SMULATON O VEHCLE COLLSONS N REAL TME Mrk Knigh Los Alos Nionl Lorory MS C97 Los Alos, NM 87545 Phone: 55-667-6378 Eil: knigh@lnl.go Ji Bernrd Virul Reliy Applicions Cener, ow Se Uniersiy 74 Howe Hll, Roo 6 Aes, A 5-74 Phone: 55-94-39 x: 55-94-553 Eil: ernrd@ise.edu Ocoer 8, 3 ABSTRACT Typicl ehicle siulions require nuericl inegrion n inegrion ie sep no lrger hn. seconds, usully less hn hlf h ie. This does no lee enough ie o crry ou he coplex clculions required for deiled collision clculions in rel ie. This pper presens ehod h srikes coproise, which, lhough no crrying ll he deil necessry for ery ccure collision clculions, llows useful siulions o proceed in rel ie. The ehod hs hree prs: collision deecion, esiion of he oenu rnsfer expeced o resul fro he collision, nd pplicion of forces o proide he desired oenu rnsfer. The ehod uses coon scene grph for collision deecion, which llows he syse o work wih os of he coon scene dse fors wihou he need of specilized preprocessing. All of he collision deecion nd response clculions eploy open-source code nd re designed o work well speeds required y rel-ie ehicle siulion. Exples sed on he VDANL ehicle dynics siulion illusre he uiliy of he ehodology. NTRODUCTON Our ineres in collision in rel ie follows fro our ineres in driing siulion, which dends rel ie clculions. References [,,3,4] presen descripions of seerl driing siulors. Reference [5] descries four coponens coon o ll driing siulors: A siulion of he physics of he ehicle odel nd he rod surfce A siulion of he surrounding enironen Video nd udio displys o disply se oupu o he operor npu conrol deices for he operors Reference [6] discusses hese coponens of ehicle siulion nd dds wo ddiionl coponens, collision inercion nd neworking ngeen, for collorie driing siulion pplicion. This pper focuses on siuling ehicle collisions in rel ie. The oiion is o llow driing siulions o coninue in he fce of glncing ipcs wih rriers rher hn disrc he user y going hrough he rrier or y cusing he siulion o sop. There re wo key chllenges, deecing h collision hs occurred, nd copuing he effecs of he collision.
BACKGROUND Deiled collision siulion hs een n cie re of reserch since he 96 s. Vrious luped ss spring odels were presened in he erly 97 s [7,8] s ehod o elue crshworhiness of ehicles in ore cos effecie wy. n 973 McHenry [9] presened he Siulion Model of Auooile Collisions (SMAC) copuer progr s ool for cciden reconsrucion. All of hese ehods were inended o siule soewh deiled collision eens, nd in he cciden reconsrucion cses, were ofen used in n ierie wy o ch physicl eidence. They were no concerned wih rel ie perfornce. n 983 Mcilln [] presened rigid ody ipulse response clculions specificlly for ehicle collisions. The ehod ssued he pre nd pos collision elociies he ipc poin were goerned y coefficien of resiuion. This ehod of clculion is ppeling for rel-ie siulion ecuse of he sipliciy nd speed of he clculions. Hhn [] in 988 presened rigid ody ipulse response clculions for ore generl rigid odies in copuer niions. Aou h se ie Moore nd Wilhels [] discussed he opics of collision deecion nd collision response. They presened wo response ehods, spring sed penly ehod nd n ipulse sed soluion. The ipulse ehod ws ypiclly fser o copue, especilly in iolen collisions, nd hd n dded enefi in h he resuling syse of equions need only e soled once per collision insed of eery ie sep s required y he spring sed ehods. This pper ipleens he ipulse ehods gien y Mcilln nd presens ehod sed on he loss of kineic energy during he collision. Boh hese response ehods gie resonle looking resuls in