Learning-based control strategy for safe human-robot interaction exploiting task and robot redundancies

Transcription

1 The 2 IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems Ocober 8-22, 2, Taipei, Taiwan Learning-based conrol sraegy for safe human-robo ineracion exploiing ask and robo redundancies Sylvain Calinon, Irene Sardellii and Darwin G. Caldwell Absrac We propose a conrol sraegy for a roboic manipulaor operaing in an unsrucured environmen while ineracing wih a human operaor. The proposed sysem akes ino accoun he imporan characerisics of he ask and he redundancy of he robo o deermine a conroller ha is safe for he user. The consrains of he ask are firs exraced using several examples of he skill demonsraed o he robo hrough kinesheic eaching. An acive conrol sraegy based on askspace conrol wih variable siffness is proposed, and combined wih a safey sraegy for asks requiring humans o move in he viciniy of robos. A risk indicaor for human-robo collision is defined, which modulaes a repulsive force disoring he spaial and emporal characerisics of he movemen according o he ask consrains. We illusrae he approach wih wo humanrobo ineracion experimens, where he user eaches he robo firs how o move a ray, and hen shows i how o iron a napkin. I. INTRODUCTION Roboic applicaions are bringing robos ino unsrucured environmens populaed by humans. These robos are expeced o achieve a large range of skills ha canno be preprogrammed. Conrollers capable of handling several ypes of exernal perurbaions are required o le he robo generalize he skill o new siuaions. Flexible learning mechanisms are also required o le non-exper users each new skills in a user-friendly manner. Providing robos wih learning by imiaion capabiliies is an approach o reduce he search space of he possible acions ha he robo can ake, while sill allowing he robo o furher refine is model of he demonsraion hrough reinforcemen learning [], [2]. Research in safey is carried ou in wo main direcions, passive and acive safey. The former is mosly implemened during he design of he robo o reduce he collision forces in he case of an unexpeced impac. Variable siffness acuaors have been proposed as a safe approach for driving robos ha inerac wih humans [3], [4]. These acuaors allow a robo o boh absorb he energy of an impac hrough a complian mechanism, and o achieve precise join posiioning hrough variaion of he siffness gains. The acive safey approach, insead, aemps o preven collision a he conroller level []. Moreover, sraegies for deecing he collision ogeher wih an appropriae reacion behavior have also been proposed [6]. The auhors are wih he Advanced Roboics Deparmen, Ialian Insiue of Technology (IIT), 663 Genova, Ialy. {sylvain.calinon,irene.sardellii, darwin.caldwell}@ii.i. This work was suppored in par by he AMARSi European projec under conrac FP7-ICT The concep of risk assessmen, which is mosly used for indusrial applicaions, is conained in he sandards which prescribe ha safey is guaraneed by defining an area where he robo sops when a human inrusion is deeced [7], [8]. These well-esablished sandards remain valid for a broad range of siff robos. They, however, rarely mee he requiremens of close human-robo ineracion in applicaions such as collaboraive asks, or in asks where he robos move in he viciniy of users. Wih he developmen of orqueconrolled robos such as he Barre WAM arm used in his paper, novel flexible and adapive conrol sraegies can be explored for human-robo ineracion. Consequenly, novel risk managemen policies and associaed conrol scheme also need o be examined. In his paper, we refer o he kinemaic redundancy of he robo when he robo possesses an infinie number of generalized inverse conrol sraegies, see e.g. [9], []. We refer o ask redundancy when he ask can be achieved hrough an infinie number of soluions, see e.g. []. We ake he perspecive ha boh he robo and ask redundancies can be exploied o regulae he dynamics of he movemen and he siffness of he robo during reproducion. Afer having observed several demonsraions of a similar ask, he robo creaes a compac model of he skill, by aking ino accoun he variaions and correlaions observed along he movemen. If a par of he movemen was consisen across he differen rials, his par of he ask should probably be reproduced in his specific manner. On he oher hand, if a large variabiliy was observed during he differen demonsraions, reproducing a specific reference rajecory is no required o fulfil he ask requiremens. During reproducion, he robo is using his informaion o se an adapive siffness marix compaible wih he ask requiremens. High compliance will allow here he simulaneous consideraion of oher consrains. We consider wo siuaions where he ineracion can benefi from he variabiliy and correlaions of he ask: (i) o le he user physically move he robo while reproducing he ask; (ii) o le he robo modify he generalized rajecory o adop gesures ha are safer for a user who is close o he robo. Insead of seing in advance a pre-deermined pah o follow, he robo hus makes use of he ask redundancies and is kinemaics redundancies o fulfill consrains relaed o safey and obsacle avoidance. Through his approach, he robo can sill follow a specific pah if he ask sricly requires i o do so (i.e., he skill showed a srong invariance across he muliple demonsraions). Oherwise, he robo will loosely generalize he skill by adaping is movemen //$2. 2 IEEE 249

