Development of Inverse Dynamic Controller for Industrial robots with HyRoHILS system

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1 June 2-5, KINTEX, Gyeongg-Do, Korea Development of Inverse Dynamc Controller for Industral robots wth HyRoHILS system Je Sung Yeon*, Eu Jn Km**, Sang-Hun Lee**, Jong Hyeon Park*, and Jong-Sung Hur** * {Department of Precson Mechancal Engneerng School of Mechancal Engneerng}, Hanyang Unversty, Seoul, Korea (Tel : ; E-mal: mydoban@hanyang.ac.kr, jongpark@hanyang.ac.kr) ** Electro-Mechancal Research Insttute, Hyunda Heavy Industres Co, Ltd Mabuk-r, Guseong-eup, Yongn-s, Gyeongg-do, Korea (Tel : ; E-mal: {ejkm mrshlee jshur}@hh.co.kr) Abstract: In ths work, an nverse dynamc control method s developed to enhance trackng performance of ndustral robots, whch effectvely deal wth the nonlnear dynamc nterferental forces. In general, the DFF (Dynamc Feed-Forward) controller and the CTM (Computed-Torque Method) controller are used for dynamc control for ndustral robots. We study on the practcal ssues for mplementng these nverse dynamc controllers va smulatons and experments. We develop the dynamc models n two dfferent ways. One s a model desgned through Newton-Euler method for real tme computaton and the other s a model desgned through SmMechancs for evaluatng the developed controller va smulatons. We evaluate the nomnal performance and robustness of the controller va smulatons and experments usng seral 4-DOF HyRoHILS (Hyunda Robot Hardware-In-the-Loop Smulaton) system. The results show that the nverse dynamc controller s effectve and practcally useful for a real control structure. Keywords: Dynamc Control, DFF (Dynamc FeedForward), CTM (Computed Torque Method), SmMechancs, HILS. INTRODUCTION A mult-lnk ndustral robot s a typcal MIMO (Mult Input Mult Output) system whose states are dynamcally coupled each other. Because there s a large torque varaton from state condtons of each jont of the robot, t should be consdered about the robot dynamcs for ts control. And the lnks of the robot move together to track the reference trajectory, so each lnk receves far nterference forces from the other lnks. In order to deal wth these nterference forces and to optmze the trackng performance and robustness [2][3][4], t s necessary to develop an nverse dynamc control method that can effcently take care the nonlnear nterference forces such as nerta, colols, centrfugal and gravtatonal forces [3]. A PD and PID controller wth gravty compensator were used to reflect the dynamc feature of a robot untl CTM (Computed-Torque Method) was proposed by Paul and Markewcz n the early 8th century. CTM guarantees a hgh accurate trackng performance, however t may have mplementaton ssues because computaton of complex dynamc equatons n real-tme s requred. To allevate these, DFF (Dynamc Feed-Forward) was proposed by Legeos and others. Bascally the controller based on the dynamcs guarantees a hgh accurate trackng performance and robustness [9][0]. And there s lttle dfference between the basc performance of CTM and DFF controller. But CTM has better features f the extensve vbraton or external force appled on the robot. Glbert and Ha proved a robustness of CTM n 984 and Khosla proved that shorter calculaton perod and more exact system parameters make better performance. Our work s to develop an nverse dynamc controller for ndustral robot and to apply the developed control algorthm to HyRoHILS (Hyunda Robot Hardware-In-the-Loop Smulaton) system for evaluaton ts performance. In Secton 2, we desgned a SmMechancs model for evaluatng the developed controller va smulaton, and a model usng Newton Euler method to decrease computaton tme. Also we developed the DFF and the CTM controller n Secton 3. We evaluated the path trackng performance and robustness and analyzed merts and demerts of these controllers va smulatons usng SmMechancs smulator and experments usng the HyRoHILS system n Secton 4 and SmMechancs model 2. ROBOT MODELING It s very dffcult and take takes sgnfcant computaton tme to model a mult-lnks seral robot, because of ts complex structure n physcal relatonshp. So we used MATLAB/SmMechancs toolbox that makes t easy to desgn the rgd body mechancal system connected by jonts. Owng to ts block dagram based nature, MATLAB/ SmMechancs constructs a mechancal system model by connectng some basc model blocks lke MATLAB/Smulnk routnes, and can encompass herarchcal subsystems. It can smulate translatonal and rotatonal motons n the three dmensons. And t provdes users wth a tool to specfy bodes and ther mass propertes, ther possble motons, knematc constrants, coordnate systems and the means of ntatng and measurng motons. Ths makes t unnecessary to go through a complex analytcal modelng process. To verfy the valdty of SmMechancs model, we compared the SmMechancs model wth the Newton-Euler model by trajectory trackng smulaton. In the result of smulaton, two nput torques of models are same. The ndustral robot has many parts such as bodes, motors, gears, shafts, and so on. And each part has mechancal characterstcs. For example, there s mass, nerta, centrfugal force. Therefore t s dffcult to model the robot ncluded every dynamcal effect. So generally, we model the robot wth only effectve terms. Non-effectve terms are gnored and smplfed.

In ths paper, many terms are smplfed to rgd body. But because the motor nerta affects robot dynamcs durng rotatng at hgh speed, the motor dynamcs s ncluded n the smulaton model. Fg.