rel-ie. While his pper focuses on collision response clculions, i will lso deonsre h he rel-ie perfornce is highly dependen on he collision deecion lgorih speed. Lin [3], Jiénez [4], nd Ki [5] he proided recen sureys of collision deecion ehods. The following secions ddress he issues of rel-ie collision deecion nd response nd ddress he chllenge of rel ie ipleenion. COLLSON DETECTON Typiclly collisions re deeced y serching dse of collidle ojecs o find he inerference. f collision is deeced, he collision poin nd collision plne norl re sed o enle clculion of he resuling response. There re seerl wys o perfor he deecion operion [3, 4, 5]. We seleced Open Scene Grph [7] o perfor collision deecion gins isul scene grph dse. This opion proides gre del of flexiiliy in dse fors while sill inining ple copuion speed. n ddiion, Open Scene Grph is free, open source, nd cn run on seerl copuer plfors. Oher ehods y he fser deecion speeds, priculrly wih dses conining high nuer of polygons, u ofen hey require specilized file fors nd susnil preprocessing [5]. To es for collision gins he scene grph, he ehicle is represened s se of line segens h genere horizonl D recngulr ple round he ehicle he CG heigh. or ech inegrion ie sep, he ounding recngle is esed gins he scene for inersecions. igure shows he fron-righ corner of he ounding recngle inersecing wih wll. A collision is deeced when ny segen inersecs n ojec. To enle clculion of he ehicle response o he collision, siple lgorihs ypiclly require specificion of he poin of force pplicion nd he direcion of he force. Here we find he poin of pplicion of he force y king he idpoin of he line of inerference eween he wo ojecs. As n exple, in igure he poin of pplicion would e he idpoin of he line segen -. Since we re concerned in his pper wih flexile ehicle odies hiing rigid rriers, he collision plne norl will e he surfce norl of he rigid rrier.
GURE Vehicle collision ounding recngle in fron righ side collision. GURE Aerge inersecion poin nd collision norl. The cllou shows how he wo segen inersecion poins re erged o find he finl collision poin. The collision norl ecor is shown perpendiculr o he rigid rrier. COLLSON RESPONSE Our gol is o siule collisions in useful wy h kes sense u is no inended o e correc in engineering deil. Seerl siplifying ssupions enle rel ie clculions:. The ipc is eween ehicle nd rigid wll.. The norl ecor o he wll is in he yw plne of he ehicle. 3. The forces of ipc re in he yw plne nd he ss cener heigh of he ehicle. 3
4. The ie durion of he ipc is sll copred o he ie scle of yw plne ehicle oion. 5. There is only one ipc force, nd his ipc force reins fixed relie o he ehicle hroughou he ipc. This secion presens wo ehods for copuing he collision response. Boh ehods egin wih he pplicion of oenu relionships. Liner nd Angulr Moenu irs pply liner oenu: d = ( V V ) () where he collision occurs o, he durion of he collision is, is he force ecor pplied o he ehicle y he wll, is he ss of he ehicle, V is he yw plne elociy ecor of he ehicle's ss cener jus efore he force is pplied, nd V is he yw plne elociy ecor of he ehicle's ss cener jus fer he force is pplied. We presue he ie inerl is so sll h oher forces, forces fro he rod on he ires for exple, do no ffec he oenu rnsfer. We he resriced our nlysis here o one ipc force. The exension o ore ipc forces, les fro oenu poin of iew, is srighforwrd. A siilr relionship pplies o ngulr oenu, nely, ( r r ) ρ d = () where is he ehicle's ol yw oen of ineri ou is ss cener, ρ is he ecor fro he ol ehicle ss cener o he ipc, nd r nd r re he ehicle's yw res efore nd fer