and producs a lft-thrust. b. Mor powr to th diagonally arrangd rotors rotating in th sam dirction causs a diffrnc in inducd momnt. rotors causs th HovrBot to fly forward. Th implmntation of horizontal rotation control is lss obvious: Whn a rotor turns, it has to ovrcom air rsistanc. Th ractiv forc of th air against th rotor causs a ractiv momnt calld th Ainducd momnt.@ Th inducd momnt acts on th rotor in th dirction opposit to th rotation of th rotor. As vryon knows, convntional hlicoptrs rquir th tail-rotor to countract th inducd momnt. In th HovrBot both sts of diagonal rotors turn in opposit dirctions (as indicatd by th opposit dirction of th arrows in Fig. 4b). As long as all rotors xprinc th sam inducd momnt, which is mostly a function of spd of rotation and rotor blad pitch, th sum of all inducd momnts is zro and thr is no horizontal rotation. If on st of rotors, for xampl th on that turns countr-clockwis in Fig. 4, incras thir rotational spd or thir pitch, th rsultant nt inducd momnt will caus th HovrBot to rotat clockwis. It is important to not that bcaus of th diagonal arrangmnt, this opration has no ffct on translation Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 10

8 in x or y dirction. Th ffct on up/down motion can b compnsatd by rducing th pitch or spd of th othr diagonal pair, although in practic this is not quit so asy without som sort of fdback control. In our xprimntal prototyp w wr abl to implmnt ths control functions with good rsults. Sction 4 discusss th xprimntal rsults obtaind to dat in mor dtail. 3.4 Stability W bliv that stability is th formost challng for any ffort to build a modl-sizd robotic rotorcraft. As xplaind bfor, in th absnc of natural damping, all rotorcrafts must b constantly stabilizd by th pilot or auto-pilot. In modl-sizd hlicoptrs this prsnts a formidabl difficulty, bcaus of th much smallr tim-constants. This is th rason why modl-hlicoptr pilots nd months and months of training, just to kp thir hlicoptrs in stabl hovring. Modl hlicoptr pilots w talkd to confirm that stabilizing a small modl hlicoptr is vn mor difficult than stabilizing a largr modl hlicoptr Largr Tim-Constant With th Proposd HovrBot Th 4-rotor dsign of our proposd HovrBot C originally motivatd by considrations of payload C appars to hav on uniqu advantag ovr convntional hlicoptr dsigns: th distributd wight of th 4 rotor hads incrass th momnt of inrtial and thrby th tim constant of th systm. To illustrat this point, w can roughly stimat that th momnt of inrtia, J, of a 6 kg convntional (singl rotor) hlicoptr modl around its longitudinal axis is J = 0.06 Kgm 2. By comparison, th 4-rotor HovrBot with th sam wight has a momnt of inrtia of J = 1.53 Kgm 2 around its last favorabl axis. In othr words, th momnt of inrtial of th HovrBot is approximatly 1.53/0.06 = 25 tims largr than that of a comparabl convntional hlicoptr. Sinc th tim-constant J of th systm is proportional to th squar root of th momnt of inrtia (J % J 2 ), th tim-constant of th HovrBot is (25) 2 = 5 tims largr than that of th convntional hlicoptr dsign. Stabilization of this rotorcraft will b gratly facilitatd by th much largr tim-constant Th Dual Control Approach Anothr important advantag of our 4-rotor dsign is th control flxibility gaind from th us of four indpndnt motors. As w xplaind in Sction 3.3, th HovrBot can b fully controlld by controlling th thrust of th four rotors. In convntional hlicoptrs thrust is controlld in two diffrnt ways: a) by adjusting th motor powr and b) by adjusting th rotor blad pitch (th angl of attack of th rotor blads). Adjusting th motor powr is usually not an fficint mans of control, bcaus gasolin powrd ngins do not rspond quickly nough (spcially with th larg inrtia of th rotor) Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 11

