Improving Machining Accuracy with Robot Deformation Compensation

Transcription

1 he 29 IEEE/RSJ International Conerence on Intelligent Robots and Systems October 11-15, 29 St. Louis, USA Improving Machining Accuracy with Robot Deormation Compensation Jianjun Wang, Hui Zhang, and homas Fuhlbrigge, Member, IEEE Abstract Industrial robots oer a cheaper yet more lexible alternative to the CC machines in the cleaning and premachining applications o automotive aluminum castings. But the low stiness has limited the application o industrial robots to the machining tasks with very low precision requirement. his paper presents a practical method to compensate the robot deormation caused by the machining orce. A constant joint stiness model based eed orward compensation scheme is implemented in the robot controller. he compensation scheme is shown to be able to reduce the position error by more than 6%. Application test in milling a standard aluminum block has demonstrated the eectiveness o the proposed deormation compensation method. he surace error is reduced rom.5mm to.1mm. I. IRODUCIO he automotive industry represents the astest-growing market segment o the aluminum industry, due to the increasing usage o aluminum in cars or lower uel consumption and better vehicle perormance. Most o the automotive aluminum parts start rom a casting in a oundry plant, ollowed by the downstream processes usually including cleaning and pre-machining o the gating system and riser. Robot based lexible automation oers an ideal solution or the cleaning and pre-machining applications due to its programmality, adaptality, lexility and relatively low cost. evertheless, the oundry industry has not seen many success stories or such applications and installations. he major hurdle preventing the adoption o robots or the machining processes is the act that the stiness o today s industrial robot is much lower than that o a standard CC machine. Field tests using industrial robots or heavy machining such as milling oten ound that a perect robot program without considering contact and deormation ails to produce the desired path once the robot starts to execute the machining task. Due to the much lower stiness, a 5 cutting orce during a milling process will cause a 1 mm position error or a robot compared to a less than.1mm error or a CC machine. Since the robot typically has.1mm motion error without contact, the majority o the position error in heavy machining operations comes rom the contact orce induced deormation. hereore, to achieve Manuscript received March 1, 29. his work was supported by ABB Corporate Research Funding. All authors are with Corporate Research Center o ABB Inc., Windsor, C 695. All corresponds should be addressed to Jianjun Wang. (phone: ; ax: ; Jianjun.Wang@ us.abb.com). higher accuracy in robotic machining, the deormation must be accurately compensated. he existing research o robot deormation compensation is mostly ocused on gravity and delection compensation o lexible manipulators [1], [2]. o increase the position accuracy, rigid manipulators are treated lexible so that the compliance rom the joints and links are included in the compensation model [3]. In these research eorts, the external load applied on the manipulator is basically a dead weight ixed to the robot end eector. ot much attention has been paid to the compensation o process orce induced robot deormation. Methods or compensating the robot deormation can be classiied as model based and sensor based. Model based compensation uses a model to predict the robot deormation and then modiy the robot position reerence accordingly. [4]-[7] described the modeling and identiication o the robot stiness or milling and cutting applications. A complex joint stiness model was used to include not only the elasticity in the direction o the joint motion but also the compliances orthogonal to the joint motion. Unlike the model based method, the sensor based methods sure the deormation induced position error in either the joint space or the Cartesian space and then adjust the position reerence accordingly. In [8], a linear scale unit was placed on each prismatic link o a hexapod parallel kinematics machine to sure the link deormation caused by external orces and heat. It is natural to apply the eedback scheme or the sensor based methods to continuously adjust the robot position until the position error is within the speciied limit. However, the setting time will be a concern i the robot is moving with high speed. Although sensor based compensation methods oer higher position accuracy, they are very diicult to implement on an existing robot manipulator. Even it is possible to install the sensor, the inal system cost would be expensive because o the sensor cost. his makes the sensor based methods more suitable or high accuracy discrete processes such as drilling, while the model based methods are better or continuous processes such as milling and roller hemming. he goal o this paper is to present a practical method to improve the machining accuracy through robot deormation compensation. his paper does not strive to achieve the maximal possible deormation compensation, but rather a reasonable cost to beneit ratio as oten requested in an industrial product. Under this guideline, a constant diagonal /9/$ IEEE 3826