he collision respeciely. Equions () nd () he ol of hree unknowns, he elociy of he ss cener fer he ipc, he ngulr elociy fer he ipc, nd he ipulse. or he hird equion needed o sole he syse, we rely on coinion of inuiion nd experience. Coefficien of Resiuion Mehod irs consider he ehods of Mcilln [], who clls for he norl elociy chnge of he ehicle he poin of ipc o e funcion of coefficien of resiuion e. Vp N = e ( Vp N) (3) Vp nd Vp re he elociy ecors of he ehicle he poin of ipc efore nd fer he ipc nd N is he uni norl o he rigid surfce. The coefficien of resiuion e is funcion of he deils of he collision. Mcilln suggess lues in he rnge of. o.3. Equions (), (), nd (3) yield he ipulse nd he pos collision ngulr elociy nd elociy of he ss cener. The lgorih ipleenion defines he collision fre of reference ou he poin of collision wih he priry force long he surfce norl of he collision nd fricionl force long he ngen direcion. Mcilln s presenion illusres he generl wo-ehicle collision, u he presenion here is liied o single ehicle hiing sic rigid ody. 4
Gien he ehicle elociy ecor projeced ino he collision norl nd ngenil direcions, he following oenu equions rele he pre nd pos collision elociies wih he ipulse. ( n n ) pulse (4) = ( ) = µ pulse (5) Where n is he ss cener elociy norl o he collision surfce, is ss cener elociy ngenil o he collision surfce, µ is he coefficien of fricion, nd pulse is norl o he collision surfce, pulse = n d (6) The chnge in ngulr oenu is gien y Equion (), which expnds o he for, ( r r ) = d x d y n µ n (7) Coining Equions (6) nd (7) gies he for, ( r r ) = pulse( µ x y) (8) Where r is he yw re nd x nd y re he disnces fro he ol ehicle ss cener o he poin of collision s illusred in igure 3. The pre- nd pos-collision elociies re reled y he coefficien of resiuion s sed in Equion (3). To siplify he noion we use p o represen Vp N, which is he elociy he poin of ipc nd norl o he collision surfce. p = e (9) p is cler fro igure 3 h p = n r y () p = n r y () where y is he oen r fro he ehicle s ss cener o he collision norl. 5
GURE 3 Resiuion ehod collision digr. According o Mcilln, ypicl ehicle collisions he coefficiens of resiuion of eween. nd.3. Since we need o e prepred for wide rnge of collision ngles, we he found i useful o use cosine shped funcion, s shown in igure 4, o inerpole he coefficien of resiuion s funcion of he ngle of ck eween he ehicle nd he wll, fro.3 for sll ngles o.5 9-degree ipc. When he ngle of ck is sll, coefficien of.3 yields sll loss in kineic energy nd he ehicle is siply redireced wy fro he wll. or collisions ner niney degrees ngle of ck, he coefficien of.5 leds o loss of los ll of he kineic energy, n expeced resul of hed on collision..3 Resiuion s. Angle of Ack Coefficien of Resiuion e( α).4.8..5.5..4.6.8..4 α Angle of Ack.57 GURE 4 Coefficien of Resiuion s. Angle of Ack 6
The coefficien of resiuion relionship nd oenu equions yield he ipulse. Susiuing Equion () ino Equion (9) yields: n r y = e p () where, p is copued fro Equion () nd he pre-collision elociies. Using he oenu equions, rerrnging nd susiuing he ino Equion () yields n pulse pulse µ y r ( x y) = e p (3) Siplifying, y x y p pulse = e p µ (4) Now, if, y h = (5) nd, x y k = (6) hen he ipulse is e pulse = p h µ k (7) Kineic Energy Loss Mehod or cerin specil pplicions, going hrough rrier for exple, we he found i useful o sipule he energy loss during he collision rher hn cll for coefficien of resiuion. n priculr, consider he preer P h indices he yw plne energy efore nd fer he collision. P = ( V V ) r ( V V ) r (8) Agin, we find i useful o ke P cosine funcion of he ngle of ck eween he ehicle nd rigid wll, rnging fro.9 sll ngles of ck o.4 9-degree ipcs. These energy loss lues pper o genere resonle responses. The collision force cn e roken ino coponens long he ehicle s locl coordine syse. 7
