ANALYZE OF A COLLISION AVOIDANCE STRATEGY FOR COOPERATIVE ROBOTS

Transcription

1 ANALYZE OF A COLLISION AVOIDANCE STRATEGY FOR COOPERATIVE ROBOTS ANALYZE OF A COLLISION AVOIDANCE STRATEGY FOR COOPERATIVE ROBOTS Prof. Eng. A. Frau PhD 1, Prof. Eng. M. Dambrine PhD 2, 3 1 Universiy Transilvania from Braşov, Brasov, Romania 2 Univ Lille Nord de France, F Lille, France 3 UVHC, LAMIH, F Valenciennes, France REZUMAT. Aceasa lucrare prezina o analiza a unei sraegii noi de eviare a coliziunii roboilor cooperaivi. Fiecare robo fizic acioneaza oal independen, comunicand cu prooipul virual corespunzaor si imiand omologul sau virual. v Fiecare robo fizic reproduce comporamenul prooipului sau virual. Esimarea aciunilor fara coliziuni, folosind roboii viruali, si munca in colaborare a roboilor fizici care imia prooipurile lor viruale sun ideile ile originala ale a lucrarii. rii. Noi am esa prezena sraegie pe caeva scenarii de simulare care implica doi roboi viruali, esimand aciunile fara coliziuni in impul sarcinilor de cooperare. Cuvine cheie: Roboi viruali, Roboi cooperaivi, Eviarea reciproca a coliziuni ABSTRACT. This paper, presens an analyze of a new collision avoidance sraegy for cooperaive robos. Each physical robo acs fully independenly,, communicaing wih corresponding virual prooype and imiaing her virual homologue. Each physical robo reproduces he behaviour of her virual prooype. The esimaion of he collision-free acions of he virual robos and he collaboraive work of he physical robos who imiae here virual prooypes, are he original ideas.. We esed he presen sraegy on several simulaion scenarios, involving wo virual robos and esimaing collision-free acions, during of he cooperaive c operaive asks. Keywords: Virual robos, Cooperaive robos, Reciprocal collision avoidance 1. INTRODUCTION Collaboraive robos, we see being deployed nowadays in research or indusry, are permanenly in danger o be in collision. Therefore insallaions wih muliple robos in real world, such as collaboraive work and mainenance he good sae of he line producion, require collision avoidance mehods, which ake ino accoun he muual consrains of he robos. A key requiremen for heir efficien operaion is good coordinaion and reciprocal collision avoidance. The conac of he robo wih an obsacle mus bee deeced and i will cause he robo o sop quickly and hereafer back off o reduce forces beween he robo and environmen. The problem of he conac wih obsacle imposes he null velociy in he momen of he impac. The problem of he conac deecion is beer analyzed on he virual prooype in he virual environmen, where he virual objecs can be inerseced and here no exis he risk o be desroyed. The problem of he conac deecion in he virual environmen on he virual robos is imporan for he reason ha his buil-in funcion is proven superior o mechanical collision deecion devices. Using his sraegy one deecs collisions in all direcions, proecing no only he physical end-effecors bu also he work pieces and he physical robo iself. In he case ha he real (physical) robo will imiae her virual prooype, i has no mechanical pars which gives i higher reliabiliy and more cos efficiency. Also, since here is no device aached o he real robo ool, one no exends he ool offse disance, which allows bigger maximum ool weigh and beer reorienaion performance. The problem of local collision-avoidance differs from moion planning, where he global environmen of he robo is considered o be known and a complee pahway owards a goal configuraion is planned a once. So, he collision deecion simply deermines if wo geomeric objecs are inersecing or no. The inersecing of wo objecs is possible in he virual world, where one may predic here behavior. The abiliy of predicing of he behavior of cooperaive manipulaors is imporan for several reasons: for example, in design he designers wan o know wheher he manipulaor will be able o perform a cerain ypical ask in a given ime frame; in creaing feedback conrol schemes, where sabiliy is a major problem, he conrol engineer canno risk a valuable piece of equipmen by exposing i o unesed conrol sraegies. Therefore, a facile sraegy for collision avoidance, capable of predicing he behavior of a Buleinul AGIR nr. 4/2012 ocombrie-decembrie 1 7

