Trajectory Planning of Welding Robot Based on Terminal Priority Planning

Transcription

1 Sensors & Transducers 4 by IFSA Publshng, S. L. Trajectory Plannng of Weldng obot Based on Termnal Prorty Plannng, Ch GAO, Mnhou LUO, Fayong GUO, Hu GAO Mechancal and Electronc Department of Lawu Vocatonal and Techncal College, Lawu, Shandong Provnce, 7, Chna Insttute of Advanced Manufacturng Technology, Changhou, Jangsu Provnce, 64, Chna Tel.: , fax: E-mal: wwwgc9@6.com eceved: 6 December /Accepted: 7 March 4 /Publshed: Aprl 4 Abstract: In order to mprove the trajectory plannng effcency and accuracy of mult-jont weldng robot, accordng to the movement feature of mult-jont weldng robot, the paper analyed on exstng problems n spatal jont plannng of the robot, proposed a termnal prorty plannng method of robot jont plannng, based on the study of energy conservaton and accuracy of robot termnal. Usng ths method, the paper proceeded plannng of weldng robot jont, stated mplementaton procedure of jont plannng, conducted smulated test smulatng weldng robot, the result demonstrated that the research s of hgh feasblty and technologcal applcaton values. Copyrght 4 IFSA Publshng, S. L. Keywords: Weldng robot, Trajectory plannng, Termnal prorty plannng, Energy conservaton, Accuracy.. Introductons Jont-space trajectory plannng commonly adopt Cartesan model [], but ths model has some degenerate problems, such as complcated calculaton, unable to deal wth changng envronment and uncertan factor, and so on. For the past few years robot trajectory plannng has acqured many research achevement [-7], for example, probablstc roadmap method PM and rapdlyexplorng random trees T [8], apply to hgh redundant robot trajectory plannng. eference [9] researched on the manpulator of gven manpulator termnal task; t planned a free path for moble manpulator. eference [] researched on energy consumpton of manpulator and presented an approxmate algorthm of mnmal energy consumpton. eference [] completed jont-space trajectory plannng by real-tme nterpolaton algorthm. However, the researches above are all conducted on the condton of meet the plannng requrement and lack of study n the mass and energy dstrbuton. On the bass of the movement feature of multjont weldng robot and prncple of energy confguraton, the paper analyed on energy conservaton and mprovng termnal accuracy, proposed a termnal prorty plannng method of robot trajectory plannng, t can smplfy the Cartesan equatons of moton durng the jont plannng of weldng robot, optme the movements of the jonts, solved exstng problems, mproved the fttng precson of robot space trajectory, and acheved reasonable dstrbuton of weldng robot s energy. Artcle number P_7