= ( i j) (9) where i nd j re uni ecors in he ehicle s coordine syse s illusred in igure 5 nd is he gniude of he force. ollowing he procedure of he resiuion ehod, we pply liner oenu for he syse. Referring o igure 5, Equion () cn e wrien in sclr for. ( u ) u = () ( ) = () where u nd re he longiudinl nd lerl coponens of he ss cener elociy. GURE 5 Collision wih sic rrier on he fron righ corner of he ehicle. Siilrly, he chnge in ngulr oenu ou he ss cener gien y Equion () cn e copued in sclr for s ( r r ) ( d c) = () where r is he yw re, is he yw oen of ineri, nd he ecor fro CG o collision poin is ( c i dj) ρ = (3) The relionship eween pre- nd pos-collision kineic energy is gien y E = P (4) E where, P is he frcion of energy reining fer he collision nd, 8
( ) 5..5 r u E = (5) ( ) 5..5 r u E = (6) Equions (,, nd hrough 6) yield he gniude of he force required o chiee he ipulse cross he specified collision ie sep. Begin y reling pos-collision elociy nd yw re o he gniude of he force of ipc: u u = (7) = (8) r d c r = (9) Now Equion (6) yields ( ) ( ).......5 r u u E = (3) which cn e rewrien s ( ) ( ) ( ) ( ) [ ] ( ).............5 r u d c r u c d c d E = (3) The soluion for is: A C A B B 4 ± = (3) Where: ( ) ( ) c d c d A = (33) ( ) ( d c r u B ) = (34) ( ).5 E r u C = (35) 9
This ehod yields wo soluions. We ypiclly ipleen he soluion wih he lrger of he wo forces ecuse i preens he ehicle fro going hrough he rrier. Noe h he lower of he wo forces y lso e lule if we wn he ehicle o lose energy while reking hrough he rrier. DYNAMCS MPLEMENTATON The ehods presened here cn e used wih ny ehicle dynics plfor. There re wo choices for ipleenion: Upon collision deecion, clcule he oenu chnge using he ehods presened here, rese he se riles of he siulion wih he pos collision elociy nd yw re, nd coninue inegrion. Upon collision deecion, clcule he oenu chnge using he ehods presened here. Then pply force oer shor ie period o cuse he desired oenu chnge. The firs ehod, reseing he se riles, is only suile for odelers who he conrol of he ehicle dynics sofwre. is no ery prcicl for odelers using coercil code ecuse in he conex of such code he odeler does no ypiclly he he iliy o oerwrie he se riles nd resr he oion quickly enough o ee rel ie consrins. This pper uses he second ehod, nely, pplying he force required o cuse he desired oenu chnge. We ipleened oh he coefficien of resiuion ehod fro [] nd he energy ehod gien here in he coercil sofwre VDANL [6]. We ssued consn force eween he rigid rrier nd he ehicle for sll period of ie o yield he desired oenu chnge, nd we used VDANL s User Defined Module opion o pply he collision forces nd oens o he ehicle odel. or oh ehods, he force of ipc included force norl o he surfce of collision nd fricionl force ngen o he surfce. We used coefficien of fricion µ o define he fricion force s µ = (36) n ollowing Mcilln, who suggesed coefficien of fricion lues fro.-.3 for ypicl collisions, we found i useful o ry he coefficien of fricion fro. for hed on collisions o.3 for sll ngles of ck. We rried his pproch on prgic grounds he coefficien.3 kes good sense for sll ngles of ck nd sees o work well in he odels. A high ngles of ck, ner-hed-on collisions h chrcerisiclly led o ery high norl forces, we lowered he gniude of he fricion coefficien o preen unrelisiclly high pos-collision yw res. niilizion Prior o sring he inegrion, he user us iniilize he collision scene grph nd supply ehicle preers for he collision esing nd response clculions. The collision scene file cn e ny isul dse for suppored y Open Scene Grph [7]. The following preers re required: Vehicle ss Vehicle yw oen of ineri Disnce fro he CG o he fron of he ehicle ody Disnce fro he CG o he rer of he ehicle ody Vehicle ody widh CG heigh
