并联机器人原文

1、Virtual Prototyping of a Parallel Robot actuated by Servo-Pneumatic Drives using ADAMS/ControlsWalter Kuhlbusch, Dr. Rudiger Neuma nn, Festo AG & Co., Germa nySummaryAdvanced pneumatic drives for servo-pneumatic positioning allow for new generations of handlings and robots. Especially parallel r

2、obots actuated by servo-pneumatic drives allow the realization of very fast pick and place tasks in 3-D space. The design of those machines requires a virtual prototyping method called the mechatronic design 1. The most suitable software tools are ADAMS for mechanics and Matlab/Simulink for drives a

3、nd controllers. To analyze the overall behavior the co-simulation using ADAMS/Controls is applied. The combination of these powerful simulation tools guarantees a fast and effective design of new machines.1. IntroductionFesto is a supplier for pneumatic components and controls in industrial automati

4、on.The utilization of pneumatic drives is wide spread in industry when working in open loop control. It'slimited however,when it comes to multipoint movement or path control. The development has been driven to servo-pneumatic drives that includeclosed loop con trol. Festo servo-p neumatic axes a

5、re quite accurate, thus they can be employed as drives for sophisticated tasks in robotics. The special adva ntage of these drives is the low in itial cost in comparis on to electrical and hydraulic drive systems. Servo-p neumatic drive n parallel robots are new systems with high potentials in appli

6、cations. 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 ndard han dli ngs and robots (Fig. 1).The comp

7、lexity of parallel robots requires the use of virtual prototyp ingmethods.TripodFig. 1. Prototypes of servo-pneumatic driven multi-axes machinesPreferred applicati ons are fast multipo int positi oning tasks in 3-D space. Free programmable stops allow a flexible employme nt of the mach ine. The poin

8、t to point (ptp) accuracy is about 0.5 mm. The continu ous path con trol guara ntees collisi on free moveme nt along atrajectory.1.1. Why parallel robots?The main ben efits using parallel in stead of serial kin ematics is show n in Fig. 2.-dynamical performance： high speed and acceleration -high sti

9、ffness:-simple construction：closed kinematic system identical parts, modular co nee ptreducedmoving mass loadintelligent motion control with 匚ontinuous path controlFig. 2. Ben efits of robots with parallel kin ematicsHigh dyn amical performa nee is achieved due to the low moved masses. While in seri

10、al robots the first axis has to move all the followi ng 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 stiff ness. Due to the closed kin ematics the moveme nts of parallel robots are vibra

11、ti on free for which the accuracy is improved.Fin ally the modular con cept allows a cost-effective producti on of the mecha ni cal parts. On the other hand there is the higher expe nse related to the con trol.1.2. Why Pn eumatic Drives?The adva ntages of servo-p neumatic drives are:direct drives f

12、high accelerating power compact (especially rodless cyli nders with in tegrated guida nee)robust and reliablecost-effectiveDirect drives imply a high acceleration power due to the low equivale nt mass in relati on to the drive force. With pn eumatic drives the relatio nship is particularly favorable

13、. Festo has already built up some system solutions, predominantly 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. This prototype is equipped with an adva need model based con troller that makes use

14、 of the computed torque method 3.Frame space80C1x750mmh -1100-Vorkspaced 二400mm(cylindncal)h 二200M-ax. acceleration(5 bar； 0 3 kg lead)50Max velocity3,5mmJsAbsolute accuracy0.5mmRepetition accuracy0.1mmLoad< 1网Technical Data:Fig. 3. Performance of the Tripod2. Desig n MethodThe system design, whe

15、re several engineering disciplines are involved in, requires a holistic approach. This method is the so-called mechatronic design. The components of a mechatronic system are the mechanical supporting structure, the servo drives as well as the control. All these components are mapped into the compute

16、r 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 mechatronic design are first building models in each discipline, and secondly the analysis and synthesis of the whole

17、 system. These steps are done in a cycle for the optimization.The modeling can be carried out in two ways: Either you apply one tool to build up models in all disciplines, but with restrictions. The other way is to use powerful tools in each discipline and to analyze the whole system via co-simulati

