A HYDRAULIC OPEN LOOP SYSTEM FOR CONTROLLED EXCAVATION ALONG PRESCRIBED PATH. E. Bundy, W. Gutkowski

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1 A HYDRAULIC OPEN LOOP SYSTEM FOR CONTROLLED EXCAVATION ALONG PRESCRIBED PATH E. Bundy, W. Gutkwsk Insttute f Buldng Mechanzatn and Rck Mnng Ul.Racjnalzacj 6/8, 0-67 Warszawa Pland e-mal: eb@mbgs.rg.pl;wtld.gutkwsk@ppt.gv.pl Abstract: In ths study, an pen lp hydraulc system fr cntrlled excavatn s prpsed. It s based n a knematcally nduced mtn f the excavatr bucket. The three degrees f freedm f the latter are drven, n a unque way, by three ndependent hydraulc actuatrs. All f them are flled wth the l n such a way that, at any nstant f tme, ther lengths defne pstn f the bucket. A system f three frce-ndependent valves s appled. Ths way the executn f desred trajectry can be perfrmed even n cases f sme varatns f sl prpertes. Keywrds: excavatn, cntrlled mtn, hydraulc cntrller, autmatn, pen lp system.. INTRODUCTION Recently, there s an ntensve research carryng n n the feld f autmatn and rbtcs f excavatn prcesses. Tw man grups f nvestgatn can be here recgnzed.the frst cnsstng n the remte cntrlled f earth mvng machnes and pure autnmus excavatrs. These studes are rented n wrks n hazardus and nnstructured envrnments, such as nuclear waste and spatal applcatns []. The secnd grup f nvestgatn s cncentrated mre n lmtng the human effrt, and lmtng the need fr very hgh skll peratrs. The nvestgatns cnsst mstly n the autmatn f a number f repettve tasks. Here are cnsdered excavatns alng prescrbed paths, dggng hles and trenches, as well as drllng and plng. Cllectng expermental data cmng frm the bucket pstn and the frce at ts tp, Bernld [ ] nvestgated the pssblty f autnmus excavatn fr dfferent tasks, 007_TB.dc- sl prpertes and bucket cnfguratns. A smulatn study f cllectng a scpful f sl fr a bucket, fllwng the gven trajectry was dscussed by Vähä and Skbnewsk [ ]. Ha et al. [ 4 ] presented the methdlgy, desgn and expermental results f frce and bucket pstn cntrl applyng electrhydraulc serv systems. Kesknen et al. [ 5 ] dscussed cntrl f a trajectry f excavatr - based sheet pler system. Ther nvestgatns are based n angular and actuatr sensng methd. Cntrl n abve wrks was mstly prpsed as clse lp systems schematcally presented n Fg.. Fgure. A clse lp cntrl wth lad-dependent prprtnal valves In ths study, an pen lp hydraulc system fr excavatn, and ther wrks usng

2 an excavatr, s dscussed. It s based n the prevus authr s wrks [6,7], cnsstng n knematcally nduced mtn f the excavatr bucket. The three degrees f the latter are drven, n a unque way, by three ndependent hydraulc actuatrs. All f them are flled wth the l n such a way that at any nstant f tme ther lengths defne pstn f the bucket. The presented system allws the bucket t vercme small bstacles ccurrng n the sl. The mtn s lmted nly by maxmum pssble frces exerted by actuatrs and by ttal pwer f excavatr engne. It means that n cases f larger bstacles, the actn f the peratr s necessary. The flw Q f the hydraulc l nt -th actuatr s defned n the fllwng way. Frst, three ndependent varables descrbng the bucket mtn are assumed. In ths case, they are tw crdnates f the bucket edge, and rentatn f the bucket as a rgd bdy. Thrugh knematc relatns, the bucket three crdnates are defned by lengths f three actuatrs. Knwng the velcty f the actuatr cylnders and ther crss sectn areas, the flw Q s defned. Ths apprach can be als appled t drllng and plng. In ths case ether a drllng unt r vbratry unt replaces wth the bucket. It s assumed that the system can wrk autmatcally. Hwever, t s als pssble that t may assst the peratr n easng hs wrk. The assumptn n the autmatc cntrlled excavatng s vald nly fr cases wth resultantly small senstvty f the tl mtn n perpendcular drectns t ts trajectry.. KINEMATICS Cnsder an excavatr wth three cplanar rgd lnks, ntercnnected by jnts n an pen chan ( Fg. ). Assumed are jnt varables α, α and α, relatve angles between the lnks. The cnfguratn f the mechansm s gven by a vectr α = [α, α, α ] T wth cnstrants α - α α. The cnstrants cme frm the lmted lengths f actuatrs drvng the mechansm. All admssble α cnsttute the cnfguratn space f t. In rder t specfy the space, a base frame s establshed at the jnt between the bm and the excavatr bdy. The task space fxed wth the bucket and rgn at ts tp, s a space f all bucket pstns x and rentatns α. The frward knematcs fr ur prblem s then determnng the mappng Fgure The excavatr under cnsderatns X = [ x( α ), z( α ), α ] T ( ) In the frm l cs( α ) l cs( α ) ( α ) x = l cs ( α ) l sn( α ) ( α ) z = l l sn sn dz = ctg( α dx δ () (4) where l, l, and l are lengths f the bm, the arm, and the bucket respectvely. It s assumed that the rentatn f the bucket s gven wth respect t the tp trajectry, accrdng t the relatn (4), n whch δ s a cnstant dependng n the bucket shape ) ()

