Real-time 3D Collision Avoidance Method for Safe Human and Robot Coexistence

Transcription

1 Plee cite thi finl verion: Bln, L. n Bone, G. M.,"Rel-time 3D Colliion Avoince Metho for Sfe Humn n Robot Coexitence", Proceein of the 2006 IEEE/RSJ Interntionl Conference on Intellient Robot n Sytem, Beijin, Chin, October 2006, pp DOI: 0.09/IROS Rel-time 3D Colliion Avoince Metho for Sfe Humn n Robot Coexitence Lucin Bln n Gry M. Bone* Deprtment of Mechnicl Enineerin McMter Univerity 280 Min St. Wet, Hmilton, Ontrio, Cn L8S 4L7. *Correponin uthor. E-mil: ry@mcmter.c Abtrct A novel olution to the three-imenionl ynmic humnrobot colliion problem i preente. Sphere-be eometric moel re ue for the humn n robot ue to the efficiency of the itnce computtion. The colliion voince lorithm erche for colliion-free pth by movin the eneffector lon et of pre-efine erch. An optimiztion metho i employe to elect the erch tht blnce between the robot pprochin it ol loction, n mximizin the itnce between the humn n robot moel. The optimiztion incorporte preiction of the motion of the robot n humn to reuce the netive effect of non-intntneou robot time repone. The robot preiction i be on trnfer function moel of it experimentl time repone t the joint level. The humn preiction i performe t the phere level uin the weihte men of pt velocitie. Preictin t the phere level elite the ifficulty introuce by the limb movin in ifferent. After ecribin the colliion voince lorithm, humn wlkin towr movin Pum robot rm i imulte. Cpture motion t i ue to mke the humn motion relitic. Monte Crlo imultion uin 000 rnom humn wlkin pth pin throuh the robot workpce re ue to evlute the lorithm. The lorithm prevente ll colliion ue to the robot. The lorithm i eteritic n efficient enouh to be ue in rel-time. On.8GHz Pentium IV PC, 40 Hz mplin rte w chieve. Inex Term - mnipultor motion-plnnin, intellient robot, eometric moelin, mnipultor, fety. I. INTRODUCTION In mnufcturin ppliction, robotic mnipultor re iolte from humn for fety reon uin phyicl brrier or enor curtin. If thee robot were ble to voi humn the fe environment coul be mintine without the nee for eprte robot work re, n expenive fctory floor pce coul be ve. In the ce when the robot mut be ner to humn, uch with mobile robot, the pee i kept low to prevent hrmful colliion from tkin plce. If the robot w cpble of voiin humn-robot colliion it coul be operte t hiher pee n fctory prouctivity woul improve. The bility to fely coexit with humn i even more importnt for ervice n peronl robot. The fety pect of humn-frienly robot ein h been n ctive re of recent reerch. Some reercher hve focue on pproche for imizin the ner of humnrobot contct, e.. bckrivble joint n rvity compention []; fer mechnicl ein [2]; improve ctution/controller ein [3]; n combintion of hih enery motor, crbon fibre link n impence control [4]. Our interet re in ppliction where humn-robot contct houl be voie, n in olvin the ocite rel-time three-imenionl (3D) colliion voince problem. Humn-robot colliion voince i chllenin problem ince, from motion plnnin point of view, humn i ynmic, multi-link, 3D obtcle whoe motion i ifficult to preict. In [5] mobile robotic pltform i moele by encloin it with mll number of lre phere. The initil plnne pth for the pltform i moifie in rel-time for movin obtcle uin novel eltic trip technique. A