2 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 2013 roboic manipulaor, or of a sysem a whole, for ha maer becomes imperaive. In a real world, like collision deecion, where he robos need o inerac wih heir surrounding, i is imporan ha he compuer can simulae he ineracions of he cooperaive paricipans, wih he passive or acive changing environmen, using virual prooyping. In his paper, we propose a fas mehod ha simulaneously deermines acions for wo virual robos ha each may have differen objecives. The acions are compued for each virual robo and are ransferred o corresponding physical robo, wih a cenral coordinaion for he cooperaive asks. Ye, we prove ha our mehod guaranees he collision-free moion for each of he robos. We used a simplified robo model, where each virual robo end-effecors is assumed o have a simple spherical shape moving in a hree-dimensional workspace. Furhermore, we assume ha each virual robo end-effecors can moves in any direcion, such ha he conrol inpu of each robo is given by a hreedimensional velociy vecor. Also, we assume ha our algorihm is able o deduce he exac shape, posiion and velociy of obsacles and of he virual robos, in he virual environmen. The presen simulaion mehod is based on velociy approach which provides a sufficien condiion for each robo o be collision-free for a leas a fixed amoun of ime ino he fuure. Tha implies, ha each robo akes ino accoun he observed velociy of oher robos in order o avoid collisions wih hem, and also ha he robo selecs is own velociy from is velociy space in which cerain regions are marked as forbidden because of he presence of oher robo. In his paper we develop an formally analyze of a new collision avoidance sraegy for a group of wo collaboraive robos. 2. STATE-OF-THE-ART AND POSSIBLE EXTENSIONS The problem of collision avoidance has been exensively sudied. Many approaches assume he observed obsacles o be saic (i.e. non-moving), and compue an immediae acion for he robo ha would aver collisions wih he obsacle, in many cases aking ino accoun he robo s kinemaics and dynamics. If he obsacles are also moving, such approaches ypically repeaedly plan again based on new readings of he posiions of he obsacles. However, such approaches are insufficien for mulirobo locaion, where he robo encouners oher robos ha also make decisions based on heir surroundings: considering hem as moving obsacles neglecs he fac ha hey reac o he robo in he same way as he robo reacs o hem, and inherenly causes adverse acions in he moion of he robos [9]. Velociy Obsacles (VO) [1, 3] have been a successful velociy-based approach o avoid collisions wih moving obsacles; hey provide a sufficien and necessary condiion for a robo o selec velociy ha avoids collisions wih an obsacle moving a a known velociy. Besides he Velociy Obsacle approach, many oher mehods have been proposed for collision-avoidance, navigaion, and planning among moving obsacles [3]. There is also Recursive Velociy Obsacles and Common Velociy Obsacle mehods. There is also an exensive amoun of lieraure on muli agen navigaion, in which each agen navigaes individually among he oher agens, which are considered as obsacles, e.g. [3, 4, 11]. Mos of hese echniques have focused on muliude simulaion. Also in hese cases, he oher agens are assumed o be eiher passively moving obsacles or saic obsacles. A number of approaches follow he Velociy Obsacle concep o avoid oher agens. However, he robo may no be able o communicae wih oher eniies and may no know heir inens. I is he case of Reciprocal Velociy Obsacles(RVO) problem [9 ], in which robos are ypically given half he responsibiliy of avoiding pair pruden collisions. This formulaion only guaranees collision-avoidance under specific condiions, and does no provide a sufficien condiion for collisionavoidance in general. For overcomes his limiaion here exis Opimal Reciprocal collision Avoidance (ORCA) ha provides a sufficien condiion for muliple robos o avoid collisions among one anoher, and hus can guaranee collision-free navigaion. One disinguishes decoupled muli-agen navigaion from cenralized muli-agen planning. In his paper, we presen a sudy ha provides a sufficien condiion for wo virual cooperaive robos o avoid collisions among one anoher. The virual cooperaive robos move in a complex virual environmen conaining boh saic and moving obsacles. Our approach reas he virual prooype of wo cooperaive robos who navigae while guaraneeing collision-free moion. In a fuure paper we ransfer he rajecory of he virual robos o physical robo in he real environmen, assuming ha each physical robo can perfecly imiae he movemen of her virual prooype. 3. COLLISION DETECTION Collision deecion frequenly arises in various applicaions including virual prooyping, dynamic 2 Buleinul AGIR nr. 4/2012 ocombrie-decembrie 8

