并联机器人原文知识分享

1、并联机器人原文Virtual Prototypi ng of a Parallel Robot actuated by Servo-P neumatic Drives usi ng ADAMS/Co ntrolsWalter Kuhlbusch, Dr. Rdiger Neuma nn, Festo AG & Co., Germa nySummaryAdva need pn eumatic drives for servo-p neumatic positi oning allow for new gen erati ons of han dli ngs and robots. Esp

2、ecially parallel robots actuated by servo-p neumatic drives allow the realizati on of very fast pick and place tasks in 3-D space. The desig n of those machi nes requires a virtual prototyp ing method called the mechatronic design 1. The most suitable software tools are ADAMS for mecha nics and Matl

3、ab/Simuli nk for drives and con trollers. To an alyze the overall behavior the co-simulati on using ADAMS/C on trols is applied. The comb in ati on of these powerful simulati on tools guara ntees a fast and effective desig n of new mach in es.1. In troducti onFesto is a supplier for pn eumatic comp

4、onents and con trols in in dustrial automation.The utilization of pneumatic drives is wide spread in industry when working in open loop control. It imited however, when it comes to multipoint moveme nt or path con trol. The developme nt has bee n drive n to servo- pn eumatic drives that in clude clo

5、sed loop con trol. Festo servo-p neumatic axes are quite accurate, thus they can be employed as drives for sophisticated tasks in robotics. The special advantage of these drives is the low in itial cost in comparis on to electrical and hydraulic drive systems. Servopneumatic driven parallel robots a

6、re new systems with high potentials in applicati ons. The dyn amical performa nee meets the in creas ing requireme nts to reduce the cycle times.One goal is the creation and optimization of pneumatic driven multi-axes robots. This allows us to support our customers, and of course to create new sta n

7、dard han dli ngs and robots (Fig. 1).The complexity of parallel robots requires the use of virtual prototyp ing methods.Two-axes machine with pneumatic musclesTripodFig. 1. Prototypes of servo-pneumatic driven multi-axes machinesScraPreferred applicati ons are fast multipo int positi oning tasks in

8、3-D space. Free programmable stops allow a flexible employme nt of the mach ine. The point to point (ptp) accuracy is about 0.5 mm. The con ti nu ous path con trol guara ntees collisi on free moveme nt along a trajectory.1.1. Why parallel robots?The main ben efits using parallel in stead of serial k

9、in ematics is show n in Fig. 2.-dynamical performance： high speed and acceleration-high stiffness:-simple construction：intelligenl motion control withI -lriliinious nath rentreiclosed kinematic system identical parts, modular co nee ptFig. 2. Ben efits of robots with parallel kin ematicsmoving massH

10、igh dyn amical performa nee is achieved due to the low moved masses. While in serial robots the first axis has to move all the following axes, the axes of a parallel robot can share the mass of the workpiece. Furthermore serial axes are stressed by torques and bending mome nts which reduces the stif

11、f ness. Due to the closed kin ematics the moveme nts of parallel robots are vibrati on free for which the accuracy is improved. Fin ally the modular con cept allows a cost-effective production of the mechanical parts. On the other hand there is the higher expense related to the control.1.2. Why Pn e

12、umatic Drives?The adva ntages of servo-p neumatic drives are:direct drives f high accelerating powercompact (especially rodless cyli nders with in tegrated guida nee) robust and reliablecost-effectiveDirect drives imply a high accelerati on power due to the low equivale nt mass in relati on to the d

13、rive force. With pn eumatic drives the relati on ship is particularly favorable. Festo has already built up some system soluti ons, predo minan tly parallel robots (see Fig. 1), to dem on strate the tech ni cal pote ntial of servo-p neumatics. Which performa nee can be reached is show n in Fig. 3. T

14、his prototype is equipped with an adva need model based con troller that makes use of the computed torque method 3.Frame space800x750 h 二1100mmWorkspaced = 400mm(cylindrical)h = 200Max. acceieration(5 bar, 0 3 kg load)50rrnV曰Max velocity35mm/sAbsolute accuracy0.5mmRepetition accuracy0.1mmLoad< 1k

15、glTechnical Data:Fig. 3. Performa nee of the Tripod2. Desig n MethodThe system desig n, where several engin eeri ng discipli nes are invo Ived in, requires a holistic approach. This method is the so-called mechatr onic desig n. The comp onents of a mechatr onic system are the mecha ni cal support in

16、g structure, the servo drives as well as the control. All these components are mapped into the computer and optimized with respect to the mutual interaction. This procedure can be used to analyze and improve existing systems as well as to create new systems. The two main steps of the mechatr onic de

17、sig n are first build ing models in each discipli ne, and sec on dly the analysis and synthesis of the whole system. These steps are done in a cycle for the optimizati on.The modeli ng can be carried out in two ways: Either you apply one tool to build up models in all discipli nes, but with restrict

18、io ns. The other way is to use powerful tools in each discipline and to analyze the whole system via co- simulati on. In this case you have to con sider some specials of the solvi ng method like com muni cati on step size or direct feedthrough behavior.2.1. Why Co-Simulatio n?Co-simulation is used b