2 ophiticte pproch be on hierrchy of bounin phere i ue to moel both the mnipultor n the humn in [6] for the purpoe of colliion etection. They report wort-ce colliion etection time of 40m for imultion of two Pum robot rm n wlkin humn. They i not preent colliion voince metho. Ref. [7] ecribe n optimiztion-be metho for humn-robot fety. They preent imultion reult for mnipultor pprochin ttionry humn. A hih-pee mchine viion-be pproch to the humn-robot colliion etection problem i preente in [8]. Their ytem en n emerency-top commn to the robot when the humn et too cloe. A plnnin metho for fe interction between humn rm n robot mnipultor w preente in [9]. They firt contruct colliion-free romp in C-pce offline. Thi romp i upte online to hnle the humn movin rm. They imulte two mnipultor workin in cloe proximity to two rnomly movin humn rm. On 2.8GHz Pentium IV PC the wort-ce time for uptin the romp w 453m. In thi pper we preent novel olution to the humnrobot colliion voince problem. Our pproch i ecribe in ection II. Simultion reult be on relitic ynmic moel for the robot, n on empiricl humn motion t, re preente in ection III. Concluion re iven in ection IV. II. HUMAN-ROBOT COLLISION AVOIDANCE APPROACH A. Problem Formultion n Overview of Solution A brief ecription of the colliion voince problem we im to olve i follow: Given trt confiurtion n ol confiurtion for the en-effector of robot rm, compute trjectory for the commne vlue of the robot joint, uch tht the ol i reche without the robot colliin with ynmic humn obtcle preent in it workpce. The joint vlue t ech time-tep houl be compute ft enouh to llow for rel-time implementtion of the metho. In the bence of the humn, the robot houl move in triht line from it current loction towr the ol. Fi. Geometric moel of workcell continin Pum-762 robot rm n humn. Our colliion voince pproch i heuritic; we im for efficiency rther thn optimlity of the olution (i.e. it trie to obtin oo olution quickly). It require eometric moel of the robot n humn. We ume tht enor meurement of the poition n orienttion of the humn he, toro n limb re vilble t ech time-tep. Recent vnce in humn trckin metho for cluttere environment (ee [0-3]) uet tht thi umption will be relity in the ner future. Our olution inclue relitic moel of the ynmic repone of the robot. Preiction of the robot n humn motion re utilize to mitite the etrimentl effect of nonintntneou robot opertin in ynmic environment. B. Geometric Moelin The eometric moel of the robot n the humn re necery for trnltin phyicl pce into the virtul worl of the computer. The eciion of wht type of eometric moel to ue i relte to the type of the colliion etection query we nee to olve. We re minly interete in the iml itnce between the two object involve: the robot n the humn. Althouh mny of the vilble colliion etection pcke mke ue of polyher, we electe phere-be moel for our pproch becue of it implicity n efficiency. To compute the iml itnce between two phere only require few bic computtionl opertion, where for polyherl moel the computtion i fr more complicte, i.e. cloet itnce coul be vertex-vertex, vertex-ee, ee-ee, vertex-urfce, etc. With our moel, ech robot link, n ech obtcle (the humn in thi pper), i pproximte by union of phere. Whenever the robot link or the humn move, the center of the phere re upte with new vlue. An exmple of phere-be moel for robotic workcell compoe of Pum 762 robot rm (with 6 eree-of-freeom (DOF)), n erch 3 erch 4 erch 2 preicte robot eneffector poition t timetep (t+), (t+2),(t+3),etc. when movin lon the firt erch ( ) R(t+) u 2 u u 3 R t u u n 4 u... u5 Robot en-effector poition t the moment of nlyi, time-tep (t) erch 5 R(t+2) R(t+3) R(t+ n p ) O(t+) O(t) O(t+3) O(t+2) O(t+n p ) erch erch 6 preicte obtcle (humn) poition t future time-tep (t+), (t+2), (t+3),etc. Finl ol for robot en-effector erch 0 erch n Obtcle poition t the moment of nlyi, time-tep (t) Fi. 2 Illutrtion of the colliion voince metho for the ce of implifie plnr robot n obtcle.

