A Robot Assisted Assembly System for Large and Heavy Components in Products Assembly

Transcription

1 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, 205 do: /gpa A Robot Asssted Assembl Sstem for Large and Heav Components n Products Assembl Zhang Ljan *, L Lun 2, Y Wangmn 2, Yang Ln 2 Chna Academ of Space Technolog, No04, You Road, Bejng, Chna 2 Shenang Insttute of Automaton, Chnese Academ of Scences, No4, Nanta Street, Shenang Ct, Chna zljcast@63.com; 2 Llun@sa.cn; 3 zlj008224@63.com; angln@sa.cn Abstract The purpose of ths paper s to propose a robot-asssted assembl sstem for the nstallaton of a varet of heav components n the assembl sstem. The robot-asssted assembl sstem s composed of an ndustral robot sstem, a robot path plannng sstem, a vsual postonng sstem and an addtonal robot moton platform. Stereo vson sstem s used to mprove the accurac the of robot postonng sstem. Probablstc roadmap (PRM) method s used to plan robot path n 3D space wth obstacles. The PRM planner dvdes plannng nto two phases: the learnng phase and the quer phase. In the learnng phase, collson-free roadmap s bult. In the quer phase, the nodes of roadmap are connected. We use the A-star algorthm to fnd a feasble path between the ntal node and the goal node. Experment results show that our method can effcentl make a collson-free path n the workspace wth obstacles n the products. Kewords Assembl Sstem; Computer Vson; Robot Path Plannng Introducton In product assembl feld, such as aerospace product assembl, some techncal components need to be fxed onto the product precsel. These components are characterzed wth heav weght, and the nstallaton accuraces of these components are strngentl requred to guarantee the product qualt. For these heav components, t s dffcult for the operator to hold the component manuall through the entre assembl tme. In recent ears, robot-asssted assembl sstem, combnaton of the automated postonng and the precson measurement sstem has been developed to mprove the assembl qualt and effcenc. Wth the advantage of hgh-repeatablt accurac, the ndustral robot s becomng an mperatve component n product assembl feld. Utlzng the hgh flexblt of the artculated arm robot, the nstallaton of a varet of large and heav components can be asssted b a sngle ndustral robot. However, the absolute postonng accurac of the ndustral robot cannot meet the precson requrement n product assembl. The methods to mprove the assembl accurac of the ndustral robot sstem are performed wth the ad of hgh-precson measurement technolog, e.g. stereo cameras n ths paper. Secondl, n order to fx the component to the desgnated poston, the robot has to plan a collson-free path usng product exteror structure as the robot envronment. In ths paper, a robot path plannng software sstem s developed to solve ths problem. The Prncple of the Proposed Sstem The robot-asssted assembl sstem s composed of an ndustral robot sstem, a robot path plannng software sstem, a vsual postonng sstem and an addtonal robot moton platform (FIG ). The PC connects robot and bnocular stereovson sensor smultaneousl. The ndustral robot s used to transport heav components along the plannng trajector generated b robot path plannng sstem and re-algn them accordng to the 3D nstallaton nformaton receved from vsual postonng sstem. The end effector can be replaced b the fast-change flange to satsf the needs of varous components. 7

2 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, 205 FIG. THE COMPOSITION OF ROBOT ASSISTED ASSEMBLY SYSTEM The robot works n a specfc envronment flled wth some fxed obstacles. The robot path plannng sstem provdes the off-lne programmng collson free path wth robot poston and atttude accordng to the CAD models. The CAD models nclude the heav components and the nstallaton envronment. Ths paper apples the probablstc roadmap (PRM) method to robot path plannng n 3D space wth obstacles. The PRM planner dvdes plannng nto two phases: the learnng phase and the quer phase. In the learnng phase, collson-free roadmap s bult. In the quer phase, the nodes of roadmap are connected, and then a feasble path could be searched usng the graph searchng algorthm. The vsual postonng sstem provdes the accurate 3D locaton nformaton of the mountng holes. The sstem s equpped wth bnocular stereovson sensor. Measurement based on bnocular stereovson s an mportant technolog to locate object s spatal poston. It smulates the wa of human beng to deal wth the scener b bnocular stereovson. However, the dstance from bnocular stereovson sensor to the target must be wthn a reasonable range b robot movng along the off-lne plannng path. And then t can compute the 3D scene nformaton of the object b shootng two mages of the same scene. In the end, the component could be mounted to a reasonable poston b vsual orentaton. The robot moton platform s desgned to expand the workng space for the assembl sstem. The robot and ts controller are mounted on the moton platform. The platform s fxed to the ground to ensure the stablt of the whole assembl sstem when the robot s n workng status. When the assembl task s complete n the desgnated workng area, the platform can be moved to the next one. The platform s also be used to adjust to the best locaton for the entre robot asssted assembl sstem n the process. Accurac Improvement b Stereo Computer Vson The basc prncple of stereo vson sstem s dentcal to the human bnocular vson, and t uses two horzontall dsplaced cameras to obtan two dfferng vews on a scene. Based on the trangle measure theor, the dspart mage obtaned from the dfferng vews s used to calculate the 3-d coordnate of the selected ponts on the assembl product. Stereo Computer Vson Model Based on the pn-hole camera model, projecton from a 3-d space pont n the world coordnate sstem to the 2- dmenson coordnate on the mage plane can be expressed b: Xw Xw u m m2 m3 m4 Y w Y w Zc v M m2 m22 m23 m = = 24 Z w Z w m3 m32 m33 m 34 () 8