3 .TRAJECTORY PLANNING The frst step n the present cnsderatns s trajectry plannng f the excavatr bucket r f a tl fr plng r drllng. Let assume a repettve curve alng whch the dggng has t be executed. Ths may be dggng f a trench r drllng alng a straght lne. The trajectry plannng cnssts n checkng f assumed trajectry can be physcally realzed. In the ther wrds, f the bucket travellng alng assumed trajectry s hldng n the admssble wrkng space. The latter cnssts nt nly f the bucket tp pstn, but als f bucket rentatn, whch s defned tgether wth the trajectry lne ( Fg. ). The admssble wrkng space s f curse lnked t the excavatr pstn n the dscussed prblem. The latter s defned by just mentned crdnate system attached t the excavatr bdy. 4.TRAJECTORY GENERATION The trajectry s calculated n the hst cmputer. Then the flw Q cmmand s cnverted thrugh PLC nt the sgnal vltage needed t actuate the lad-ndependent prprtnal valve transferrng the l flw t actuatrs. It s assumed that mtn s slw enugh t neglect the nerta terms, and t treat the mtn as knematcally nduced. Addtnally t s pstulated that the ttal pwer needed t perate the mechansm desn t reach at any nstant f tme ts maxmum value. Under abve cndtns, the lad-ndependent prprtnal valves are assumed t assure the desred bucket mtn. The whle prcess s then defned by the fllwng system f equatns. Frst, the varables α are calculated applyng the nverse knematcs. Next, jnt space elements α are related t actuatr lengths h. In the case f cnsdered excavatr, after nspectng Fg.,4,5 these relatns can be fund as fllws. Let's start wth h, the length f the frst actuatr. In Fg. all dmensns needed t defne h =h (α ) are gven. Wth smple trgnmetrcal relatns we fnd: h = r s sn α t csα (6) where: r = a a b 0 0 b = a0a b0b s = a0b ab0 t Fgure. Dmensn jned wth the frst actuatr In the same way we fnd the length h = h (α ) (Fg. 4) f the secnd actuatr. The length depends nly n α. h δ where: = r s sn( α δ 0 ) t cs( α 0 ) (7) = a b c ab bc r s = t = α = α (x, z, α ) ( 5 )

4 sught relatn f h wth respect t α. Reassumng, all tgether, fr a gven x A we have eght unknwns, namely: z A ; h ; h ; h ; α, α ; α and β. They can be slved frm eght equatns frm () t (5 ) wth ( 7 ) t (9). Fgure 4. Dmensn wth the secnd actuatr The h wth respect t α relatn s mre cmplex than the prevus nes. In ths case t s cnvenent t ntrduce an addtnal varable β shwn n Fg.5. Frst, the pentagn BCDEF s cnsdered. Frm trgnmetrc relatns we get where h = r s sn β cs β (8) t r = a c d g ag s = d( a g) t = c d Fgure 5. Dmensns jned wth the thrd actuatr Next, nspectng the pentagn DEFGH, we get relatn between β and α n the frm b 4 = r d( g sn β e( g d sn β ) csα where f csβ ) e( f d csβ )snα r 4 = d e f g (9) After fndng β as a functn f h frm (8), and substtutng t nt (9) we can fnd the 5. THE HYDRAULIC OIL FLOW INTO ACTUATORS. We have just fund the actuatr lengths as functns f the bucket mtn. Havng ths we can determne the requred amunt f the hydraulc l, whch has t be pumped n partcular actuatrs. Ths shuld assure the rght tl mtn. Let dente: dh Q = dt = A h A =,, (0) The vlume f the l per unt tme enterng nt cylnder f -th actuatr. A start fr the crss sectn s f the cylnder. Takng tme dervatve f α ( =,,) n the frm dα α =, and bearng n the mnd ntatns dt assumed n the prevus chapter, we fnd: Q Q t sn α s csα = α A () h t s n ( δ ) s c s( δ ) = α A () h Q t sn β s cs β = β A () h wth β and α related by tme dervatve f (9): [d( g csβ f sn β ) ed sn β snα = [e( d csβ f )csα e( g d sn β )snα ] α The ttal prcess f supplyng the l n the actuatrs, n accrdance wth the assumed trajectry generatn, s presented n Fg. 6 ed csβ csα ] β =