3 humn obtcle i iven in Fi.. The humn i moele by 46 phere n the robot by 4 phere. Note tht more etile moel my be ue if eire. C. Colliion Avoince Alorithm The colliion voince lorithm erche for colliionfree pth by movin the en-effector lon et of preefine erch. Humn-robot colliion check re compute for number of time-tep he be on the preicte motion of the robot n humn. An optimiztion metho employin penlty fctor i ue to elect the erch tht blnce between motion towr the ol n mximizin the itnce between the phere of the humn n the robot. The bet i then ue to compute the commne en-effector poition n orienttion for the next time-tep, n the lorithm i repete. A implifie plnr ce, with the robot n the humn ech moele by inle phere, will be ue to explin the lorithm. In thi exmple, we ume the robot phere i locte t the en-effector, but thi i not requirement of the lorithm. The ynmic repone of the robot i moele intntneou. Fi. 2 illutrte wht the colliion voince lorithm oe t time-tep of the imultion when humn obtcle obtruct the robot motion towr the ol. Both robot n obtcle phere re epicte t the moment when the nlyi i performe, time-tep number t (lbele R(t) n O(t) in the fiure). The erch- re,... 0, 2, with their unit vector u, u, u2,, un, repectively. The number of erch- in the et i n + becue triht line motion towr the ol i lwy e to the fixe et of. For ech erch, i, the eneffector i commne to move incrementlly lon u i up to n time-tep he. The humn moel phere poition re p lo preicte over thee future time-tep (ee ection E for more etil). A cot function incorportin cumultive penlty fctor i ine to ech erch for ll humn-robot preicte loction (i.e. R(t) v. O(t), R(t+) v. O(t+),, R(t+n p ) v. O(t+n p ) ) be on the itnce between robot-humn pir of phere. The cot function for ech erch i compute by: np nr nh Ψ ( t) = + p ( t + k) for =0,,, n () where: u u + k = i= j= ij u i unit vector towr the ol, vector for the erch, n u i the unit n p i the number of time-tep to erch he, n + i the number of erch, n R the number of robot moel phere, n i the number of nh humn moel phere. The term p ( t + k) einte the penlty fctor ine to the pir of phere ( i th from robot moel n th k th j from humn moel) when they re t the time-tep in the preiction erch. It i compute uin: ij MAXF ij L b pij ( t + k) = L < ij < Lmx (2) ( ij ) b ij L mx ( Lmx ) where: ij i the itnce between the urfce of the two phere (i th n j th ), L i the imum cceptble itnce between the two phere before the pir i coniere to be in virtul colliion tte, Lmx i itnce limit beyon which the me penlty fctor i pplie to ll pir of phere (rerle of their itnce), MAXF i the lret flotin point number poible in the computer (ue to efine + which i ine when virtul colliion i foun), b n re the prmeter of ecrein polynomil function which correlte the penlty function with the phere-pir itnce. Note tht true colliion only occur when ij 0. A rphicl repreenttion of the penlty function ecribe by (2) i iven in Fi. 3. A ecrein polynomil function (i.e. of eree < ) w choen to enure the penlty fctor incree t fter rte thn the itnce ecree. For exmple pir of phere locte 50 mm prt will receive more penlty thn the cumulte penlty for two pir of phere t 00 mm prt. In other wor, the phere mot likely to collie re the mot importnt. The firt term in () i meure of how much the eneffector trjectory i preicte to evite from the triht line to the ol when the robot follow the erch. It i imize when the robot move towr the ol. The econ term in () i meure of how cloe the humn-robot phere re one from nother. The cloer the pir of phere, the lrer the penlty fctor ine to tht erch. If t let one pir of phere i foun to be cloer thn L tht erch receive the lret poible penlty fctor. Penlty fctor, p ij L MAXF p b ij = L ecrein polynomil function L mx Sphere-pir itnce, ij p b ij = L Fi. 3 Penlty fctor v. phere-pir itnce. mx