3 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, The projecton matrx M s composed of nteror parameter and exteror parameter of the cameras. From equaton (), we can get the followng relatonshps: X m + Y m + Z m + m u X m uy m u Z m = u m w w 2 w 3 4 w 3 w 32 w X m + Y m + Z m + m v X m vy m v Z m = vm (2) w 2 w 22 w w 3 w 32 w If we know the coordnate value of the pont n the world coordnate sstem and the coordnate value of the projecton pont on the mage plane, b utlzng the orthogonalt characterstc of the transformaton matrx, the coeffcent of the projecton matrx M can be calculated. In the stereo vson setup, two cameras are used to capture mages of the calbraton plate, and the transformaton matrx between the calbraton plate and the two cameras can be calculated, and then the relatve poston and orentaton relatonshps between these two cameras can be calbrated. Besdes ths, the nteror parameter of the two cameras can also be determned. Robot Hand-Ee Calbraton As shown n the FIG 2, the procedure of hand-ee calbraton s descrbed as followed. Because we alread know the dstance between the grd corners of the calbraton plate, we can calculate the transformaton matrx C between the calbraton plate and the two cameras. The transformaton matrx X between the end effector and the stereo cameras s the unknown parameters. The transformaton matrx between end effector and the robot base coordnate sstem s denoted b D. B readng the poston data of robot x,, z, a, b, c from the robot controller, the RPY angle can be calculated. cos acosb cos asn bsn c sn acos c cos asn bcos c+ sn asn c x sn acosb sn asn bsn c+ cos acos c sn asn bcos c cos asn c D = sn b cosbsn c cosbcos c z (3) The relatve poston and orentaton between calbraton plate and the robot base coordnate sstem s unchanged, and the relatve poston between robot end effector and the stereo vson sstem s also unchanged,.e. matrx X s unchanged. We use W c to denote the calbraton plate coordnate sstem, and W b to denote the robot base coordnate sstem. Based on the above descrptons, we can get the followng relatonshps: And, W C XD W (4) c c = 2 2 = b W C XD W (5) b C2XD2= CXD (6) C C2X = XDD 2 (7) The above equatons can be wrtten as: C X = XD () In onl matrx X s unknown, whch s the poston coeffcent. Redundant equatons are used to mprove the accurac of the hand-ee calbraton result. 3-D Reconstructon As shown n the fgure, assume the coordnate sstem O xz of left camera s on the orgn of the world coordnate sstem, and ts mage coordnate sstem s denoted b O XY, and ts focus length s f. Coordnate sstem of the rght camera s O r xz r r r, ts mage coordnate sstem s O r XY r r, and ts focus length s f r. Accordng to the perspectve transformaton model of camera: 9

4 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, 205 P z z r X r O X l O r o o r x r Y l x Y r r FIG. 2 ROBOT HAND-EYE CALIBRATION FIG 3 3-D RECONSTRUCTION X l fl x sl Y l f l = z Xr fr xr s r Y r f r = r z r (2) The transformaton between O xz and Or xz r r r can b expressed as a transformaton matrx M lr : x x xr r r2 r3 tx r M lr r4 r5 r6 t = =, Mlr = R T z z z r r7 r8 r9 t z [ ] (3) In whch RTs, the rotaton matrx between left camera and rght camera, and translaton between two orgns, and the can be obtaned b camera calbraton. For an pont n the O xz coordnate sstem, the relatonshp between two ponts on the mage plane of the two cameras s So the coordnate value of the pont n the space can be determned b: zx / f l l xr fr r fr r 2 fr r 3 ft r x zyl / f l r r fr r 4 fr r 5 fr r 6 ft = r (4) z z r r7 r8 r9 t z ρ x = zx l / fl = zyl / fl fl( ft r x Xt r z) z = Xr( rx 7 l + ry 8 l + fr l 9) fr( rx l + ry 2 l + fr l 3) fl( ft r Yt r z) = Yr( rx 7 l + ry 8 l + fr l 9) fr( rx 4 l + ry 5 l + fr l 6) (5) Accordng to the eppolar geometr, the polar les on the plane formed b the two camera center and the characterstc pont, and eppoles les on the connecton lne of two camera optcal centers. Based on these two constrants, the matchng of the ponts can be accomplshed, and 3-d reconstructon can be establshed. 0