19、ecause of the powerful tools, each specialized in its own discipline. ADAMS is an excellent tool for the mechanical part and Matlab/Simulink is the suitable tool for controller development and simulation of pn eumatics.The behavior of the mecha ni cal part is modeled at best using ADAMS/View. The ad

20、va ntages of ADAMS are:fast physically modeli ng of rigid and elastic bodiesexte nsive features for parameterizati onani mati on of simulati on resultssol ving in verse kin ematics by“ gen eral point moti onvisualizatio n of eige nm odes (ADAMS/LINEAR)export of lin ear models (A,B,C,D)A big adva nta

21、ge is the automatic calculati on of the direct and inv erse kin ematics. The direct kin ematics of parallel structures ofte n cannot be solved an alytically. Furthermore differe nt kin ematics can be compared to each other very easily whe n you defi ne a trajectory of the end-effector via “ ge neral

22、 pointmotion ”.Applying these two software tools guarantees a high flexibility regarding the design of new systems. It is very important to analyze the closed loop behavior at an early stage. This makes a big differe nee betwee n the mechatr onic desig n and the conven ti onal desig n. Furthermore t

23、he visualizati on of the mecha ni cal system makes the discussi on within a team very easy.2.2. Restricti onsA disadvantage is that the model of the mechanics is purely numerically available. However some symbolic code of the mecha ni cal system is n eeded for the con trol hardware whe n the system

24、becomes realized. In gen eral we have to derive the equations of the inverse kinematics, which are used in the feed forward con trol. For specific robot types a con troller with decoupli ng structure is necessary in order to fulfill the requirements. Then the symbolic code of the dyn amics is n eede

25、d. For this we have to pull up further tools to complete the task.2.3. What has to be an alyzed?For the desig n of new robots it is importa nt to know about the effect on the system stability and accuracy. The mai n properties that in flue nee stability and accuracy are opposed in Table 1 for differ

26、e nt kin ematical structures.Table 1: Properties of different kinematical configurationsserial robotsF)arallel robotRobot Type:HflklJ# IMi 1* q 1.t 詳-护1L * :cartesiancylindricalarticulatedPosition dependency on inertianoneminorEtmngmedialPosition dependency on gravity forcesnonenonemedial (scara: no

27、ne)existingCoupling between axesnonenonestrongmedialGyroscopic forcesnoneminorstrongmedialWith respect to the con trol the cartesia n type is the best one. But the main disadvantage of a serial robot compared with a parallel one is the lower dyn amics and the lower stiff ness (see Fig. 2).Depe nding

28、 on the requireme nts with regard to dyn amics and accuracy differe nt con trol approaches must be applied. As men ti oned above we prefer to employ a standard controller SPC200 for a single axis. Due to the coupling of the axes the stability of the closed loop system must be checked.3. Model of the

29、 TripodThe model of the Tripod con sists of three parts: the mecha ni cs, the pneumatic drives, and the controller.3.1. Mecha nics (ADAMS)We apply the so-called delta-k in ematics which causes a purely translational movement of the tool center point (tcp). An additional rotary drive allows the orien

30、tation of the gripper in the horizontal plane. Together with the rotary drive the mach ine has four degrees of freedom.upper plate(fixed to ground)sliderof the driverodprofile tubeof the drivetcp platerotary drivegripperlower plate(fixed to ground)Fig. 4. Degrees of freedom and structure of the Trip

31、odThe tripod is modeled using rigid body parts what is ofte n sufficie nt for the prese nt type of parallel structure. The upper and lower plates are fixed to ground. The profile tubes are conn ected to these plates via fixed joi nts. Each slider has one tran slati onal degree of freedom. Both ends

32、of a rod are conn ected to the n eighbored parts by uni versal joi nts. I ncludi ng the rotary drive, the model verification results in four Gruebler counts and there are no redundant con stra in ts. The model is parameterized in such a way that differe nt kin ematical con figuratio ns can be gen er

33、ated very easily by means of desig n variables. The most importa nt parameters are the radiuses of the plates (see Fig. 4) and the distances to each other. For instance the following con figurati ons can be achieved just by variati on of these parameters or desig n variables.Fig. 5. Variati on of ki

34、n ematics by“ desig n variables3.2. Servo-P neumatic Drives (Simuli nk)The models of the servo-p neumatic drives are developed by means of Matlab/Simuli nk. Depe nding on the requireme nts several con troller models were developed. It is com mon to all that they are highly non-li near. Mainly the co

35、mpressibility of air makes a more complex con trol system n ecessary. All con troller models in cludi ng the sta ndard con troller SPC200 are available as C-coded s-functions. This allows to use the same code in the simulation as well as on the target hardware.A survey of the control scheme is shown

36、 in Fig. 6. For this contribution it is importa nt to know about the in terface for the co-simulatio n. The calculated forces of the servo pn eumatics are the in puts to the mecha ni cs. The slider positions are the outputs of the mechanics. Detailed information on the con trollers can be found in 2