4 n The of motion with the mllet cot function ( ( Ψ ) =0 ) i electe the bet choice for the robot motion commn for the next time-tep of the imultion. If ll the erch re preicte to prouce colliion t ome point lon the n p time-tep winow, the robot i commne to top for the next time-tep, until the humn move wy. The erch lorithm i repete t every time-tep. Note tht the invere Jcobin mtrix of the robot i ue to convert ech incrementl Crtein pce motion commn to joint pce. The proceure for the 3D itution i imilr, the min ifference bein tht the et of erch i evenly ptilly itribute in 3D pce. The unit vector u, u, u..., u cn be eily erive from the vertice of n 2, n Archimeen oli (e.. icoheron) encloe in phere with riu of one. An exmple of et of 5 erch (4 fixe n one pointin towr the ol) i hown in Fiure 4. D. Robot Motion Preiction Computin the ij vlue over the erch winow require preiction of the phere poition. To properly preict the poition of the phere for the robot eometric moel ynmic moel of the robot time repone mut be ue. The ynmic repone of ech of the joint poition controller for typicl robot cn be reonbly pproximte by the followin icrete-time firt orer plu etime trnfer function moel: τ θ ( z ) z G( z) = = (3) θ ( z) z c where θ c i the commne joint vrible, θ i the ctul joint vrible, τ i the number of time-tep of etime, i moel prmeter n z i the bckwr hift opertor. The etime cn inclue computtionl ely n communiction ely. Applyin the invere Z trnform to (3) yiel the ifference eqution: θ ( t) = θ ( t τ ) + θ ( t ) (4) c The preiction re prouce by recurively uin (4) follow: ɶ θ ( t + ) = θ ( t τ + ) + θ ( t) (5) c ɶ θ ( t + k) = θ ( t τ + k) + ɶ θ ( t + k) for k = 2,, τ (6) c ɶ θ ( t + k) = ɶ θ ( t τ + k) + ɶ θ ( t + k) for k = τ,, n (7) c p where ɶ θ i the preiction of the ctul joint vrible n ɶ θc i the preiction of the commne joint vrible compute from the incrementl erch. The preiction eqution re pplie eprtely to ech joint to obtin the complete et of joint vrible. Finlly, uin thee joint vrible the forwr kinemtic eqution for ech phere re ue to compute their preicte poition. E. Humn Motion Preiction For relible colliion voince preictin the humn motion i require. Our preiction metho i be on weihte vere velocitie pplie t the phere level of the humn eometric moel. Pt phere poition t i tore in buffer n bckwr ifferencin i ue to etimte the intntneou velocity of the phere t ech time-tep. Averin i ue to reuce the effect of rnom velocity vrition. For ech phere of humn moel the men intntneou liner velocity vector v i compute with: n h w( t i) v( t) = v ( t i) (8) i= 0 W where: nh i the ize of the hitory buffer, v ( t i) i the intntneou liner velocity vector of the phere for the i th previou time-tep, w( t i) i weihtin fctor, n W i the um of ll weihtin fctor. In (8) W i ue to normlize the weiht on v. The weihtin fctor re iven by: w( t i) = ( 2n h i) n h (9) Thi choice weiht recent t more hevily to reuce the phe l cue by oler t. The preicte poition of ech phere i then obtine by um it current ctul poition n the numericl intertion of v over the erch winow. By chooin to pply the preiction metho t the phere level, ech phere poition will be preicte inepenently, o there i no ifficulty prouce by the limb movin in ifferent. Thi metho lo work when there re everl humn movin in the me workcell. III. SIMULATIONS Fi. 4 Serch in 3D pce. A. Proceure Numerou imultion were run to tet the effectivene of the lorithm. The oftwre w written in C++. The imulte environment i compoe of ix DOF Pum 762 robot, n humn wlkin in triht line pth into it workpce. To mke the imultion more relitic we ue t from BVH file of cpture humn motion to nimte the humn moel. BVH i the tnr formt ue by motion

5 cpture ytem. The vere pee of the choen humn moel w 650 mm/ (with ome phere movin up to 2300 mm/). The tk ine to the robot conite of repetitive triht line motion between two preefine en-effector loction. Such motion occur in prctice when robot i perfor pick-n-plce opertion, n imilr tk. The trtin poition in joint pce w: j = {.807, 0.999, 2.744, , 0.786, 0.654} rin. The ubequent ol loction j, j..., j were efine : j = { 5.447, , 2.263, , , 5.590} rin, j = j, j = j, j = j n j = j. Frme zero of the Denvit-Hrtenber kinemtic robot moel w locte t X = 92 mm, Y = 82 mm n Z = 940 mm in the workcell. The input prmeter of the imultion were follow: T = 33.3 m i the time-tep, n = 463 i the totl number of imultion time-tep (urtion 5 ), n = 4, n = 46, v = 900 mm/ i the eire