5 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, Robot Path Plannng Automatcall fndng a feasble path for a robot n a fxed envronment wth obstacles s an mportant problem n robotcs. Robot moton plannng s an essental part for ths area. The moton plannng s a dffcult problem and exact algorthms are rarel useful. However, there s a knd of algorthms known as probablstc roadmap (PRM) methods. Probablstc roadmap dvdes plannng nto two phases. The frst phase s a learnng phase, durng whch a roadmap s constructed n the free confguraton space C-free. And the second phase s a quer phase. The userdefned quer confguratons are connected wth the pre-computed roadmap. The nodes of roadmap are confguratons n C-free and the edges of roadmap correspond to free paths. The Learnng Phase The learnng phase could be consdered as constructon phase. Its objectve s to obtan a reasonabl connected graph, whch conssts of a reasonable qualt of collson-free ponts of confguraton space and the local paths for connectng the ponts. Intall the graph G = (V, E) s empt. Then, repeatedl, a confguraton s sampled from C space. If the confguraton s collson-free, t s added to the V. The process s repeated untl collson-free confguratons have been sampled. For ever new node q, a number of closest neghbor nodes from V are selected to tr to connect the new node usng the local planner. If the planner succeeds n gettng a feasble path between q and a selected node q, the edge (q, q ) wll be added to E. A number of components n ths algorthm are stll unspecfed. In partcular, t needs to be defned how random confguratons are created n lne, how the closest neghbors are computed n lne, how the dstance functon D used n lne s chosen, and how local paths are generated n lne. The Quer Phase The quer phase needs to fnd a feasble path between arbtrar nput confguraton qnt and qgoal usng the roadmap constructed n the learnng phase. Assume for the moment that C-free s connected and that the roadmap conssts of a sngle connected component. The man queston s how to connect qnt and qgoal to the roadmap. We tr to use the nodes n set V to connect qnt and qgoal b lne path Pnt and Pgoal. A feasble path from qnt and qgoal s eventuall constructed b concatenatng Pnt, the contnuous path correspondng to P, and Pgoal. The frst queston s how to connect qnt and qgoal to set V. Our method s ncreasng the dstance (accordng to D) and tr to connect qnt and qgoal to each node of set V wth local planner untl one connecton succeeds. Then some graph searchng algorthm s used to search the actual path to fnd the path P. It should be noted that the learnng phase needs to be executed onl once, snce the same roadmap can be used to solve man dfferent queres. Our work focuses on fndng a feasble collson-free path for the ndustr robot n a reasonabl cluttered envronment. We take the KUKA KR30-3 robot as the 6-DOF robot model. q nt q goal FIG. 4 PROBABLITY ROADMAP FIG 5 FINDING A FEASIBLE PATH

6 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, 205 The approach s appled n the dscretzed C-space of the arm. We convert worksapce from the cartecan coordnate to confgure space.the robot workspace s confgured nto jont space. Each revolute jont J ( =,..., 6) has defned certan nternal lmts, denoted b low and up, wth low < up.snce the robot base s fxed, we present the C-space of such a 6-lnk artculated robot b {[ low, up]... [ low6, up6]}.suppose that (k,m) C C, J ( k), =,...,6 denote the poston of pont J n the workspace, when the robot s at confguraton k. The dstance between confguraton m and confguraton k can be defned b functon D: Where J ( m) J ( k) s the Eucldean dstance between J ( m ) and J ( k ). 6 = 2 D( m, k) = J ( m) J ( k) (6) In the dscretzed confguraton space, we need to set a reasonable resoluton for the sx jonts. we have adopted a heurstc method nstead of havng unform resoluton along each confguraton coordnate. For the -th coordnate J of the confgure space. N = (nt) J max J θ mn (7) MaxMove θ = 2 arc( ) 2l (8) max mn where J and J are the lmts of jont motons, l s the length between the center of the jont to the farthest pont of the end can reach., and MaxMove s a pre-set dstance the robot moves along the coordnate at one step. Usng ths method to dscretze resoluton of the jont, the jont of the robot moves θ at each movement step, where ( θ, θ, θ, θ, θ, θ ) = (.56,.56,2.72,5.33,5.33,8.56) (9) After settng the resoluton of the sx jonts, we tr to connect each node to the H closest nodes n the confgure space. On the other hand, too small wll affect the success rates to fnd a collson-free path. In our experments, H=20 s far enough. FIG 6 ROBOT COLLISION-FREE PATH PLAN Collson checkng for 3D manpulators can be mplemented usng the dscretzed confgure space for each lnk of the robot. Each jont of the robot s free to translate and rotate wthn ts lmts. When testng for collson, we choose a random sx-dmenson confgure space vector from the lnks, and check each lnk aganst the obstacles. 2