3 ANALYZE ANALYZE OF A OF COLLISION A COLLISION AVOIDANCE AVOIDANCE STRATEGY STRATEGY FOR COOPERATIVE FOR COOPERATIVE ROBOTS ROBOTS simulaion, ineracion, navigaion and moion planning. Collision deecion has been exhausively researched for more han hree decades. In his secion, we presen a sudy based on collision deecion algorihm for compuing all he conacs beween muliple moving virual objecs in a large virual environmen. I uses he visibiliy reducing algorihm described in [2]. The overall algorihm is general and applicable o all environmens. We also highligh many opimizaions and he visibiliy queries used o accelerae he performance of he algorihm. Algorihms for narrow phase can be furher subdivided ino efficien algorihms for convex objecs and general purpose algorihms based on spaial pariioning and BVHs for polygonal models [2]. However, hese algorihms ofen involve precompuaion and are mainly designed for rigid models. The performance of collision deecion depends on he inpu model complexiy and he problem oupu, which is he number of colliding or overlapping primiives. However, exising algorihms may no achieve ineracive performance on large models consising of housands of riangles due o heir high complexiy and oupu of he problem. Moreover, he memory requiremens of hese algorihms are ypically very high. Poenially Colliding Se. We compue a Poenially Colliding Se (PCS) of objecs ha are eiher overlapping or are in close proximiy [2]. If an objec O i does no belong o he PCS, i implies ha O i does no collide wih any objec in he PCS. Based on his propery, we can reduce he number of virual objec pairs ha need o be checked for exac collision. This is similar o he concep of compuing he poenially visible se (PVS) of primiives from a viewpoin for spaial relaion. We perform visibiliy compuaions beween he objecs in image space o check wheher hey are poenially colliding or no. Given a se S of objecs, we es he relaive visibiliy of an objec O wih respec o se S using an image space visibiliy query. The query checks wheher any par of O is spaial inerseced by S, raserizing all he objecs belonging o se S. The objec O is considered fully-visible if all he fragmens generaed by he raserizaion of O have a deph value less han he corresponding pixels in he frame buffer. Many applicaions need o compue he exac overlapping feaures (e.g. riangles) for collision response. We iniially compue he PCS of objecs based on he algorihm highlighed above. Insead of esing each objec pair in he PCS for exac overlap, we again use he visibiliy formulaion o idenify he poenially inersecing virual regions among he objecs in he PCS. Iniially, all he objecs belong o he PCS. Firsly we perform reducing along each coordinae axis by using he axis aligned bounding boxes as he objec s represenaion for collision deecion. We decompose each objec ino sub-objecs. A subobjec can be a bounding box, a group of k riangles (say a consan k), or a single riangle. We have exended his approach o sub-objec level and compue he poenially inersecing areas. 4. RECIPROCAL COLLISION AVOIDANCE For wo robo end-effecors A and B, he velociy obsacle, VO (read: he velociy obsacle for A induced by B for ime window ) is he se of all relaive velociies of A wih respec o B ha will resul in a collision beween A and B a some momen before ime [9]. I is formally defined as follows. Le be an A robo end-effecor wih radius r A, posiioned a p A on a horizonal disc. For a configuraion of wo robo end-effecors A and B, he horizonal disc of radius (r A + r B ) is cenered a (p B p A ) in he Carezian space. Le S (p, r) denoe an open horizonal disc of radius r cenered a vecor posiion p and defined by he (1). S( p, r) = { s S, s p r} (1) Then he velociy obsacle