robot en-effector pee (i.e. 30 R mm per time-tep), n p = 0, n = 4, n = 80, L = 400 mm, L mx = 750 mm, = 3, n b = 5 mm3. Ltly, be on experimentl t the etimte ynmic moel prmeter for the Pum 762 robot t 33.3 m time-tep re: τ = 6 n = B. Sinle Simultion Run Exmple Reult from one imultion run re hown in Fi The cloet itnce between the humn n the robot i plotte v. time in Fi. 5. Since thi vlue i lwy reter thn zero no humn-robot colliion occurre. Thi rph lo uet tht uin mller L vlue coul hve prouce colliion. L mut be choen properly to both mintin robot efficiency n enure the humn fety. We hve etere tht fety i enure if L i choen to be reter thn the toppin itnce for the en-effector, fe. It cn be hown tht thi itnce i iven by: fe = vr T + ( τ + ) (0) Cloet humn to robot itnce (mm) time-tep R h H time-tep when t, 2n, 3r n 4th ol hve been reche L mx COLLISION-FREE AREA COLLISION AREA L Fi. 5 Cloet humn to robot itnce v. time. fe Orienttionl error (%) Poitionl error (mm) Thi eqution inclue n itionl time-tep of ely to ccount for the time require to trnmit the commn to the robot. For the eire en-effector pee of 900 mm/ n the 33.3 m time-tep, (0) ive: fe = 347 mm. Thi et the lower boun for L. If we chooe too lre n L vlue the robot will not execute it ine tk ince it will be force to voi the humn even when fety i not n iue. So, for efficiency n fety L houl be me cloe to fe intermeite ol reche time-tep Fi. 6 Poitionl n orienttionl error v. time. n hence our choice of 400 mm. new intermeite ol loe Fi. 6 how the poitionl n orienttionl error of the en-effector with repect to the ol loction. The poitionl error w compute the itnce from the en-effector to the ol, where the orienttionl error w compute uin the eqution: ( ) ( ) ( ) o nc n oc o c () e = + + where nc, oc, n c ; n n, o, n re the norml, liin n pproch vector of the en-effector t the current loction n the ol loction, repectively. Thi eqution chrcterize the milinment between the current n ol orienttion. When both error re zero the intermeite ol h been reche, n the next one cn be ctivte. The rph how tht the robot uccefully reche three of the ol loction before the imultion w toppe. The joint nle re plotte v. time in Fi. 7. Thee plot how tht the joint pce trjectorie re mooth, which i eirble for implementin thi pproch in prctice. The oftwre lo prouce n nimte output of the workcell. A top view howin the robot t it trtin confiurtion, the ol loction n the complete en-effector trjectory i hown in Fi. 8. The color br my be ue to ue the Z vlue. Selecte till ime from the nimtion re iven in Fi. 9. In 9 the robot firt repon to the preence of the humn n trt to evite from it triht line motion towr the ol. In 9b n 9c the humn i wlkin towr the robot n the robot i ctively voiin him by movin bckwr n upwr. When the humn h pe by, the robot move to

6 Robot joint vlue (r) b e h o u l e r e lb ow to o l y w to o l p itc h to o l r o ll tim e- te p Fi. 7 Robot joint nle v. time. Fi. 8 Top view of the workcell howin the complete trjectory of the en-effector. it immeite ol loction (i.e. ol ) n then continue it ine tk (ee 9, 9e n 9f). With the oftwre runnin on.8ghz Pentium IV PC the mximum time require to execute time-tep w 25 m. Therefore, with thi PC n the pecifie lorithm prmeter, the lorithm cn be ue in rel-time with 40 Hz mplin rte. C. Vlition uin Monte Crlo Simultion Metho To vlite the colliion voince lorithm, Monte Crlo imultion were performe. Ech imultion conite of 000 tril. The prormme tk for the robot i the me ue in ection B n the me prmeter were employe, except for: τ = 3, = 0.6 n fe = 67 mm. In ech tril the humn wlk lon rnomly choen triht line pth throuh the robot workcell. For the purpoe of electin the rne of the rnom pth, the workpce limit of the Pum robot were pproximte by cyliner of riu of.5 m centere t the fixe robot be. The humn motion trt from n outer circle with riu of 3 m, n it rnom will be efine by two nle: α n α 2. Detil re iven in Fi. 0, where the humn wlk from A to B, throuh the robot workpce. The et of Fi. 9 Still ime from the imultion output tken t time: ().27, (b) 4.03, (c) 4.33, () 5.47, (e) 6.93, n (f) rnom pth w enerte by uniformly rnomly itributin α n α2 over the rne [0, 2 π ] n [ π / 6, π / 6] repectively, n torin the firt 000 pth tht i not p throuh or ner to the robot be. The et of pth i plotte in Fi.. Ech pth w rwn inle line correponin to the toro trjectory of the humn eometric moel. Thi fiure emontrte tht the et of 000 pth cover lre percente of the robot workpce. D. Dicuion of Monte Crlo Simultion Reult Before icuin the reult, it i importnt to clify colliion between humn n robot into two type. Jut we on t blme the oor when we wlk into it, robot t fult colliion (RFC) mut be itinuihe from humn t fult colliion (HFC). If the robot i toppe or bckin wy