2 o he user s proximiy and aenion. The proposed sraegy offers he possibiliy o cope wih unprediced evens in a safe way, as he robo remains complian in he pars of he ask ha do no require o rack precisely a reference rajecory. II. CONTROL STRATEGY To conrol he robo, we exploi he orque-feedback properies of he manipulaor, where he robo remains acively complian for he degrees of freedom ha are no relevan for he ask. We conrol he n degrees of freedom (DOFs) robo hrough inverse dynamics solved wih recursive Newon Euler algorihm [2]. The join forces f i a each join i {,...,n} are herefore calculaed as f i = fi a fi e + f j, j c(i) where fi a is he ne force acing on link i, f j wih j c(i) are he forces ransmied by he child c(i) of link i, and fi e are he exernal forces defined as fi e = F T + F O + F G. In he above equaion, F O =[f O, ] R 6 is a repulsive force applied o he poin x O in he kinemaic chain (when x O is on he link i) and hen projeced a he cener of graviy of he link; F T =[f T,M T ] R 6 is he vecor of force and momenum requesed o accomplish he ask (only applied a he end-effecor, i.e. when i = n), and F G =[f G, ] R 6 is he graviy compensaion force. Tracking of a desired pah in Caresian space is insured by he force command f T = m T ˆ x, where m T is a virual mass and ˆ x is a desired acceleraion command (described in nex subsecion). A. Learning he ask consrains M examples of a skill are demonsraed o he robo in slighly differen siuaions. Each demonsraion m {,...,M} consiss of a se of T m posiions x, velociies x and acceleraions x of he end-effecor in Caresian space, where each posiion x has D =3dimensions. A daase is formed by concaenaing he N = M m= T m daapoins {{x j, x j, x j } Tm j= }M m=. By considering flexibiliy and compacness issues, we propose o use a conroller based on a mixure of K proporional-derivaive sysems K [ ] ˆ x = h i () Ki P (μ X i x) κ V x. () i= The above formulaion shares similariies wih he Dynamic Movemen Primiives (DMP) framework originally proposed by Ijspeer e al [3], and furher exended in [4], [] (see [6] for a discussion on he similariies of he proposed conroller wih DMP). The principal difference is ha we consider a full marix Ki P associaed wih each of he K primiives (or saes) insead of a fixed κ P gain. This allows us o ake ino consideraion variabiliy and correlaion informaion along he movemen for learning and reproducion. Noe ha his process can generically be applied o oher movemen represenaions based on a superposiion of affine linear sysems, see e.g. [7], [8]. The superposiion of basis force fields is deermined in () by an implici ime dependency, bu oher approaches using spaial and/or sequenial informaion could also be used [7], [8]. Similarly o DMP, a decay erm defined by a canonical sysem s = αs is used o creae an implici ime dependency = ln(s) α, where s is iniialized wih s = and converges o zero. We define a se of Gaussians N (μ T i, ΣT i ) in ime space T, wih ceners μt i equally disribued in ime, and variance parameers Σ T i se o a consan value inversely proporional o he number of saes. α is iniially fixed depending on he duraion of he demonsraions. The weighs h i () are defined by h i () = N (; μ T i, ΣT i ) K k= N (; μt k, (2) ΣT k ). By deermining he weighs hrough he decay erm s, he sysem will sequenially converge o he se of aracors in Caresian space defined by μ X i. The ceners μx i in ask space and siffness marices Ki P are learned from he observed daa, eiher incremenally or in a bach mode (hrough leassquares regression). For example, pars of he movemen where he variaions beween he demonsraions are high indicae ha he reference rajecory does no need o be racked precisely. By using his informaion, he conroller can focus on he oher consrains of he ask such as moving away from he user. On he oher hand, pars of he movemen exhibiing srong invariance among he demonsraions should be racked precisely, i.e., he siffness used o rack he posiion errors needs in his case o be high. In a bach mode, by concaenaing he raining examples in a marix