2 joint stiness model is used or easy identiication and real time implementation in the industrial robot controller. he remaining paper is organized as ollowing. Section 2 and 3 describe the modeling and identiication o the robot deormation, while section 4 is devoted to the implementation o deormation compensation in the robot controller. he perormance o the model based deormation compensation is veriied through a pliied milling test in section 5. II. ROBO DEFORMAIO MODELIG A robot manipulator deorms under external orces because o its compliance. he sources o the compliance are the compliances at the manipulator base, gearboxes, motors, links and other transmission elements, in addition to the active stiness provided by the position control loop. For many industrial manipulators it is reasonable to assume that: 1) the compliance in the joints (gearbox and motor) is the dominant source o the robot deormation, 2) the links are ininitely sti, 3) a joint PID control loop is used and the active joint stiness provided by the control loop has small variation over time at the steady state. hese assumptions are ilar to those stated in [9]. It is worthwhile to point out that, robot manuacturers are moving toward the new generation slim manipulators and these 3 assumptions might be invalid. Especially, the links might contribute equally to the deormation as the joints. where Jt is the Jacoan matrix that transorms a small joint angle displacement θ to the translational and rotational displacements xt o a Cartesian rame attached to the tool tip xt = J t θ (3) he delection caused by the external orce vector can be calculated through the Cartesian stiness as: Ft = Kt xt = J t Kθ J t xt (4) he joint stiness matrix K θ relects the natural entity o a manipulator structure. It is diagonal, positive deinite and constant irrespective o the external orce or the robot coniguration. In contrast, the Cartesian stiness matrix K t is coniguration dependent. ote that here we did not use the enhanced stiness modeling as shown in [9][1], where an external orce and robot coniguration dependent stiness term is included in the Cartesian stiness ormulation. his is because under the rated robot payload range, the contribution o this extra stiness term to the total robot deormation is very small. In addition, the conventional ormulation (2) has the computational advantage. C. Deormation Characteristics o a serial manipulator Unlike the Cartesian robots, serial manipulators demonstrate counter intuitive deormation phenomena at certain conigurations and load conditions due to the coupling o its joints during a Cartesian motion. Fig. 2 ulates the deormation o an ABB IRB robot under a series o load conditions. he robot joint stiness matrix is assumed as: 3 [ ] 1 m/rad K θ = Fig. 1. A 6-axis serial robot manipulator. Fz() A. Joint Stiness With the above three assumptions, the stiness o a 6-axis serial robot manipulator shown in Fig. 1 can be represented by its link side joint stiness: a constant 6*6 diagonal matrix with each diagonal term deining the stiness o a joint. K Diag( [ k k k k k k ] ) θ = θ1 θ 2 θ 3 θ 4 θ 5 θ 6 (1) B. Cartesian Stiness As the deormation is oten observed and compensated at the tool tip, the Cartesian stiness at the tooltip K t is important. It can be computed as t = J t K J t K θ (2) Dz total Dz contribution rom Fz Dz(mm) Fig. 2. Simulated load-deormation curve or an IRB 44 demonstrates the apparent negative and piecewise linear stiness in a Cartesian direction. he loading starts rom (-1,2,-3), then ramps down to (,,) and inally ramps up to (1,- 2,1). he counter intuitive phenomenon is due to the odiagonal terms in the Cartesian stiness matrix mathematically, and the coupling o the robot joint motion physically. he contribution o Fx and Fy orces to the deormation in z direction (Dz) is signiicant. Figure 2 clearly shows that in a Cartesian direction a serial manipulator can exhit 1) the apparent negative stiness and 2) totally dierent stiness or dierent 3827

3 loading curves. hese unique deormation characteristics are the key to the explanation o many seemingly strange phenomena occurred during contact operations perormed by a serial manipulator. III. ROBO DEFORMAIO IDEIFICAIO A. Mathematical Formulation A least square solution o (4) can be used to identiy the joint stiness provided that the ull orce/torque vector and the ull translation and rotation displacement can be sured in the same coordinate rame. In reality, this is hard to achieve since the surement o a rotational deormation is diicult. In addition, the torque surement is oten less accurate than the orce surement. Due to the space constraint, the setup o the stiness identiication oten requires the external orce acting on a location dierent rom the deormation surement location. As a result, (4) has to be modiied to account or these constraints. For convenience, we deine two tool rames: the orce action rame as identiied by subscript and the deormation surement rame m as identiied by subscript m. he external load and the corresponding deormation can be then expressed in and m respectively as Fx Dx F y D y Fz Dz F = D m = (5) x φx y φy z φz Using the duality between the joint space and the Cartesian space, the joint torque needed to balance the external orce F is calculated as Γ = J F (6) he joint deormation caused by this joint torque is obtained through joint stiness matrix as θ = K θ Γ (7) his joint deormation will be relected at the surement rame and the corresponding Cartesian delection can be calculated through the Jacoan matrix as m = J m θ = J m Kθ Γ = J m Kθ J F (8) D I only the translational displacement can be sured, then (8) should be changed to = Xm = [ Dx Dy Dz ] = [ I ] m [ I ] J diag{ J F } C θ m m J m Kθ J where C [ 1 k 1 k 1 k 1 k k ] F (9) θ = 1 kθ1 θ 2 θ 3 θ 4 θ 5 1 θ 6 is the joint compliance vector. he diagonality o the stiness matrix is used in the derivation o (9). I the surement is taken times, the least square solution o the joint compliance vector is C θ = (1) i= 1 i= 1 he itting error is given by e = ei ei = i= 1 i= 1 i= 1 i= 1 i= 1 where A [ ] ( ) { ( ) } i i = I J m θ i diag J θi F i m (11) = X (12) B. Experimental setup or stiness surement Fig. 3 shows a setup or identiying the stiness o an ABB IRB44 robot. An AI Omega orce sensor is mounted on the robot wrist and used to sure the external orce acting on the robot. o sure the deormation, a portable coordinate surement arm rom Romer, the CimCore series 3i, is attached to the robot end eecter. he claimed accuracy o this digitizer is about ±.16mm in a surement volume o.9 m 3. he external orce is exerted by an air cylinder through a pulley relayed string. he magnitude o the external orce can be adjusted by changing the air pressure, while the direction o the orce can be altered by the position o the pulley on the column. In this setup there will no torque applied at the orce action point due to the use o the string and the point connection o the string to the robot end eector. Using the static Fig. 3. Experimental setup or robot stiness identiication. he orce action rame is parallel to the deormation surement rame m but with a dierent origin. equilibrium, the orce vector at the orce action rame is the same as the one at the orce sensor rame. his setup is intentionally designed to avoid the usage o the torque surement since the torque component surement in m 3828