2 The trajectory plannng method can not only reale jont-space trajectory plannng of weldng robot, but also can be appled to other mult-axs systems especally jont-space plannng of redundant robots.. Prncple of Termnal Prorty Plannng Weldng robot s usually mult-dof and multjont manpulator. Durng the weldng process, the end jont has lghtest weght, needs least moton energy, the moton energy confgured goes hgher as the seres of jont and termnal ncreases. At the meantme, rotaton angle of the jonts n the jont plannng are usually obtaned by Cartesan equaton, maybe there re multple solutons n the actual plannng, t wll make the plannng result space of robot especally mult-dof redundant robot larger, equates the moton probablty of the jonts, and the jonts have to move n every step adjustment, such solutons usually are not the shortest and most energy-effcent path of robot step adjustment. In the second place, n order to mprove the trajectory runnng accuracy, we can ncrease step number and reduce stepover n nterpolaton plannng, n the general sense, reducton of stepover can mprove the accuracy of trajectory, but t needs the coordnaton between motor accuracy and machne accuracy, so when the stepover s reduced to a certan value, t can not only mprove the nterpolaton accuracy, but also make the robot vbrate larger, t s dsadvantage of robot workng steadly. Then usng Cartesan movement plannng may lead to a stuaton that termnal plannng s stable but devaton angle of other jont s much hgher, although t can meet requrements of startng pont and termnal pont, but t may cause vbraton and even ncreasng error durng the movement, t s bad for weldng accuracy mantanng. In the last place not all the jonts wll partcpate n the movement adjustment n a step adjustment. In many cases t only needs two-stage or multstage jonts next to the termnal to take part n the moton adjustment. If t could accomplsh jont moton adjustment of one step by ths way, then other jonts don t need to partcpate, so the shortest path plannng and mnmum energy confguraton can be realed. In concluson, when we tred to conduct jont plannng by Cartesan equaton, we began wth termnal jont, determne the movement rotaton angle of robot termnal jont plannng, then preferentally planned the movement rotaton angle of the second and thrd termnal jont n turn, at last determned the movement rotaton angle of robot base jont. So as to make the jont plannng wth mnmum energy, shortest path, perfect runnng status, and optmum angle value of jonts plannng movement. As the plannng was started from termnal jont prorty of robot, so we called ths jont plannng method termnal prorty plannng.. Implementaton of Termnal Prorty Plannng.. Implementaton of Termnal Jont Prorty Plannng Durng the plannng of weldng robot, t should meet the requrement of weldng trajectory accuracy Δ; the accuracy s determned by the moton state of robot termnal manpulator. As Fg. shows, the dotted lne stands for the plannng trajectory, O stands for robot termnal jont axs, OA stands for the ntal poston of robot termnal plannng, OB stands for the fnal poston of robot termnal plannng, Δθ stands for rotaton angle of robot step plannng, ΔL stands for the stepover. In order to mantan the weldng accuracy Δ, stepover of robot trajectory plannng Δ L should less than weldng accuracy Δ. After stepover ΔL determned, as the length of manpulator termnal jont has determned, so Δθ s determned. Because the stepover ΔL s very short actually, the dfference between OB and OA s not bg, so let OA = OB, then the value of Δθ could be obtaned by arc angle,.e. 6Δθ 8Δθ Δ θ = = () π OA π OA There are errors between value of Δθ obtaned by ths method and actual poston value, t s less than the actual value, but ths method s under the premse of fulfllng accuracy Δ, so ths method must meet the requrement of robot accuracy. After the value of Δθ s determned, suppose poston angle of poston A on manpulator termnal jont s θ A, then the poston rotaton angle θ B of poston B s where θ, A θ = θ +Δ θ, () B A θ are equal to the nverse soluton of B Cartesan moton equatons correspondng to poston A and poston B on manpulator termnal jont, then when we proceed Interpolaton plannng of weldng robot jonts, the nverse soluton of Cartesan moton equatons correspondng to poston on the manpulator termnal jont θ n s determned, t s equal to θ B. So we determned the nverse soluton of Cartesan moton equatons correspondng to manpulator termnal jont by termnal prorty plannng. In addton, durng the jont plannng, we always encounter the crcumstance that termnal plannng jont n place, but angular dsplacement of mddle jont n some step s overse. When we encounter

3 ths stuaton by usng termnal prorty plannng, we ncrease proper stepover n ths step, by equdstance ncreasng or equdstance ncreasng, n accordance wth specfc condtons. As the plannng step has fulflled the weldng accuracy, so the ncrease of stepover n ths step wll not affect the weldng accuracy. We can also use another way to solve the problem, we can replan a trajectory, take the begnnng of the step as new begnnng of the trajectory. Frst of all, accordng to the theory of Cartesan robot knematcs, we can get the transformaton matrx of base coordnate system relatve to N-Dof seral robot [],.e. AAAA A = T () 4 n H In Eq. (), =,,, n, A stands for the matrx of relatve poston relaton between jont and jont -, t s usually represented as: A C θ - SθC α- SθS α- a-c θ S θ CθC α - CθC α a S θ = S α- C α- d (4) Fg.. The dagram of robot termnal prorty plannng. When we get θ n by termnal prorty plannng, the poston angle of robot termnal jont can be calculated drectly, but the calculaton can t determne rotate drecton of termnal jont, the determnaton of drecton can be determned by the extenson drecton of trajectory plannng on the bass of trajectory s shape shftng. Specal trajectory needs to be determned by tral-and-error method, that s fnd two successve soluton, and then calculate and verfy whether t can satsfy Cartesan equaton. The analyss above s for straght trajectory. For curve trajectory, we always cut the curve nto tny straght step nterpolaton, so ths method apples to curve trajectory too... Implementaton of Common Jont Prorty Plannng The mplementaton of common jont plannng follows termnal prorty plannng method, fnd nverse soluton of other jont besde termnal jont,.e. fndng moton nverse soluton θ, θ, θ, θ, θ of other jont besde termnal 4 n jont by Cartesan equaton. For termnal jont rotaton angle θ n of N-Dof robot, t has been determned by Eq. () and Eq. () usng termnal prorty method, here we ll fnd,,,,. θ θ θ θ θ 4 n- In the matrx stands for A, sθ stands for cosθ, smlarly, parameter snθ, cθ d stands for the normal dstance between jont and jont +, stands for the lnk length between jont and jont +, α stands for the torsonal angle of jont and jont +, θ stands for the lnk angle of jont and jont +. T n Eq. (4) stands for the matrx of H expected goal, ts value can be determned n accordance wth expected goal durng plannng. T s usually represented as: H T n x o x a x p x n o a p y y y y H = n o a p a (5) As the rotaton angle of termnal jont θ n has determned, so the matrx A turns nto constant n matrx, marked as B n, then the transformaton matrx of base coordnate system relatve to N-Dof seral robot turns nto: AA A B = T (6) n- n H Usng ths method to solve Cartesan moton equaton, the seres of equaton reduces one seres, so the calculaton and soluton s smplfed. We fnd nverse soluton of the second termnal jont θ by n- matrx (6) through termnal prorty plannng method.