Y = [ + x κv + x] R N D, and by κ P κ P concaenaing he corresponding weighs compued wih (2) in a marix H R N K, we can wrie he linear equaion Y = Hμ X, wih μ X R K D represening he concaenaed aracor ceners μ X i. The leas-squares soluion o esimae he aracor ceners is hen given by μ X = H Y, where H is he pseudoinverse of H. To ake ino accoun variabiliy and correlaion along he movemen and among he differen demonsraions, we compue for each sae i {,...,K} he residual errors of he leas-squares esimaion, in he form of covariance marices Σ X i = N N (Y j,i Y i )(Y j,i Y j= i ) i {,...,K}, where Y j,i = H j,i (Y j μ X i ). (3) N (μ X i, ΣX i ) hus describes a Gaussian in Caresian space X. TheseofK Gaussians defines he sequence of virual aracor poins in Caresian space ha he sysem will ry o reach, where each aracor encapsulaes variabiliy and correlaion informaion. The residuals erms of he regression process are hen used o esimae he siffness marices Ki P 2

3 in Eq. () hrough eigencomponens decomposiion Ki P = V i D i V i, wih D i = κ P min +(κ P max κ P min) λ i λ min. (4) λ max λ min In he above equaion, λ i and V i are he concaenaed eigenvalues and eigenvecors of he inverse covariance marix (Σ X i ). The basic idea is o deermine a siffness marix proporional o he inverse of he observed covariance. For example, if high variabiliy is observed, siffness will become low as he racking does no need o be precise. If D i in (4)isseoλ i, he eigencomponens decomposiion gives Ki P = (Σ X i ). We rescale D i o obain siffnesses in he desired range [κ P min,κp max] (deermined by he user and hardware s limiaion) based on he iniial range of eigenvalues [λ min,λ max ] (deermined by he variabiliy wihin he moion and among several demonsraions). Sourcecode for he algorihms in his secion are available a hp://programming-by-demonsraion.org/sylvaincalinon/. B. Risk indicaor When he robo and he user are closely ineracing in an unsrucured environmen, he inenions of he human operaor are largely unpredicable. The experimen, ha we propose as a case sudy, considers he posiion and orienaion of he human s head wih respec o he moving robo arm. This scenario has been presened in lieraure as one of he mos imporan danger evens ha mus be addressed, see e.g. [3], [9]. In [2], we proposed an aenion mechanism based on he area covered by a vision cone inersecing wih a able on which a se of objecs were placed. The proposed approach was resriced o predeermined 2D planes, where he level of aenion was used o modify one exising ask, insead of considering several consrains simulaneously. We propose in his paper a more generic mechanism in 3D Caresian space based on he user s head pose. A moion capure sysem is used o rack he pose of he head, described by is posiion x U and orienaion marix R U. The closes posiion x O on he robo s kinemaics chain o he posiion x U of he user is firs compued. The vecor beween he user and he robo s closes poin is defined by v = x U x O, wih associaed norm d = v. The user s gaze direcion is approximaed by his/her head direcion vecor u = R U e, wih e =[] being a uni vecor. The angle beween he user s gaze vecor and he vecor direced owards he robo s closes poin is deermined by ω = arccos(u v). Disance d and angle ω are boh considered as parameers for he deerminaion of a risk facor relaed o he user s proximiy and aenion awareness. When humans move heir head, he indicaor hus scales he risk of human-robo collision on he basis of a funcion r = f(d, ω, σ d,σ ω ) R [,], ha depends on he angle ω in-beween he user s gaze direcion and he robo s closes poin, and disance d of he human s head from he robo. We define he risk indicaor as r = N (d;,σ d) N (ω; π, σ ω ) N (;,σ d ) N (π; π, σ ω ), fo α ( 2, Σ 2 ) ( 3, Σ 3 ) ( 7, Σ 7 ) ( 6, Σ 6 ) (, Σ ) ( 4, Σ 4 ) (, Σ ) 2 Fig.. Illusraion of he learning and rerieval processes. Top-lef: Four examples of he ask provided as demonsraions. Top-righ: Learned model and muliple reproducion aemps by rerieving for each reproducion a se of aracors from he Gaussian disribuions N (μ X i, ΣX i ). Cener: Consideraion of he user in he reproducion of he ask. The user s head is represened by a red poin, wih he black line showing is orienaion. The rajecory in green lines shows a generalized reproducion aemp wihou consideraion of he user. The rajecories in red and blue lines show he rerieved pah when he user is close o he robo a he beginning and a he end of he movemen, for wo differen head direcions. Those in red lines correspond o he siuaion where he user is on he pah bu remains aenive o he robo s movemen (lef). Those in blue lines correspond o he siuaion where he user looks away from he robo (righ). The dos show posiions a consan ime inervals. Boom: Norm of he