5 Fgure 6 An pen lp cntrl fr a fully actuated, lad ndepended valve 6. A NUMERICAL EXAMPLE Cnsder the mtn f a mn- excavatr bucket alng a straght lne gven by the relatn: z = 0.5x [m] 5.0 E E E E E E Q,Q.0 E E E E E E E E -0 4 Q Q Q Q -.0 E E E E -0 4 Fg.7. Flws Q, Q, Q wth respect t x and a cnstrant mpsed n x n the frm.[m] x.8 [m] The straght lne mpses cnstant value f α = α α. Wth an assumptn that δ = 0 we get ctg(α ) = Substtutng the value f α nt () and (), we arve t tw equatns wth tw unknwns α and α. Numercal calculatns are perfrmed fr a mn-excavatr wth the fllwng parameters specfed n Fg., 4, 5. l =. m; l =. a = 0.0 [m] b = 0.00 [m] c = 0.94 [m] a = 0.00 [m] b =.0 [m] c =.07 [m] a = [m] b = 0.00 [m] c = 0.75 [m] a = 0.69 [m] b = 0.90 [m] d = 0.60 [m] A = [m ] e = 0.99 [m] A = [m ]

6 f = 0.75 [m] A = [m ] g = 0.00 [m] h =.00 [m] The slutn f the nverse knematcs fr α s carred ut at twenty equdstant pnts between fr between..8 [m], frm the fllwng equatns x x = l csα l cs( α ) l csα = l sn α l sn( α ) l sn α (4) α = α Nw, btaned values f x we substtute nt equatns (), () and () expressng flws Q. In Fg.7 a dagram relatng these flws t x s presented. 7. CONCLUSIONS It has been shwn that there s a pssblty t apply a rbust, pen lp cntrlled system fr excavatn, and ther excavatr-based wrks. The dea cnssts n ntrducng three ndependent hydraulc valves fr each f three actuatrs. Ths makes pssble t cntrl three degrees f mtn f the bucket n a unque way. The appled ladndependent valves allw t cntrl the mtn alng prescrbed trajectry n a sl wth sme varatns f ts prpertes. The trajectry s generated frm the hst cmputer t a PSC, changng the cmmand t a vltage system whch n turn drves the valves. REFERENCES [] Barrents A.., Lueng O., Mra A.. Teleperaded backhe excavatr wth haptc cntrl Prceedngs f 6th Int. Symp. Autmatn and Rbtcs n Cnstructn, pp [] Bernld L. I., Mtn and path cntrl fr rbtc excavatn, J. Aer. Engr. ASCE, vl. 6, N, pp - 8, 99 [] Vaha P.K., Skbnewsk M.J., Cgntve frce cntrl f excavatrs, J. Aer. Engug. ASCE vl.6, N, 99 [4] Ha Q.P., Nguyen O.H., Rye D.C., and Durrant- Whyte H.F., Frce and pstn cntrl fr electrhydraulc systems f a rbtc excavatr, Prceedngs f 6 th Int. Symp. Autmatn and Rbtcs n Cnstructn.pp , 999 [5] Kesknen E., Launs S., Ctsafs M., Raunst Y., Trajectry Cntrl Perfrmance Analyss f Excavatr Based Sheet Ples System, Prceedngs f 6 th Int. Symp. n Autmatn and Rbtcs n Cnstructn, pp55 540, 999 [6] Budny E., and Gutkwsk W., Knematcally nduced excavatn by backhe excavatr, th ISARC, Prceedngs, 996, pp [7] Gutkwsk W., Chłsta M., Senstvty f the Bucket Mtn n Cntrlled Excavatn, ANC 8th Int. Tpcal Meetng n Rbtcs and Remte Systems, Aprl 5-9, 999, Pttsburgh