4 The frst step s to suppose θ, θ, θ n- are known, the values are current poston angle, and then A,A,, A are constant matrx, marked n- as B,B,, B, so the transformaton matrx of n- base coordnate system relatve to N-Dof seral robot turns nto: BB B A B = T (7) n- n- n H Only A corresponds to θ whch s n- n- unknown n matrx (7), so t s easy to fne the value of θ. Accordng to the theory of matrx nverson, n- matrx (7) turns nto: [ ] A = BB B T B (8) n- n- H n The second step s to solve matrx (8), determne whether there s a reasonable nverse soluton θ. If n- any, the problem s solved; f not, we fnd the soluton by matrx of the second and thrd termnal jont,.e. solutons of the second and thrd termnal jont are unknown. Suppose others are known, smlarly, matrx (7) turns nto: BB B A A B = T (9) n- n- n- n H In matrx (9), only θn and θ n- A and n- A correspond to n- are unknown, so accordng to Cartesan equaton, matrx (9) turns nto: [ ] A A = BB B T B () n- n- n- H n Then fnd θ and θ by matrx (). n- n- The thrd step s to solve matrx, determne whether there s a reasonable nverse soluton θ. If n- any, the problem s solved; f not, fnd the soluton by matrx of the second, thrd and fourth termnal jont usng Cartesan equaton theory n a smlar way, untl fnd reasonable soluton completely. The mportant thng to note here s we can fnd θ and n- θ by Cartesan matrx when we solve them by the n- second and thrd matrx of termnal jont, and n general the two solutons can fulfll the equaton probably, but only soluton θ s found by termnal n- prorty method, although θ can fulfll the n- equaton too, but t may not the optmal soluton, so we should solve and valdate them separately by the plannng method above. Fnally, we can fnd moton solutons of all jonts by termnal prorty plannng method, but solutons found by ths way are totally dfferent from solutons got by Cartesan equaton. Especally n the motor process, usng termnal prorty plannng method follows meetng the moton requrement of termnal manpulator frst, moton frst, and other jonts keep stll or move less, by ths way t can reach that the least movement of all jonts, shortest trajectory, least energy consumpton durng the actual mplementaton of robot trajectory jont plannng. In the meantme t can reduce the seres of knematcal equaton, decrease calculaton and pck up the pace of plannng. Therefore ths method has mportant technologcal values to mult-jont robot especally redundant robot, real-tme teachng plannng robot, and robots workng n the energy lmted place such as outer space. 4. Tests and Analyss 4.. Data Sortng In order to verfy the termnal prorty plannng method, we adopt three-jont weldng robot as research model, model and conduct smulaton tests. In the condton of default weldng speed s 5 cm/mn, weldng accuracy s less than 5 mm, we found manpulator model of three-jont weldng robot, determne Cartesan moton parameter, establsh Cartesan moton equaton, plannng and solve the trajectory of straght lne and curve. The data of the same straght lne are sorted and shown n Fg. and Fg. 4. Choose two groups of the data n dfferent begnnng of manpulator. Due to space constrants, Fg. and Fg. 4 only choose partal data, and extract 5 nterpolaton ponts n each group. Fg. shows data extracted from the frst poston, Fg. 4 shows data extracted from the second poston. At the same tme we smulate the straght trajectory shown n Fg. and curve trajectory shown n Fg. 5 to verfy the termnal prorty plannng method. Z X x y Fg.. Trajectory dagram of straght lne nterpolaton. Y.5.5 4