These diensions re used o genere D ounding recngle, which is se he CG heigh. Collision Tesing nd orce Copuion or ech dynics ie sep he siulion proides he collision lgorih wih he siulion ie, liner posiion nd elociy, nd ngulr posiion nd elociy of he ehicle. This plces he ounding recngle in he scene o es for inerference wih ny of he scene s eleens. f collision is deeced, he collision poin nd collision surfce norl re sored o copue he forces nd oens for pplicion o he sprung ss. Applicion of orces nd Moens Equions () nd () plus equion (3) or (8) enle he clculion of he ipulse d nd he ngulr ipulse ρ d. We he ipleened hese ipulses in he conex of VDANL y ssuing he force is consn. Thus, d = (37) We erified h he fixed sep inegror of VDANL proides ccure resuls wih one inegrion ie sep, =.5 seconds (38) The perfornce esing focused on he wo priry ojecies, resuls h look resonle nd follow rigid ody oenu nd energy relionships correcly, nd lgorihs h work in rel ie. TESTNG OR ACE VALDTY We esed he lgorihs in seerl scenrios, fro olique side ipcs o hed on collisions, nd he perfornce in ll cses ws sisfcory in he sense h he resuls seeed o ke good sense. igures 6 nd 7 proide n illusrion, which ws crried ou using he dse of igure 8 nd he coefficien of resiuion-sed clculions. As igure 6 indices, he ehicle egins driing srigh hed; he elociy is 6 ph. The righ fron corner ipcs he side wll ou.5 seconds, cusing spike in negie yw re. This is followed los iediely y he righ rer corner of he ehicle hiing he wll, reersing he direcion of he yw re, u wih he new elociy of he ss cener direced slighly wy fro he wll. A ou.5 seconds, he lef fron corner of he ehicle his he end wll effeciely sopping forwrd oion nd resuling in residul negie yw re, which grdully dies ou.
GURE 6 Vehicle rjecory of side collision followed y fron collision. GURE 7 Vehicle yw re for he side collision followed y fron collision.
TESTNG OR REAL TME PERORMANCE We esed he rel-ie perfornce of he lgorih using wo dses, one quie siple nd one i ore coplex. The coplexiy of dse is pririly esured y polygon coun. igure 8 presens he siple dse, es scene conining n L-shped wll nd fl driing surfce. The dse conins 6 ringles, ll of which were used o es for collisions. igure 9 presens pr of he ore copliced Wkins Glen rcerck scene. The enire isul scene consiss of 878 ringles, u we creed ersion of he dse wih only he ericl eleens for collision esing. This reoed unnecessry errin nd sky polygons nd rough he collision ringle coun o 838. GURE 8 L-shped es scene. Nuericl experiens erified our expecion h he collision copuion speed is inly dependen on collision scene coplexiy. All of he experiens were run on 3 Mhz Peniu PC wih 9 MB of RAM. Boh he resiuion nd kineic energy sed ehods yield fs collision response copuion ies erging.3 s per inegrion ie sep independen of he coplexiy of he dse. This shows he response clculion ie is negligile s i is only.6% of he VDANL inegrion ie sep of 5 s. GURE 9 Wkins Glen Trck 3