7 B pth wlke by humn motion preiction reuce the RFC to zero n the HFC to.5%. Thi finl reult emontrte the importnce of incorportin humn motion preiction, n the ucce of our lorithm in preventin colliion ue to the robot. α reference line Sphere from humn moel Sphere from robot moel Y X α 2 A robot be robot workpce (top view) outer limit of robot workpce Common centerline v' H v' R Fi. 0 Top view of the robot workpce howin the humn wlkin pth prmeter. Fi. Top view of the 000 rnom wlkin pth ue with ech Monte Crlo imultion. from the humn when the colliion occur then the humn, n not the robot, i t fult. We ientify thee HFC by nlyzin the intntneou velocity of the pir of phere * tht come into contct firt. Our metho i illutrte in Fi. 2. A colliion h occurre t the current time-tep. The intntneou velocity of ech phere i firt etimte by bckwr ifferencin it poition t. Thee component of thee velocitie lon the common centerline of the two phere re enote v H n v R hown. The colliion type i then etere uin: HFC v H v R 0 n v H > v R colliion type = (2) RFC otherwie Three Monte Crlo imultion were performe. In the firt imultion the colliion voince lorithm w turne off n RFC occurre in 49% of the tril. HFC occurre in.5% of the tril. When the colliion voince lorithm w ue without incluin humn motion preiction there were RFC in 2.0% of the tril n HFC in.2% of the tril. Uin the colliion voince lorithm incluin the humn * Althouh it i poible tht more thn one pir of phere collie imultneouly thi i hihly unlikely. Fi. 2 Metho for etectin humn t fult colliion. IV. CONCLUSIONS A novel olution to the 3D ynmic humn-robot colliion voince problem w preente. The metho exploit the efficiency of phere-phere itnce computtion by employin phere-be eometric moel for the humn n robot. A heuritic optimiztion pproch i ue to fin motion tht blnce between the robot pprochin it ol loction, n mximizin the itnce between the humn n robot moel. Preiction of robot n humn motion re employe to reuce the netive effect of nonintntneou robot repone in ynmic environment. A metho i preente for clcultin the key colliion voince prmeter L tht i be on the ynmic moel of the robot n it eire pee. Cpture motion t w ue to mke imultion of humn wlkin towr Pum robot more relitic. The inle run imultion reult how tht the robot voi colliion with the humn n then continue with it ine tk. Monte Crlo imultion uin 000 rnom humn wlkin pth pin throuh the robot workpce were ue to further vlite the colliion voince lorithm. The lorithm prevente ll colliion ue to the robot. The colliion voince lorithm i eteritic n efficient enouh to be ue in rel-time. On.8GHz Pentium IV PC, 40 Hz mplin rte w chieve. The metho i pplicble to robot with more or le DOF, n to environment with multiple humn n other obtcle. REFERENCES [] J. Heinzmnn n A. Zelinky, The fe control of humn-frienly robot, Proc. 999 IEEE Int. Conf. Intel. Rob. & Syt., pp , 999. [2] K. Ikut n M. Nokt, Generl evlution metho of fety for humn-cre robot, Proc. 999 IEEE Int. Conf. Rob. & Auto., pp , 999. [3] M. Zinn, O. Khtib n B. Roth, A new ctution pproch for humn frienly robot ein, Proc IEEE Int. Conf. Rob. & Auto., pp , [4] G. Hirziner, N. Sporor, A. Albu-Shffer, M. Hhnle, R. Krenn, A. Pcucci n M. Schel, DLR torque controlle liht weiht robot III re we rerchin the technoloicl limit now?, Proc IEEE Int. Conf. Rob. & Auto., pp.70-76, [5] O. Khtib, K. Yokio, O. Brock, K. Chn n A. Cl, Robot in humn environment, Proc. IEEE Firt Workhop on Robot Motion n Control, pp , 999.

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