18、on. In this case you have to consider some specials of the solving method like communication step size or direct feedthrough behavior.2.1. Why Co-Simulation?Co-simulation is used because of the powerful tools, each specialized in its own discipline. ADAMS is an excellent tool for the mechanical part

19、 and Matlab/Simulink is the suitable tool for controller development and simulation of pneumatics.The behavior of the mechanical part is modeled at best usingADAMS/View. The advantages of ADAMS are:fast physically modeling of rigid and elastic bodies extensive features for parameterization animation

20、 of simulation results solving inverse kinematics by“general point motionvisualization of eigenmodes (ADAMS/LINEAR) export of linear models (A,B,C,D)A big advantage is the automatic calculation of the direct and inverse kinematics. The direct kinematics of parallel structures often cannot be solved

21、analytically. Furthermore different kinematics can be compared to each other very easily when you define a trajectory of the end-effector via “general point motion”.Applying these two software tools guarantees a high flexibility regarding the design of new systems. It is very important to analyze th

22、e closed loop behavior at an early stage. This makes a big difference between the mechatronic design and the conventional design. Furthermore the visualization of the mechanical system makes the discussion within a team very easy.2.2. RestrictionsA disadvantage is that the model of the mechanics is

23、purely numerically available. However some symbolic code of the mechanical system is needed for the control hardware when the system becomes realized. In gen eral we have to derive the equatio ns of the in verse kin ematics, which are used in the feed forward con trol. For specific robot types a con

24、troller with decoupling structure is necessary in order to fulfill the requirements. Then the symbolic code of the dynamics is needed. 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

25、on the system stability and accuracy. The mai n properties that in flue nee stability and accuracy are opposed in Table 1 for different kinematical structures.Table 1: Properties of different kinematical configurationsseiial robotsparallel robotRobot Ty理IIH* i*r z/ 1 Vs- IU| 14tum Jwa 1 1 *X . J站 &#

26、39;cartesiancylindricalarticulatedPosition dependency on inertian oneminorstrongmedialPosition dependency on gravity forcesnonenonemedial (scars: nonm)existingCoupling between axesnonenonestrongmedialGyroscopic forcesnoneminorstrongmedialWith respect to the con trol the cartesia n type is the best o

27、ne. But the main disadvantage of a serial robot compared with a parallel one is the lower dyn amics and the lower stiffness (see Fig. 2).Depending on the requirements with regard to dynamics and accuracy different control approaches must be applied. As mentioned above we prefer to employ a standard

28、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 TripodThe model of the Tripod consists of three parts: the mechanics, the pneumatic drives, and the controller.3.1. Mechanics (ADAMS)We apply the so-called del

29、ta-kinematics which causes a purely translational movement of the tool center point (tcp). An additional rotary drive allows the orientation of the gripper in the horizontal plane. Together with the rotary drive the machine has four degrees of freedom.Fig. 4. Degrees of freedom and structure of the

30、Tripodupper plate (fixed to ground)slider of the driverodprofile tubeof the drivetcp platerotary drivegripperlower plate(fixed to ground)The 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

31、. The profile tubes are connected to these plates via fixed joi nts. Each slider has one tran slati onal degree of freedom. Both ends of a rod are conn ected to the n eighbored parts by uni versal join ts.Including the rotary drive, the model verification results in four Gruebler counts and there ar

32、e no red undant con stra in ts. The model is parameterized in such a way that differe nt kin ematical con figurati ons can be gen erated 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

33、 the following configurations can be achieved just by variatio n of these parameters or desig n variables.Fig. 5. Variati on of kin ematics bydesig 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 t

34、he requireme nts several con troller models were developed. It is com mon to all that they are highly non-linear. Mainly the compressibility 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-fun cti

35、ons. This allows to use the same code in the simulatio n as well as on the target hardware.A survey of the con trol scheme is show n in Fig. 6. For this con tributi on it is importa nt to know about the in terface for the co-simulatio n. The calculated forces of the servo pn eumatics are thein puts