37、 and 3.DAMSSimulinkR o b o t C o n toltfd forr-nf on31苗心|coFitrol二 M一一負2 -£-UO5BBS匸J=冷乩耳Llw££1密=£加餅“皿ntool 啊n牠rpglrCFig. 6. Control structure4. An alyz ing the behavior of the whole systemWhe n the modeli ng is done we can go on with the sec ond step of the mechatronic design. In

38、 the following it is assumed that the SPC200 controller always controls the machine. The task is the analysis and synthesis of differe nt parallel kin ematics relative to stability, dyn amics, and accuracy for a give n workspace.Some studies, e.g. concerning the workspace, can be made exclusive usin

39、g ADAMS. Others such as feedback an alysis are carried out by means of co-simulatio n.The workspace can be determ ined by vary ing all drive positi ons in all comb in ati ons. After simulati on the en d-effector positi ons are traced using the feature“ create tracespli ne”.Im勲曲i；：i J;. ：: , I J II 1

40、 Ma i i i J f * * I 0 nQIgm USl.Fturim jOSJDte-IOII 1.23 WLFig. 7. Drive moti ons for the workspace calculati onThe data can be visualized in ADAMS or any other graphics tool. As an example the workspace of the Tripod configuration of Fig. 7 is represented in Fig. 8Right rie#-200 C 200GO vie1*-、From

41、-200 0 200Top 'jiew 爼Fig. 8. Workspace of the Tripod (configuration as in Fig. 7)Measuring the velocity of the end-effector at the same time delivers the gear ratios of all drives over the workspace.To exam ine the behavior of the closed loop system ADAMS/C on trols is used to couple ADAMS and S

42、imulink. Before the model can be exported some in puts and outputs of the pla nt must be defi ned by state variables. The in puts of the Tripod are the drive forces. Though the con troller makes only use of the drive position some additional signals are defined as outputs: The drive velocities are n

43、eeded for solving the differential equations of the pressures in the pneumatics model. Furthermore we need the velocity of the tool cen ter point to calculate the non-I in ear gear ratios. Fin ally the drive accelerati ons serve for the calculati on of the equivale nt moved masses. The whole system

44、is show n in Fig. 9.>400 -2C00 2UQ 400XFig. 9. Model of the whole systemThe model of the mecha nics is embedded in Simuli nk. ADAMS/C on trols makes the in terface available by means of s-fun cti on.The equivale nt moved masses depe nd on the positi ons of drives. The non-li nearity of the robot

45、grows with the stre ngth of this depe nden cy. As shown in Table 1 with the parallel kinematics there is a medium strong coupli ng of the dyn amics. This coupli ng is n eglected, if we use the sta ndard SPC200 con troller. Nevertheless there is an in flue nce on the stability of theclosed loop syste

46、m. To initialize and parameterize this controller we need the followi ng in formatio n from the mecha nics model:equivale nt moved mass of each drive (depe nds on slider positi ons) gravity forces in in itial positi on Coulomb and viscous frictio nThe con troller is desig ned for a sin gle axis with

47、 a con sta nt mass. Due to the positi on depe ndency of the equivale nt moved masses of the robot we have to choose an average value for each drive. Unfortun ately with ADAMS there is no easy way to calculate the equivale nt moved masses along a trajectory. We tried to apply differe nt methods such

48、as dividi ng a drive force by its acceleration during a slow motion, but this method yielded not in satisfying results. The best method found is the linearization of the system. However this requires ADAMS/Li near. Whe n we defi ne the drive accelerati ons as pla nt outputs in ADAMS/Co ntrols the di

49、rect feed through matrix D of the exported linear system delivers the mass matrix in the defined operating point as1M (q) f D(q)Corresp onding to the three degrees of freedom of the rigid body system the size of the mass matrix M(q) is three by three. It depe nds on the vector of the gen eralized co

50、ord in ates of the drives. The non-diag onal eleme nts cause the coupli ng betwee n the axes. The factor f depe nds on the un its chose n for the in puts and outputs. When the forces are give n in N and the accelerati ons are give n in mm/s 2 f is 0.001.With a slider mass of 2 kg and an end-effector

51、 mass of 2 kg the mass matrix for the three positions shown in Fig. 10 are:pos. 0pos 1pos. 21M =>13-0.3-O.3_-03 4.B 03 -03 -0.34.13-5.01-L03 -1.05"-1.035.01 一 104-1.05 -1.045.01I ='5.14-042 -2 42-0.324.101 17L- 2.42 -L176 80The gravity forces can be calculated very easily by static simul

52、ati on. Likewise it is easy to model the friction in ADAMS. Nevertheless the parameters can differ very stro ng from one applicati on to ano ther one.With the parameterized con troller the stability should be checked in several operat ing points by means of eige nv alues and the dyn amics of the closed loop system can be an alyzed by means of freque ncy resp on ses.Of course with a robust controller you can start with a simulation in time domain. This gives information about the accuracy and system limits. For this we n eed the refere nces for