4 AI orce sensor has much poorer accuracy than the orce component surement. Beore the test, the setup needs to be calibrated. his includes the calibration o the digitizer base rame relative to the robot base, the pose o the orce action rame and the pose o the surement rame. Although the joint stiness matrix can be identiied at a single robot coniguration by altering the load magnitude and direction, perorming the test at multiple conigurations allow the veriication o the assumptions made or the deormation model, and the reduction o identiication error through averaging. At each robot coniguration, in order to have a ull picture o the deormation, the application o the external load orms a ull cycle o loading and unloading as shown in Fig. 4a. At each load condition, a one minute waiting time is imposed or the stalization o the load and the deormation. he surement rom the orce sensor and the digitizer are then taken 6 times to average the surement noise. Since the digitizer surement is actually the robot position, the deormation o the robot or a given load can be obtained by ply subtracting the robot position surement at the initial unloaded condition. F() cg=[ ] 6 Fx 4 Fy 2 Fz the irst test coniguration. he linear least square itting is perormed on the entire 6 test sets to ind the solution o the joint stiness as: K = θ 3 [ ] 1 m/rad For comparison, Fig. 4 also shows the model predicted deormation based on the identiied joint stiness. It can be seen that the modeling error is within ±.2mm over the ±1.5mm deormation range. hereore, the deormation compensation can be expected to reduce the deormation error by more than 6%. Fx() Fy() cg=[ ] err Dx(mm) err Dy(mm) 2 Dx(mm) Fz() 1-1 err Dy(mm) Dz(mm) Fig. 4b. Loading vs deormation curves at test coniguration 1. ote that the orce action rame is parallel to the deormation surement rame but with an oset. Dz(mm) Fig. 4a. Loading and deormation curves at test coniguration 1. ote that the orce action rame is parallel to the deormation surement rame but with an oset. C. Stiness Identiication Result he stiness identiication is perormed at 6 dierent joint conigurations. Fig. 4 shows the loading curve, deormation curve, and the load vs. deormation curve or IV. DEFORMAIO COMPESAIO he constant and diagonal joint stiness model lends itsel to the real time implementation due to the low computation cost. he block diagram o the real time deormation compensation is shown in Fig. 5. Ater iltering the orce sensor noise and compensating the gravity o the orce sensor payload, the orce signal was translated into the robot tool rame. Based on the stiness model identiied beore, the deormation due to the external contact orce is calculated in real time and the joint reerence or the robot controller is updated. Fig. 5 has been implemented in the ABB s IRC5 robot controller using the existing orce control platorm. he deormation is calculated every 4ms. 3829