7 Global Perspectves on Artfcal Intellgence (GPAI) Volume 3, We start fndng a feasble collson-free path after the collson-free checkng (as shown n FIG 6). The ntal node qnt and the goal node goal should be set frstl, and then we emplo the graph searchng algorthm to connect the needed nodes, the connected nodes and the local paths that connect the adjacent ponts construct the feasble path connectng the ntal node to the goal node. Conclusons In ths paper, we propose a method for robot-asssted assembl. We emplo the probablstc roadmap (PRM) method to solve robot moton plannng problem n a fxed envronment wth obstacles. The bnocular stereovson sensor s desgned to detect the nformaton of nstallaton locaton. Wth the vsual postonng sstem, the assembl accurac of the heav component s mproved greatl, and then the robot wll automatcall and effectvel transport the heav component to the desgnated locaton. REFERENCES [] Lda E. Kavralu, Petr Svestka, Jean-Claude Latombe, and Mark H. Overmars, Probablstc Roadmaps for Path Plannng n Hgh-Dmensonal Confguraton Spaces, IEEE Trans.Robot.Automat., vol. 2, no. 4, pp , August 996. [2] Lda E. Kavrak, Mhal N. Kolountzaks, and Jean-Claude Latombe, Analss of Probablstc Roadmaps for Path Plannng, IEEE Trans.Robot.Automat., vol. 4, no., pp. 66-7, Feb.998. [3] SUN Han chang,hu Hua-ong, Stud on Path Plannng for UAV Based on Probablstc Roadmap Method, Journal of Sstem Smulaton, vol. 8, no., Nov [4] B. Faverjon and P. Tournassoud, A practcal approach to moton plannng for manpulators wth man degrees of freedom, Robotcs Research 5, H. Mnra and S. Armoto, Eds. Cambrdge, MA: MIT Press, p , 990. [5] B. Faverjon and P. Tournassoud, A local approach for path plannng of manpulators wth a hgh number of degrees of freedom, Proc. IEEE Int. Conf. Robotcs andautomaton, Ralegh, NC, pp , 987 [6] K. Kondo, Moton plannng wth sx degrees of freedom b multstratergc bdrectonal heurstc free space enumeraton, IEEE Trans. Robot. Automat. vol. 7, pp , 99. [7] Th. Horsch, F. Schwarz, and H. Tolle, Moton plannng for man degrees of freedom - random reflectons at C-space obstacles, Proc. IEEE Int. Conf Robotcs and Automaton, pp , San Dego, CA, 994. [8] D. Chalou and M. Gn, Parallel robot moton plannng, Proc. IEEE Int. Conf. Robotcs and Automaton, Atlanta, GA, pp. 24-5, 993. [9] J.-P. Laumond, M. Tax, and P. Jacobs, A moton planner for car-lke robots based on a global/local approach, Proc. IEEE Internet. Workshop Intell. Robot Sst., pp [0] K. Kondo and F. Kmura, Collson avodance usng a free space enumeraton method based on grd expanson, Advanced Robotcs, vol. 3. No. 3. pp [] D. Henrch and X. Cheng. Fast dstance computaton for on-lne collson detecton wth mult-arm robots. In IEEE Int. Conf. Robotcs & Automaton, pp , Ma 992. [2] S. Cameron, A stud of the clash detecton problem n robotcs, n Proc. IEEE Int. Conf. on Robotcs and Automaton, vol., 985, pp [3] Huang Xanlong, Lang Bn, Wu Hongxn. A surve on robotcs collson avodance plannng, Aerospace Control, vol., pp , 2002 [4] Lozano-Perez T. Spatal plannng: A confguraton space approach, IEEE Transacton on Computers, 983, pp [5] Sanjeev Sccreeram and John T.Wen, A Global Approach to Path Plannng for Redundant Manpulators, IEEE Transactons on Robotcs and Automaton, 995, pp [6] N. Rahmanan-Shar and I. Troch, Collsonavodance control for redundant artculated robots, Robotca, vol. 3, pp , 995 3