repulsive force f O and value of he decay parameer α along he movemen for he differen reproducion scenarios. where σ d and σ ω are variance parameers deermined by he experimener. Fig. 6 lef shows he risk funcion used for he experimens. The highes level is considered when he user is close o he robo and facing away. The lowes and safes level is when he human operaor is ou of he robo s workspace and when he user is looking in he direcion of he robo s movemen. By aking his ino consideraion, we define a repulsive v force f O = rf max v, where f max is a maximum force value defined by he experimener. Similarly, we define he decay parameer ha les he sysem converge sequenially o he se of aracors modeling he ask (see Sec. II-A) as α = ( r)α max, where α max is deermined by he experimener. Fig. illusraes he approach using a 2-dimensional example. In he op-righ graph, we see ha he rajecories repro- 2

4 Tray handling ask Ironing ask x x Ironing ask Tray handling ask.. x x Fig. 2. Experimenal seup. duced sochasically from he learned model show differen levels of variabiliy along he ask. This variabiliy shows similar characerisics o he one in he raining se (oplef graph). In he second row, he behavior of he robo is differen in he wo reproducion scenarios. In he firs, where collision avoidance is a he beginning of he movemen, he robo goes round he user by deviaing significanly from he generalized rajecory, as he consrains of he ask are no very high in his area (i.e. he robo sill fulfils he ask consrains correcly). In conras, in he second collision avoidance siuaion, near he end of he moion, he robo only moves slighly from he generalized rajecory, since he demonsraions were showing a higher level of consisency in his par of he movemen (i.e. he robo can only slighly depar from he generalized rajecory o reproduce he ask correcly). We see ha, when he user is in he proximiy of he robo s ask pah, he ask moion is slowed down o smoohly avoid he user, wih a naural behavior ha akes ino accoun he ask requiremens. Finally, when he user is no looking in he direcion of he movemen, he robo goes round he user wih a larger ampliude. III. EXPERIMENTS A. Experimenal seup The experimen is conduced wih a orque-conrolled Barre WAM 7 DOFs roboic arm. The posiion and orienaion of he user s head are racked wih a marker-based NauralPoin OpiTrack moion capure sysem. 2 cameras are used o rack he posiion x U and orienaion of he user s head (R U in direcion cosine marix represenaion), a a rae of 3 frames per second. Fig. 3. Recordings (op row, in grey line) and sochasic reproducion from he learned model (boom row, in black line). We see ha he reproduced resuls presen a variabiliy similar o he one observed during he demonsraion rials. Two experimens are proposed. The firs consiss of holding a ray a he lef-hand side of he robo, and moving i o a able a he righ-hand side of he robo (while keeping he ray horizonal). The second consiss of ironing a square napkin. These wo skills have non-uniform consrains in posiion. For he ray handling ask, he posiion of he ray is more consrained a he end of he movemen han during is ransporaion, in order o bring i o he desired posiion. For he ironing ask, he rajecory ha he iron should follow is more consrained in he verical axis han in he horizonal plane. To fulfil he ask requiremens, i is indeed more imporan o have he iron in conac wih he able han o follow a very specific pah on he able. These consrains are refleced in he colleced daa. During demonsraion, graviy compensaion is used o allow he user o move he robo efforless. Through his kinesheic eaching process, 7 demonsraions are provided by recording he posiion and orienaion of he end-effecor. Each ask is encoded wih he proposed model, by fixing he number of saes (or primiives) wih respec o he lengh of he demonsraions. 6 and 8 saes are respecively used o encode he ray handling and ironing movemens. Fig. 2 presens he experimenal seup and he saic frame of reference ha we consider for he wo asks. B. Experimenal resuls Figs 3-6 presen he experimenal resuls. Fig. 3 depics sochasic reproducion resuls showing ha he residuals can be used o generae reproducion aemps wih similar 22