36、to the mecha ni cs. The slider positi ons are the outputs of the mecha ni cs. Detailed in formatio n on the con trollers can be found in 2 and 3.Fig. 6. Con trol structure一 兰二養二*主=L3VLPIEI3: £皂&=2一-=Mtrfrllf* OurtmtandMeatus Tif t &4. An alyz ing the behavior of the whole systemWhe n th

37、e modeli ng is done we can go on with the sec ond step ofthe mechatronic design. In the following it is assumed that the SPC200 con troller always con trols the mach ine. The task is the an alysis and syn thesis of differe nt parallel kin ematics relative to stability, dyn amics, and accuracy for a

38、give n workspace.Some studies, e.g. concerning the workspace, can be made exclusive using 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 simulatio n the en d-effector

39、positi ons are traced using the feature“reate tracespli ne ”I (I I q I , IDt5BrOQ151巾宙昭 £, !J9t filmlm 缸妙!|2007-101-11 12 El； 11!Fig. 7. Drive motions for the workspace calculation日 £eTPI-citu 百 bFoThe data can be visualized in ADAMS or any other graphics tool. Asan example the workspace o

40、f the Tripod configuration of Fig. 7 isreprese nted in Fig. 8Right >iewFrom uiew200Fig. 8. Workspace of the Tripod (configuration as in Fig. 7)200 4OCMeasuri ng the velocity of the en d-effector at the same time delivers the gear ratios of all drives over the workspace.To exam ine the behavior of

41、 the closed loop system ADAMS/C on trols is used to couple ADAMS and Simulink. Before the model can beexported 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 controller makes only use of the drive position some a

42、dditional signals are defined as outputs: The drive velocities are needed for solving the differe ntial equati ons of the pressures in the pn eumatics model. Furthermore we n eed the velocity of the tool cen ter point to calculate the non-li near gear ratios. Fin ally the drive accelerati ons serve

43、for the calculati on of the equivale nt moved masses. The whole system is show n in Fig. 9.Fig. 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-fu nctio n.The equivale nt moved masses depe nd on the positi

44、 ons of drives.The non-linearity of the robot grows with the strength of thisdependency. 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 nc

45、e on the stability of the closed loop system. To in itialize and parameterize this controller we need the following information from the mechanics model:equivalent moved mass of each drive (depends on slider positions)gravity forces in initial positionCoulomb and viscous frictionThe controller is de

46、signed for a single axis with a constant mass. Due to the position dependency of the equivalent moved masses of the robot we have to choose an average value for each drive. Unfortunately with ADAMS there is no easy way to calculate the equivalent moved masses along a trajectory. We tried to apply di

47、fferent methods such as dividing 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/Linear. When we define the drive accelerations as plant outputs in ADAMS/C

48、ontrols the direct feed through matrixD of the exported linear system deliversthe mass matrix in the defined operating point as1M (q) f D(q)Corresponding to the three degrees of freedom of the rigid body system the size of the mass matrixM(q) is three by three. It depends onthe vector of the general

49、ized coordinates of the drives. The non-diagonal elements cause the coupling between the axes. The factorf depe nds on the un its chose n for the in puts and outputs. Whe nthe forces are give n in N and the accelerati ons are give n in mm/s2 f is0.001.With a slider mass of 2 kg and an end-effector m

50、ass of 2 kg the mass matrix for the three positions shown in Fig. 10 are:pos. 0pos 1pos. 21M ='4.13 -03 -03-03 斗1303-03 -0.34.13_ 5.01 -LOS-1.035.01 一 LO4-1.05 -1 045.01_IM =_ 5.14-032 -2A2-0.324.10-1 17r 2.42 -1.176 80The gravity forces can be calculated very easily by static simulati on. Likew

51、ise 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 operati ng points by means of eige nv alues and the dyn amics of the closed loop system can be an alyzed by mea ns of freque ncy resp on ses.gen eral pointOf course with a robust controller you can start with a simulation in time domai n. This gives in formatio n about the accuracy and system limits. For this we n eed the refere nces fo