9 to th pilot's commands. By contrast, adjusting th rotor pitch has an immdiat ffct on th thrust: a largr pitch angl incrass th thrust. Howvr, a largr pitch angl also incrass th powr nds of th rotor and must thrfor b accompanid by an incras in motor powr. Bcaus of th kintic nrgy stord in th rotor, th incras in motor powr dos not hav to b availabl immdiatly, a short dlay is accptabl. Thus, th immdiat action of pitch control combind with th slightly dlayd action of motor powr control works wll. In normal-sizd hlicoptrs (without automatic control), dtrmination of th propr mixtur btwn pitch incras and motor powr incras is lft to th skill of th pilot. Th problm is diffrnt in th HovrBot. Hr, controlling th motor powr is somwhat mor ffctiv bcaus w us lctric motors. W found that w can prform th typical control functions (up/down, forward/backward and sidways tilting, rotation) just by controlling th rotor thrust. Howvr, in our systm th craft must also b stabilizd by varying th rotor thrust. In our xprimntal systm w found that th thrust control must ract at last tn tims fastr in ordr to dampn undsirabl oscillations causd by xtrnal disturbancs. Thus, w propos a dual control approach, in which fast-acting pitch control is th primary mans for damping and stabilizing, and motor powr control is th primary mans for controlling th stady stat thrust and thus th motion of th HovrBot. In practic, both control actions ar strongly intrrlatd. Any control signal going to, say, th front lft motor must also gnrat a scondary control signal that affcts th pitch actuator of th front lft rotor, and vic vrsa. Th xact natur of this intraction is xtrmly difficult to dtrmin analytically. Th intraction is highly non-linar and thr ar numrous paramtrs that ar practically impossibl to masur. Our focus in th proposd work will b to dvlop xprimntally a nw controllr capabl of prforming this complicatd stability and control task Th Control Systm Th proposd control systm rquirs ight diffrnt snsors, as shown in Figur 5. To undrstand how th systm works, w rcall that our two primary purposs ar to stabiliz and control th systm. Bcaus of th small tim-constants w will nd fast-rsponding snsors to masur th rat of rotation around th thr principal axis. Ths snsors ar th thr gyros in Fig. 5; thy will b usd primarily for damping. To control th HovrBot (i.., to hold it in stationary hovr or to mov it in a controlld fashion) w nd th thr acclromtrs. Ths snsors ar mountd at th cntr of th craft and masur th acclration of th HovrBot in x, y, and z dirction. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 12

10 Thortically, it is concivabl to us ithr th gyros or th acclromtrs, bcaus th data from ithr group can b computd from data from th othr group. For xampl: If th HovrBot was idally built and if thr wr no xtrnal disturbancs, thn tilting to th right (masurd by gyro x) would rsult in a prdictabl acclration, vlocity, and translation to th right. In rality, howvr, it is likly that vn in th absnc of masurabl tilting thr will b sidways thrust componnts that will acclrat th craft sidways (bcaus of construction tolrancs and xtrnal disturbancs). Convrsly, w bliv that th acclromtrs cannot substitut for th immdiat rspons of th gyros to tilting. Extnsiv xprimntation will b rquird to validat or invalidat ths assumptions. Additional snsors ar th ultrasonic hight snsor and th fluxgat compass. Th hight snsor will b usd nar ground lvl, to provid vry accurat hight information (on th ordr of a fw millimtrs [POLAROID, 1993]). Th fluxgat compass provids accurat hading information "0.5 dgrs if no disturbing magntic filds ar prsnt. Again,th fluxgat compass cannot rplac gyro 2 bcaus of its slow sampling tim (on th ordr of 0.4 sc [KVH, 1993]). Th signals from all ight snsors ar constantly sampld by th main control block, labld multipl input multipl output (MIMO) in Fig. 5. Th MIMO block computs control signals for all ight outputs: four motors and four pitch controllrs. To implmnt complt control and stabilization, ach output is affctd by all ight inputs, rsulting in a matrix of 8 H 8 non-zro lmnts in th MIMO control block. Attmpts to solv similarly complx control problms for convntional modl hlicoptrs ar currntly undr way; Schwartz and Klir [1992] rport on th us of fuzzy logic controllrs and Lwis t al. [1993] rport on work in progrss at Purdu, whr Ahmad applis Nural Ntworks. In prvious work with MIMO controllrs [Bornstin, 1992, 1993] and in our prototyp HovrBot (discussd in Sction 4) w hav had good rsults with an approach w call additiv control. This approach is dscribd in Sction 4, using th xampl of th prototyp HovrBot. Motor 1 Pitch 1 Motor 2 Pitch 2 Motor 3 Pitch 3 Motor 4 Pitch 4 Multipl Input - Multipl Output Additiv Controllr hobo1prp.drw.wmf acclromtr x gyro x acclromtr y gyro y ultrasonic snsor z acclromtr z compass Figur 5: Eight snsor inputs and ight actuator outputs ar intrconnctd in th HovrBot control systm. gyro Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 13