The collision deecion clculions nd nuericl inegrion cn ke he reinder of he 5 s ie sep. Tle presens he erge upde ies for he nuericl experiens. These upde ies include he norl ehicle dynics clculions s well s ll collision deecion nd response clculions. Since he dynics nd collision response clculion speeds re reliely consn, his le presens good esure of relie deecion speeds of differen scenes. The le indices h he ore copliced scene requires higher query ies nd hus longer upde ies. Boh scenes were creed wih Muligen Creor, which cn opiize scene grph hierrchy o iproe he collision deecion speed [8]. Tle shows erge VDANL upde ies for ypicl collisions wih oh scenes in non-opiized se. The le lso proides resuls for he Wkins Glen dse fer Muligen Creor opiizion, which reorgnizes he polygons spilly so collisions re deeced ore quickly y only querying polygons in close proxiiy o he ehicle. Opiizing he Wkins Glen dse iproed he oerll perfornce y oer 5%. TABLE VDANL upde ehod ies using differen collision scenes. Kineic Energy Mehod Coefficien of Resiuion Mehod Tes Ril.5 s.6 s Wkins Glen 4.69 s 4.64 s Wkins Glen Opiized y MuliGen Creor No Collision Clculion 3.88 s 3.9 s.99 s CONCLUSONS AND UTURE WORK This pper presens n lgorih h enles rel-ie collisions in driing siulions. The lgorih includes collision deecion, copuion of he resuling ipulse, nd he pplicion of forces nd oens o ehicle dynics odel. The VDANL sed ipleenion illusres rel-ie collision in siple nd oderely coplex dses. n he fuure we pln o exend he lirry o include collisions wih oing ojecs. We re pririly ineresed in ehicle-o-ehicle collisions in collorie driing siulions. Modificion of his code o llow for oing collidle odies will e chllenging, priculrly when ipleened for ehicles siuled on differen dynics engines u inercing in he se enironen. We expec coninued iproeen in copuion speed will help in he exension of his work o include ddiionl ehicles nd ore copliced dses. ACKNOWLEDGMENTS Thnks o Ole Blling nd Syses Technology nc. for heir help wih VDANL nd sple lirry code. The Wkins Glen dse is couresy of kespce Syses nc. 4
REERENCES. Rono, R.A., Soner, J.W., Ens, D.., Rel Tie Vehicle Dynics Siulion: Enling Tool for undenl Hun cors Reserch, SAE Pper 937, 99.. Greenerg, J.A., Prk, T.J., The ord Driing Siulor, SAE Pper 9476, 994. 3. Berollini, G.P., e l., The Generl Moors Driing Siulor, SAE Pper 9479, 994. 4. Chen, L.D., Ppelis, Y., Wson, G., Solis, D., NADS he Uniersiy of ow: A Tool for Driing Sfey Reserch, Pper presened he s Hun-Cenered Trnsporion Siulion Conference, ow Ciy, A,. 5. Gruening, J., Bernrd, J., Cloer, C., Hoffeiser, K. Driing Siulion, SAE Pper 983, 998. 6. Blling, O., Knigh, M., Wler, B., Snnier, A. Collorie Driing Siulion, SAE Pper --,. 7. Kl, M.M, Anlysis nd Siulion of Vehicle o Brrier pc, SAE Pper 744, 97. 8. Greene, J.E., Copuer Siulion of Cr-To-Cr Collisions, SAE Pper 775, 977. 9. McHenry, R.R., Copuer Progr for Reconsrucion of Highwy Accidens, SAE Pper 7398, 973.. Mcilln, R. H., Dynics of Vehicle Collisions, Chnnel slnds, UK: nderscience Enerprises Ld., 983.. Hhn, J.K., Relisic Aniion of Rigid Bodies, Copuer Grphics, Volue, Nuer 4, 988.. Moore, M. nd Wilhels, J., Collision Deecion nd Response for Copuer Aniion, Copuer Grphics, Volue, Nuer 4, 988. 3. Lin, C.M., Goschlk, S., Collision Deecion Beween Geoeric Models: A Surey, Uniersiy of Norh Crolin, 998. 4. Jiénez, P., Thos,., nd Torrs C., 3D Collision Deecion: A Surey, nsiu de Roòic i nforàic ndusril, Brcelon, Spin,. 5. Ki, C., Collision Deecion Algorihs, Virul Reliy Applicions Cener, ow Se Uniersiy,. 6. Allen, W.R., Rosenhl, T.J., Klyde, D.H., Chrsos, J.P., Vehicle nd Tire Modeling for Dynic Anlysis nd Rel-Tie Siulion, SAE Pper --6 7. Open Scene Grph Wepge www.openscenegrph.org, Augus,. 8. MuliGen Creor Users Guide, MuliGen-Prdig, nc. 999. 5