5 Fig. 5. Block diagram o a real time deormation compensation. A. Static perormance o deormation compensation o veriy the perormance o the deormation compensation, the same test setup or the identiication is used. he dierence is that at each joint coniguration the test procedure is perormed twice, one without the compensation and one with the compensation activated. Fig. 6 compares the sured deormation beore and ater the compensation at one joint coniguration. he magnitude o the deormation is shown to be reduced rom 1.8mm to.4mm at the maximal load condition. he compensation actually changed the direction o the deormation vector. 1-1 cg=[ ] beore compensation ater compensation response under such an impulse load. he compensation delay is about 5ms, which is signiicantly greater than 4ms. Part o the delay comes rom the poor synchronization between the orce sensor surement and the digitizer surement. he surement rom the orce sensor is directly sampled by the robot controller with 4ms rate. But the digitizer surement is irst acquired by a PC using a serial port and then orwarded to the robot controller through a ast Ethernet connection. Eorts are needed to sure the exact delay caused by this poor synchronization so that its signiicance can be evaluated. Dx (mm) Dy (mm) cg=[ ] sec Fx () Fy () Fx () sec Dx (mm) Fy () Fz () Dy (mm) beore compensation ater compensation beore compensation ater compensation Dz (mm) Fig. 6. Measured load-deormation curve beore and ater compensation at coniguration [ , , , , , ]. B. Dynamic perormance o deormation compensation Since the deormation compensation is implemented in the 4ms loop, ast response can be expected. his can be veriied by applying the robot with an impulse load. he impulse load can be realized by the sudden drop o a dead weight. his is achieved by replacing the air cylinder with a dead weight in Fig. 3. his approach makes sure all the calibrations are not aected. Fig. 7 shows the deormation Dz (mm) sec Fig. 7. Dynamic deormation response under an impulse load at joint coniguration [ ,.9757, , , , ]. V. APPLICAIO ES Fig. 8 shows the setup o a milling test where a 663 aluminum block is used or testing purpose. A laser displacement sensor is used to sure the inished surace. he surace error without deormation compensation demonstrates the counter intuitive negative stiness phenomenon ; an extra.5mm was removed in the middle o the milling path. his can be easily explained by the odiagonal terms o the Cartesian stiness matrix resulting rom the coupling o the robot joint motion. Although the normal contact orce F n pushed the cutter away rom the surace, the orce in the eed direction F and the cutting direction F c actually caused the robot to deorm into the part surace. Since the eed orce and the cutting orce are signiicant in this setup compared to the normal orce, the overall eect is that the actual depth o cut is.5mm more than the commanded. Fig. 9 compares the surace error with Fz () 383

6 and without the deormation compensation. A less than.1 mm surace error is achieved with the deormation compensation. his error is in the range o robot path accuracy. he negative surace error in the igure ns less material was removed than the commanded one. F F c F n VI. COCLUSIO AD DISCUSSIO his paper describes in detail the modeling, identiication and compensation o robot deormation caused by the external process orces rom the machining applications. Lab surement and application tests have shown that, with a ple joint stiness model based eed orward approach the deormation compensation can reduce the contact orce induced position error by more than 6%. While robot deormation compensation is technically easible, more eorts are needed to make it available as a product to be used in the ield. he main challenge is to pliy the stiness identiication process. he recommendation or uture work is to investigate the existing compliance models in the robot controller [3] and try to implement the deormation compensation using these models. Fig. 8. A milling test on a 663 aluminum block to veriy the eectiveness o the deormation compensation. REFERECES [1] D. Surdilovic and M. Vukobratovic, Delection compensation or large lexible manipulators, Mechanism and Machine heory, vol. 31, no. 3, pp , [2] J. C. Hwang, J. H Seo, Y. W. Choi, and H. J. Yim, Error compensation o a large scale LCD glass transer robot, in Proc. 17th World Congress, he International Federation o Automatic Control, Seoul, Korea, July 28, pp [3] M. Abderrahim, A. Khamis, S. Garrido and L. Moreno, Accuracy and calibration issues o industrial manipulators, in Industrial Robotics: Programming, Simulation and Applications, L. K. Huat, Ed. Germany: Pro Literatur Verlag, 27, pp [4] E. Abele, M. Weigold, and M. Kulok, Increasing the accuracy o a milling industrial robot, Production Engineering, vol. 13, no. 2, pp , 26. [5] M. Stelzer, O. von Stryk, E. Abele, J. Bauer, and M. Weigold, High speed cutting with industrial robots: towards model based compensation o deviations, in Proceedings o Robotik, Munich, Germany, 28, pp [6] E. Abele, M. Weigold and S. Rothenbücher, Modeling and identiication o an industrial robot or machining applications, CIRP Annals - Manuacturing echnology, vol. 56, no. 1, pp , 27. [7] E. Abele, S. Rothenbücher, and M. Weigold, Cartesian compliance model or industrial robots using virtual Joints, Production Engineering, vol. 2, no. 3, pp , 28. [8]. Oiwa, Error compensation system or joints, links and machine rame o parallel kinematics machines, Int. J. Robotics Research, vol. 24, no. 12, pp , 25. [9] G. Alici and B. Shirinzadeh, Enhanced stiness modeling, identiication and characterization or robot manipulators, IEEE rans. Robotics, vol. 21, no. 4, pp , Aug. 25. [1] S.F. Chen, he 6x6 stiness Formulation and ransormation o Serial Manipulators via the CC heory, Proc. o the 23 IEEE Int. Con. on Robotics & Automation, aipei, aiwan, Sept. 23, pp Fig. 9. Surace error beore and ater deormation compensation in a milling test. 3831