is defined as: VO = v [0, ], v S( p p, r + r )} (2) { B A Le v A and v B be curren he ask (operaional) velociies of he robos end-effecors A and B, respecively. The definiion of he velociy obsacle implies ha if (v A -v B )єvo, or equivalenly if (v B -v A ) єvo B A, hen A and B will collide a some momen before ime if hey coninue moving a heir curren velociy. On he oher hand, if (v A -v B ) VO, he wo robo end-effecors A and B are guaraneed o be collision-free for a leas ime. Robo end-effecor A will collide wih robo end-effecor B wihin ime if is velociy v A is inside VO and i will be collision-free for a leas ime if is velociy is ouside he velociy obsacle. For an ariculaed robo arm, he robo end-effecors velociy vecor is calculae as, v = X& where X is he Caresian posiion vecor of he robo end-effecor. The vecor X can be described as a funcion of robo joins variables vecor, q : X = f(q) (3) Equaion (3) can be obained easily wih he help of he Denawi - Harenberg operaors. Buleinul AGIR nr. 4/2012 ocombrie-decembrie 3 9

4 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 2013 The robo end-effecors velociy vecor v can be obained as: v = X & J ( q ) = q& (4) where J is Jacobian marix, and q&, he robo joins velociies vecor. Given a rajecory ha each moving robo end-effecor will ravel, we can deermine he exac collision ime. If he pah ha each robo end-effecor ravels is no known in advance, hen we can calculae a lower bound on collision ime. This lower bound on collision ime is calculaed adapively o speed up he performance of dynamic collision deecion. 5. COLLISION DETECTION THROUGH ANIMATION OF THE VIRTUAL ROBOTS Ineracive animaion of he virual agens/objecs in virual realiy sysems has been a challenging problem for years. Alhough many fas mehods of animaion have been proposed, few echniques are currenly able o dynamically animae even simple virual objecs as rigid objecs a ineracive raes. This paper proposes an approach ha finds a balance beween hese wo goals, enabling robus ineracive animaion as moving picure illusrae. Our proposed scheme for dynamic simulaion or animaion, using he disance compuaion algorihm is an ieraive process which coninuously insers and delees he objec pairs from a sack according o heir approximae ime o collision, as he objecs move in a dynamic environmen. The end-effecors pair which has a small separaion is likely o have an impac wihin he nex few ime insances, and hose virual pairs which are far apar from each oher canno possibly come o inerfere wih each oher unil cerain ime. Simulaion Framework. The essence of his framework is o describe each rigid objec in he planning scene as a dynamical sysem, which is characerized by is sae variables (i.e. posiion, orienaion, linear and angular velociy). In his framework, a robo arm can be a collecion of rigid bodies, subjec o he influence of various forces in he workspace, and resriced by various moion consrains. This ransforms a moion planning problem ino a problem of defining suiable consrains, and hen simulaing he rigid body dynamics of he scene wih each consrain acing as a virual force on he objecs such as he collision will be avoided. Curren commodiy graphics hardware suppors an image-space occlusion query ha checks wheher a primiive is visible or no. In order o suppor such a query, we change he deph es o pass only if he deph of he incoming fragmen is greaer han or equal o he deph of he corresponding fragmen in he frame buffer. Wih his deph he comparison funcion, we used an image poenially inersecing regions query o es if a primiive is no visible when rendered agains he deph buffer. We would like o invesigae differen represenaions o suppor efficien runime updaes of he model s muliresoluion. The curren algorihm is designed primarily for collision deecion. We used our layous o improve he performance of view-dependen rendering, collision deecion wihou any modificaion of he algorihm or runime applicaions. For real-world applicaions various ways o overcome his problem have been used. An exensive dissipaive force, opposie o he velociy of a mass poin, provides a good way o mainain he sabiliy of he inegraion. Planning scene formulaion for cooperaive asks. In he cooperaive asks sudies, he simulaion is used o find wheher i is