5 Muliple demonsraions Exracion of he ask consrains ˆΣ X Reproducion wih variable siffness ˆK P Sochasic reproducion aemps Fig. 4. Experimenal resuls for he ray holding ask. From lef o righ: Demonsraions. Exracion of he ask consrains hrough he residuals of he regression process. Adapive siffness gain marix compued from he residuals informaion. Sochasic reproducions of he movemen. Muliple demonsraions Exracion of he ask consrains ˆΣ X Reproducion wih variable siffness ˆK P Sochasic reproducion aemps Fig.. Experimenal resuls for he ironing ask. Top: Demonsraions. Exracion of he ask consrains hrough he residuals of he regression process. Adapive siffness gain marix compued from he residuals informaion. Sochasic reproducions of he movemen. Boom: The second row shows several perurbed reproducion aemps. The user s head is represened by red dos, wih he black lines showing is orienaion. From lef o righ: Siuaion where he user is on he pah of he robo and is no looking a he movemen. Siuaion where he user is facing he robo. Reproducion by arificially applying a consan force parallel o he able a he end-effecor of he robo. Reproducion by applying a consan force wih he same ampliude bu verically o he able. variabiliies o hose observed among he demonsraion rials. For he ray handling ask in Fig. 4, he robo becomes siffer a he end of he movemen (bigger siffness ellipsoids a he end of he movemen), in order o correcly posiion he ray on he able (he covariance marices ˆΣ X = K i= h i()σ X i and siffness gain marices ˆK P = K i= h i()ki P are respecively represened wih grey and green ellipsoids). During he course of he movemen, he ask consrains remain low, as here is no obsacle in he robo s workspace. The siffness gains reflec his characerisic by remaining low unil he robo approaches he able. We see in he second column ha he model correcly encapsulaes he variabiliy of he demonsraions hrough he X se of covariance marices ˆΣ esimaed from he residuals of he regression process. A variable siffness gain marix ˆK P is auomaically se in consequence in order o fulfil he learned ask consrains (hird column). For he ironing ask in Fig., he learned model shows ha i is more imporan o rack he movemen in he verical direcion han in he oher wo direcions of he horizonal plane (nearly fla ellipsoids in he second graph). In he hird graph, he siffness marices have consequenly an elongaed shape. We also see ha by applying a virual force o he endeffecor during reproducion, he deformaion is sronger if he force is parallel o he able han if he force is verical (las wo graphs). Fig. 6 righ presens snapshos of he robo reproducing he ironing ask, while he user eners he workspace and grasps an objec in he viciniy of he robo. A video of his experimen also accompanies his submission. IV. DISCUSSION We used in his paper a simple repulsive force fields policy as a firs approach o avoid collisions wih he user. Soluions based on superposiion of addiional force fields help preven collisions [2], bu do no necessarily guaranee ha no collision will occur. Such a policy is fas and compuaionally efficien, bu i remains adequae only for a limied subse of he possible scenarios ha one migh expec in human-robo ineracion. Considering muliple consrains wihin he same level of conrol can indeed be problemaic in cases where compeing 23

6 r d dmax ω ωmax.8 Fig. 6. Lef: Risk indicaor r = f(d, ω, σ d,σ ω). Righ: Snapshos of a reproducion aemp for he ironing ask. forces of high ampliudes sudden change in direcion or applicaion poins, which can produce unpredicable behaviors if one does no limi he maximum force allowed. One possible alernaive is o consider a hierarchical decomposiion of he ask consrains [9], [], or o adop a prioriized opimizaion sraegy [22]. This firs se of experimens opens he road for various furher invesigaions. We will explore in which manner risk indicaors can be inegraed in an overall safey sraegy, by aking ino consideraion ha hese indicaors srongly depend on he user (e.g., he risk indicaors can differ depending on he age or moor capabiliies of he person ineracing wih he robo), as well as on oher habiuaion facors. To do his, we will concenrae on learning he parameers ha are relevan for he evaluaion of he risk indicaor. We will also explore in which manner he dynamics of he user s body can be considered in he esimaion of he risk funcion (insead of a saic pose). To do so, we plan o develop predicion sraegies ha ake ino accoun: (i) he conex in which pre-collision occurs; and (ii) he robusness of he sensory informaion available o rack he user s movemen. V. CONCLUSION We proposed an acive conrol sraegy based on ask-space inverse dynamics conrol wih variable siffness. Learning of he ask is insured by he user providing muliple demonsraions of he skill. Afer exracion of he ask consrains, he robo replicaes he ask by auomaically selecing a variable level of compliance o reproduce he essenial characerisics of he skill. The redundancy of he ask and he redundancy of he robo are exploied o deermine a safey conrol sraegy hrough he esimaion of he user s head pose. We demonsraed he feasibiliy of he approach wih a ray handling ask and an ironing ask REFERENCES [] A. Billard, S. Calinon, R. Dillmann, and S. 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