5 4.. Data Analyss Analyng the data n Fg. and Fg. 4, θ, θ, θ are Cartesan moton nverse solutons of weldng θ robot found by termnal prorty plannng method, s the soluton of termnal jont poston. As t s shown n Fg. and Fg. 4, the varetes of θ are equal, n lne wth prncples. The varetes of θ are changed a lot, there s no change n the data of former ten nterpolaton ponts and latter ten nterpolaton ponts n Fg., t s stated that there s no movement n the former ten nterpolaton ponts and latter ten nterpolaton ponts of termnal jont plannng durng the plannng n the frst poston of the frst jont. The data of θ n Fg. s unchanged n all the 5 nterpolaton ponts, t s stated that the frst jont ddn t rotate durng the nterpolaton process of all the second poston. So by analyng the data of Fg. and Fg. 4, we could see that the frst jont can keep stll or move less n the nterpolaton process, through ths way t can save energy and reducng frcton and vbraton, whch fully embody the theory of termnal prorty plannng. Fg. and Fg. 5 proceed nterpolaton plannng trajectory by smulaton model of weldng robot, t can be seen n the fgure that the steps are even and mages are versmlar, t managed to recreate the straght lne and curve trajectory, t fully valdated the avalablty and valdty of the termnal prorty plannng method. Through the analyss of data and fgures, we could see that the termnal prorty plannng method successfully completes the trajectory plannng of weldng robot; t verfes the termnal prorty plannng method. Values of the second nverse solutons the thrd nverse solutons are exactly the same, so the two curves are overlapped. Graph of data extracted from the frst poston 8 Values of Correspondng nverse solutons Number of Interpolaton ponts Curve of the st nverse soluton Curve of the nd nverse soluton Curve of the rd & rd nverse soluton Fg.. Graph of data extracted from the frst poston. Graph of data extracted from the second poston 5 Values of Correspondng nverse solutons Number of nterpolaton ponts Curve of the st nverse soluton Curve of the nd nverse soluton Curve of the rd nverse soluton Fg. 4. Data extracted from the second poston. 5

6 Fg. 5. Trajectory dagram of curve lne nterpolaton. 5. Conclusons On the bass of the movement feature of multjont weldng robot and prncple of energy confguraton, the paper analyed on energy conservaton and mprovng robot termnal accuracy, t proposed a termnal prorty plannng method of robot trajectory plannng, and solved problems n fndng nverse soluton of tradtonal moton equaton, t also reduced energy consumpton n motor process, mproved the fttng precson of robot space trajectory, and realed reasonable and optmed energy dstrbuton of weldng robot. The trajectory plannng method can not only reale jontspace trajectory plannng of weldng robot, but also can be appled to other mult-axs systems especally jont-space plannng of redundant robots. The expermental data and result demonstrated that the research s of hgh feasblty and technologcal applcaton values. eferences []. Zhu Shqang, Wang Xuanyn, obot technque and applcaton, Zhejang Unversty Press, 7. []. Guo Tongyng, Qu Daoku, A method of machnng path plannng for robot based on genetc algorthm, Journal of Huahong Unversty of Scence and Technology, Vol., 4, pp. -5. []. J. U. Dolnsky, I. D. Jenknson, G. J. Colquhoun, Applcaton of genetc programmng to the calbraton of ndustral robots, Computers Industry, Vol. 58, Issue, 7, pp [4]. Jn Bao, Fu Y-L, Wang Shu-Guo, Cao Zheng-Ca, obot fuy moton plannng approach n unknown envronments, Journal of Harbn Insttute of Technology, Vol. 7, No., 5, pp [5]. Francsco Valero, Vcente Mata, Antono Besa, Trajectory plannng n workspaces wth obstacles takng nto account the dynamc robot behavor, Mechansm and Machne Theory, Vol. 4, Issue 5, 6, pp [6]. J. Aleott, S. Casell, obust trajectory learnng and approxmaton for robot programmng by demonstraton, obotcs and Autonomous Systems, Vol. 54, Issue 5, 6, pp [7]. P. Th. Zachara, N. A. Aspragathos, Optmal robot task schedulng based on genetc algorthms, obotcs and Computer-Integrated Manufacturng, Vol., Issue, 5, pp [8]. Luo Hong, Chen Xaoq, Laser vsual sensng for seam trackng n robotc arc weldng of ttanum alloys, Internatonal Journal of Advanced Manufacturng Technology, Vol. 6, Issue 9-, 5, pp. -7. [9]. Per Cederberg, Magnus Ollson, Gunnar Bolmsjö, Vrtual trangulaton sensor development, behavor smulaton and CA ntegraton appled to robotc arc-weldng, Journal of Intellgent and obotc Systems, Vol. 5, Issue 4,, pp []. J. Denavt, J.. S. Hartenberg, A knematc notaton for lower-par mechansms based on matrces, ASME Journal of Appled Mechancs, June 955, pp. 5-. []. L Xnchun, Zhao Dongbn, Y Janqang, A dynamc path plannng approach for moble manpulators along gven end effectors paths, Control and Decson, Vol., Issue, 7, pp []. L Tanyou, Meng Zhengda, Zhao Jaojao, Trajectory plannng method n jont space based on weldng robot, Electrc Weldng Machne, Vol., Issue 4, 9, pp Copyrght, Internatonal Frequency Sensor Assocaton (IFSA) Publshng, S. L. All rghts reserved. ( 6