possible o avoid he collision beween a paricular par of he robo arm and diverse objecs in he work space and so o find one possible free pah. In his secion we will describe how o render a planning scenario in he form of consrains for he consrain-based planning framework. Our visibiliy based on PCS compuaion algorihm is based on hardware visibiliy query which deermines if a primiive is fullyvisible or no. By assuming ha he geomery represening he robos and obsacles is given, as well as prescribed moion, simulaed for he obsacles over ime. Our sysem, hen defines consrains ha will resric he moion of he robos o mee he design specificaions, and also guide he robos o complee he planning asks such as he collision will be avoided. Our virual sysem was implemened on a programming plaform, using Delphi objec-oriened programming language. We have esed our sysem of wo robos for collision deecion in he following scenes for he virual prooyping applicaions: Scene 1: individual ask for each robo Each of wo robo arms is composed of rigid componens ha are held ogeher by consrains. For all of he componens of he robo arm, he planner mus compue pahs o saisfy he join consrains do no collide wih he obsacles as he conveyors and lead he end-effecors along he prescribed pah. In he scene seen in Fig. 1, wo ariculaed robo arms, wih six degrees of freedom, are used o manipulae hard objecs from a conveyor bel o anoher conveyor bel. Each robo arm follows a pah over he conveyor body while avoiding obsacles. 4 Buleinul AGIR nr. 4/2012 ocombrie-decembrie 10

5 ANALYZE ANALYZE OF A OF COLLISION A COLLISION AVOIDANCE AVOIDANCE STRATEGY STRATEGY FOR COOPERATIVE FOR COOPERATIVE ROBOTS ROBOTS moved simulaneously o posiioning he oval objec in he gap of he ellipsoid objec and o avoid he collision. The assembly line conains a suppor srucure ha is moving over he conveyer bel in he some direcion o he assembled pars. The moving srucure may become an obsrucion ha causes he robos o reacively modify is pah, o avoid he collision. Fig. 1 Scene for individual asks Scene 2: cooperaive mission In our example, a second scene shown in Fig. 2, he end-effecors of he lef robo and of he righ robo respecively, avoid each oher in a work cycle during a collaboraive ask. In his scene wo ariculaed robo arms, each oher wih six degrees of freedom, are in cooperaive mission. They are used o assembly ogeher wo rigid pieces. The robo arms avoid he moving bel o ge in ouch he wo pieces passing hem on he assembly conveyer bel. The goal o manipulae ogeher he same objec in a cooperaive mission requires boh robos o maneuver around each oher wihou colliding. The ask is for each virual robo o independenly (and simulaneously) selec a new velociy for iself such ha boh virual robos are guaraneed o be collision-free for a leas a fixed amoun of ime, when hey would coninue o move a heir new velociy. As a secondary objecive, he virual robos should selec heir new velociy as close as possible o heir preferred velociy. Fig. 3 Scene for assembly line planning Since he usual models of he cooperaive robos are raher complex and may have housands of objecs in he world, he algorihm as described in [6, 7], becomes an essenial componen o generae a realism of moions. This image sequence shows discree posiions from our dynamic simulaion applicaion. In order o show he generaliy of our approach, we compue layous of several kinds of geomeric models. We used hese layous direcly wihou any modificaion o he runime applicaion. View-dependen rendering and simplificaion are frequenly used for ineracive display of massive models. These algorihms pre-compue a muli-resoluion hierarchy of a large model (e.g. a verex hierarchy). Figures 1, 2 and 3 show various insan bliz obained during such virual realiy sessions, wih only he inverse dynamics is applied, resuling in simulaion. 6. CONCLUSIONS AND FUTURE WORKS Fig. 2 Scene for cooperaive mission Scene 3: assembly line planning In his example, shown in Fig. 3, he robo arms from scene 2 mus assembly an ellipsoid objec wih he oval objecs, on a conveyer bel. Boh robos mus be We propose an original idea ha allows us o ransfer he join rajecory of each virual robo o he corresponding join of he real (physical) robo. Wih oher worlds we prepare he free-rajecories for he pair of he virual cooperaive robos; hese rajecories can be ransferred o he pair of he physical cooperaive robos. Buleinul AGIR nr. 4/2012 ocombrie-decembrie 5 11