11 4. EXPERIMENTAL RESULTS TO DATE Figur 6 shows th HovrBot prototyp during stabl hovring, 4-5 inchs abov th floor. Th fan in th background cornr is capturd in this pictur to nhanc th viwr's prcption of airflow disturbancs. In rality, th ffct of th fan is ngligibl compard to th turbulnc cratd by th four rotors in th vicinity of th walls. Ths turbulncs ar so powrful that loos shts of papr would fly all ovr th room. W rport ths conditions hr to mak it clar that our prototyp HovrBot achivd stabl hovring undr conditions of intns turbulnt disturbancs. W bliv that our prliminary xprimntal rsults hav provn th controllability of th HovrBot and indicat that stability can b achivd in th systm. Figur 7 shows th currnt control systm for on of th four motors. Idntical control units ar implmntd for th rmaining thr motors and for th four pitch control srvos. Th fdback signal for Figur 6: HovrBot during stabl hovring. Stationary fixtur inhibits horizontal translation (x and y dirction). Pitch, yaw, and roll, as wll as vrtical motion, ar nabld. W hav built th xprimntal prototyp HovrBot shown in Fig. 6. In ordr to avoid damag to th craft during xprimntation, th prototyp is fixd in a stationary fixtur which inhibits translation in x and y dirction but prmits pitch, yaw, roll, and vrtical (z-dirction) motion. W hav implmntd control ovr th four motors and thir rotor blad pitch (i.., control ovr all ight output actuators is implmntd). W hav not yt implmntd th acclromtrs nor th gyros. Instad, w driv fdback data on tilting in th x and y dirction from a computr-gam joystick. This joystick is mountd at th cntr of th HovrBot and connctd through a vrtically sliding and frly rotating shaft to th stationary framwork shown in Fig. 6. In addition to th angl masurmnt capability, th joystick provids an inxpnsiv ball-and-sockt joint for a total of four intrscting axis of motion. Th MIMO control systm from Fig. 5 is partially implmntd: th joystick radings provid rlativly fast angular position (tilt-x and tilt-y) information, from which rat-of-rotation information can b computd to mulat th radings from gyro-x and gyro-y. W hav also installd a fluxgat compass which hlps stabiliz th orintation of th HovrBot (although its 0.4 sc sampling tim is too slow for adquat damping). Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 14