6 INT. SYMPOSIUM ON ELECTRICAL ENGINEERING AND ENERGY CONVERTERS ELS 2013 In he real world, he programming pahway of he physical robos can be realized using he pahway of he virual robo prooypes. Therefore, he virual robo behavior mus be specifically aken ino accoun in order o guaranee ha collisions are avoided. Each real robo may be able o communicae wih her virual corresponding eniy and may imiae heir inens [10, proposal paen]. In our collaboraive work sysems, he virual robo prooypes are used mainly as an inermediae resul for calculaing he neares neighbors and he poenially inersecing areas in an evenually collision of he virual robos. We compue PCS of virual objecs ha are eiher parly cover or are in close proximiy. If an objec does no belong o he PCS, i implies ha his objec does no collide wih any objec. As an alernaive of esing each objec pair in he PCS for exac parly cover, we more han use he visibiliy formulaion o idenify he poenially inersecing virual areas among he objecs. Based on his propery, we realized a programming plaform for real (physical) robos based on collaboraive virual robos pair, ha need o be checked for exac collision deecion. This plaform needs o compue he exac overlapping area of he virual cooperaive robos, as collision response. BIBLIOGRAPHY [1] C. Fulgenzi, A. Spalanzani, C. Laugier, Dynamic obsacle avoidance in uncerain environmen combining PVOs and occupancy grid. In Proc. IEEE In. Conf. on Roboics and Auomaion, pp , [2] N. K. Govindaraju, S. Redon, M. C. Lin and D. Manocha, CULLIDE: Ineracive Collision Deecion Beween Complex Models in Large Environmens using Graphics Hardware, M. Dogge, W. Heidrich, W. Mark, A. Schilling (Ediors), Graphics Hardware, [3] D. Hennes, D. Claes, W. Meeussen, K. Tuyls, Mulirobo collision avoidance wih localizaion uncerainy, In: Proceedings of he 11h Inernaional Conference on Auonomous Agens and Muliagen Sysems, Conizer, Winikoff, Padgham, and van der Hoek (eds.), June, 4 8, 2012, Valencia, Spain. [4] Y. Abe, M.Yoshiki, Collision avoidance mehod for muliple auonomous mobile agens by implici cooperaion. IEEE/ RSJ, In. Conf. Inelligen Robos and Sysems, pp , [5] K. O. Arras, J. Persson, N. Tomais, R. Siegwar, Real-Time Obsacle Avoidance for Polygonal Robos Wih a Reduced Dynamic Window in Proc. In. Conf. on Roboics and Auomaion, Washingon DC, May 2002,. [6] N. Galoppo, Animaion, Simulaion, and Conrol of Sof Characers using Layered Represenaions and Simplified Physics-based Mehods Disseraion submied o he faculy of he Universiy of Norh Carolina Chapel Hill, [7] S.E. Yoon, Ineracive Visualizaion and Collision Deecion using Dynamic Simplificaion and Cache- Coheren Layous. Disseraion submied o he faculy of he Universiy of Norh Carolina, Chapel Hill, 2006 [8] J. van den Berg e al.: Reciprocal n-body collision avoidance, Roboics Research, The 14h Inernaional Symposium ISRR, Springer Tracs in Advanced Roboics, vol. 70, Springer-Verlag, May 2011, pp [9] J. Snape, J. van den Berg, S. J. Guy, and D. Manocha, Independen navigaion of muliple mobile robos wih hybrid reciprocal velociy obsacles, IEEE/RSJ In. Conf. Inelligen Robos and Sysems, S. Louis, Mo., [10] A. Frau, M. Frau.: Mehod and insallaion for joins rajecory planning of a physical robo arm (proposal - paen) unpublished. [11] J..Snape e al. Independen navigaion of muliple robos and virual agens. In Proc. of he 9h In. Conf. on Auonomous Agens and Muli agens Sysems (AAMAS 2010), Torono, Canada, May Abou he auhors Prof. Eng. Aurel FRATU, PhD. Transilvania Universiy of Brasov, Brasov, Romania Auomaics and Informaion Technology Deparmen [email protected], Main srenghs of research aciviies: Modeling and simulaion, Robos conrol sysems, Digial conrol sysems, Prof. Eng. Michel DAMBRINE, PhD. Universiy of Valenciennes, F Valenciennes, France Indusrial and Human Auomaion, Mechanics and Compuer Science (LAMIH) Laboraory [email protected] Main srenghs of research aciviies: Sabiliy of nonlinear sysems, Robus conrol of uncerain nonlinear sysem, Real ime robo conrol. 6 Buleinul AGIR nr. 4/2012 ocombrie-decembrie 12