12 hight control shown in Fig. 7 is not implmntd. Th rfrnc signals ar sampld by th computr from a 4-channl radio-control unit. Th xprimntr can us th dual-joystick radio-control transmittr to control hight, orintation, and tilting in x and y dirction. Fig. 7 xplains our currnt implmntation of additiv control. In additiv control th control signal (in Fig. 7, th motor spd) is th rsult of adding up diffrnt branchs of inputs. For xampl: Suppos that at som tim th lft front sid of th Hovrbot is highr than th right sid, but lowr than th rar sid. Bcaus of this tilt in x-dirction, th additiv controllr will rduc powr to th lft front motor. Bcaus of th simultanous tilt in y-dirction th tilt-y snsor will incras th powr to this motor. Simultanously, th rotation snsor and th hight snsor may add or subtract powr. All this adding and subtracting of signals taks plac in on sampling intrval (20 ms) and rsults in a singl motor spd command bing snt to th motor. Intuitivly, on may not b convincd that th rsult of all ths additions and substraction is a usful control signal. Yt, our xprimnts show that th HovrBot can simultanously prform all ths corrctiv actions. Th bst way to gt an imprssion of th prformanc of th Hovrbot prototyp is to watch th first 5-minut sgmnt of th vido tap, which is submittd with this proposal as Appndix D. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 15

13 PID controllr Intgral Ki dt Proportional K p Diffrntial K d t PID controllr Intgral Ki dt Proportional K p Diffrntial K d t PID controllr Intgral Ki dt Amplifir/ Motor Proportional K p Diffrntial K d t PID controllr Intgral Ki dt Proportional K p Diffrntial K d t Figur 7: Additiv control systm in th xprimntal prototyp. Four diffrnt fdback signals ar fd into ach actuator. Th Hovrbot has ight actuators. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 16

14 7. BIBLIOGRAPHY 1. Bakr, N.C., MacKnzi, D.C., and Ingalls, S.A, 1992, "Dvlopmnt of an Autonomous Arial Vhicl: A Cas Study." Journal of Applid Intllignc Vol. 2, No. 3, Spt pp. prprint. 2. Bornstin, J., 1992, "Compliant-linkag Kinmatic Dsign for Multi-dgr-of-frdom Mobil Robots." Prsntd at th SPIE Symposium on Advancs in Intllignt Systms, Mobil Robots VII, Boston, MA, Nov Bornstin, J., "Multi-layrd Control of a Four-Dgr-of-Frdom Mobil Robot With Compliant Linkag." Accptd for prsntation at th 1993 IEEE Intrnational Confrnc on Robotics and Automation, Atlanta, Gorgia, May 2-7, BYTE Magazin, 1993, March, p Fng, L, Korn, Y., and Bornstin, J.: "An Adaptiv Motion Controllr for a Diffrntial-Driv Mobil Robot." Submittd for publication to th IEEE Journal of Robotics and Automation. Fbruary Johnson, W., 1980, "Hlicoptr Thory" Princton, N.J. : Princton Univrsity Prss. 7. KVH Industris, Inc., 1993, 110 Entrpris Cntr, Middltown, RI Lwis, M.A., Fagg, A.H., and Bky, G.A., 1993, "Th USC Autonomous Flying Vhicl: An Exprimnt in Ral-Tim Bhavior Basd Control." Submittd for publication in th IEEE Intrnational Confrnc on Robotics and Automation, Gorgia, Lightbody, A. and Poyr, J., 1990, ATh Illustratd History of Hlicoptrs.@ Publications Intrnational, Ltd., Lincolnwood, Illinois. 10. MacKnzi, D.C. and Arkin, R.C., 1992, "Autonomous Hlicoptr Position Dtrmination Using An On-board Intgratd Vision Systm." Prsntd at th Applid Machin Vision Confrnc '92, Atlanta, Gorgia, Jun 1-4, POLAROID Corporation, 1993, Ultrasonic Componnts Group, 119 Windsor Strt, Cambridg, MA Saundrs, G. H., 1975, "Dynamics of Hlicoptr Flight" Nw York : Wily. 13. Tradlius, P., 1991, ABasics of Radio Control Hlicoptrs.@ Air Ag, Inc., Wilton, Conncticut. 14. Young, W., R., 1982, "Th Hlicoptr." Publication Timlif Books, Virginia. Bornstin, "Th HovrBot C An Elctrically Powrd Flying Robot" Pag 17