2 In ths paper, many terms are smplfed to rgd body. But because the motor nerta affects robot dynamcs durng rotatng at hgh speed, the motor dynamcs s ncluded n the smulaton model. Fg. s a motor drver model wth motor nerta and reducton gear. The nput and output axes are algned usng two gear constrant blocks. Input torque s appled nto the jont actuator block. And the feedback nformaton s obtaned from the jont sensor block. Consequently the structure of 4 axs seral type HyRoHILS system s modeled as shown n Fg.2. June 2-5, KINTEX, Gyeongg-Do, Korea ˆ R Z ˆ R R Z Zˆ v R P P v v P C C P C C C C N I I v () F m v (2) Inward teraton : :6 f R f F n N R n PC F PC R f n T Zˆ (3) Fg.2 SmMechancs model of motor drver Where s rotatonal velocty, s angular acceleraton, and v s lnear acceleraton from lnk to lnk. And v C s lnear acceleraton of the mass center, F s nertal force, N s nertal Torque at mass center of each lnk. f and n are force and torque so that they appear as teratve relatonshps from hgher-numbered neghbor to lower-numbered neghbor. Fnally, R s rotaton matrx, P s poston vector from jont to jont, and s poston vector from jont to center of mass. P C Fg. SmMechancs model of HyRoHILS 2.2 Newton-Euler model In generally, mult-lnks seral robot s mathematcal dynamc equatons are obtaned usng the Euler-Lagrange equaton, Newton-Euler formaton or Kane s dynamc equaton. We model dynamc equatons usng Newton-Euler method for real-tme computaton. The complete algorthm for computng each jont torques durng some moton s composed of two processes. Frst, lnk veloctes and acceleraton are teratvely computed from lnk to lnk n and the Newton-Euler equatons are appled to each lnk. Second, forces and torque of nteracton and jont actuator torque are computed recursvely from lnk n to lnk. For the case of rotatonal jonts, these equatons are summarzed by below equatons (), (2), (3). Outward teraton : :05 Fg.3 Mechancal model of motor wth gear Fg.3 shows the mechancal model of motor for consderng motor dynamcs. As the result, the motor torques are found by equaton (4). m I mm b mm (4) r Where I s motor nerta, s vscous frcton of m bm actuator and r s gear rato. Subscrpt m means the rotatonal nformaton of actual motor. Addtonally we compensate the motor frcton of HyRoHILS robot through frcton dentfcaton. 3. DECOUPLING CONTROL Decouplng control can be accomplshed by usng the

3 nverse dynamcs control, nonlnear control, Lyapunov desgn, or feedback lnearzaton of nonlnear systems. We use nverse dynamcs control method for decreasng computaton tme and applyng to real control system. The degree of freedom of the system becomes large, the dynamc equaton of manpulator becomes complex. Therefore t s very dffcult to calculate the nverse dynamc equaton of a general mult-lnk seral robot. Though there are more deal control algorthms, most of them are dffcult to apply to real control system because they are too heavy. So we choose CTM (Computed Torque Control) and DFF (Dynamc Feed-Forward) controller whch are general dynamc controllers. 3. CTM controller The CTM controller s one of the general dynamc controllers. In computed torque control, the feedback controller sends ts output throught the dynamc model. June 2-5, KINTEX, Gyeongg-Do, Korea Fg.5 DFF controller Fg.5 s the block dagram of DFF controller, n parallel wth the feedforward computaton, there s an ndependent-jont PD controller wth velocty reference. The sum of the feedforward output and the feedback controller output then drves the robot Dynamc Feedforward output s wrtten ˆ ( ) ˆ (, ) ˆ ff D d d C d d d G ( d ) (7) Feedback output of ndependent- jont PD controller s wrtten, K ( ) K ( ) (8) fb v d p d Therefore, nput torque of DFF controller s Fg.4 CTM controller The computed torque controller computes the dynamcs on-lne, usng the sampled jont poston and velocty data. If feedback nformaton contan nose, then system performance s not good because of that reason. The smple full dynamcs are descrbed by D( ) C(, ) G( ) (5) Where s the vector of jont torques for rotatonal jonts, s the vector of jont angle, D s the nerta matrx, C s the vector of corols and centrpetal terms, G s the gravty vector n real system. The nput torque of CTM controller s Dˆ ( )( d K ( v d ) Kp ( d )) Cˆ(, ) Gˆ( ) Where ˆD s the nerta matrx, Ĉ s the vector of corols and centrpetal terms, Ĝ s the gravty vector of dynamc model. Subscrpt d s meanng the desred nformaton. 3.2 DFF controller DFF controller s an alternatve to CTM for the on-lne computaton requrements. The dynamc model s computed as a functon of the desred path only, and so when the desred path s know n advance, values could be computed off-lne before moton begns. At run tme, the precomputed torque hstores would then be read out of memory. (6) (9) ff fb 4. SIMULATION 4. Path trackng performance For evaluatng the performance of each controller, we use a rectangular trajectory as shown n Fg.6 n the 3 dmensonal spaces. Z [m] Desred Trajectory Fg.6 Rectangular trajectory for performance evaluaton Fg.7 and Fg.8 show the smulaton results of each controller, whch are jont error and trajectory error. In case of the thrd jont that has the largest moton, dynamc controllers reduce the error 0 tmes. These results verfy the superorty of dynamc controller. And there are lttle dfferences between CTM and DFF controller.

Jont Error Fg.7 Smulaton result max. jont error June 2-5, KINTEX, Gyeongg-Do, Korea uncertantes.

It s because the gap between model and real robot make a wrong compensaton torque and t causes bad performance.

8 Smulaton result max. trajectory error 4.2 Robustness to the parameter uncertantes In applcatons of robot control algorthm, one of the most mportant problems s handlng the parameter uncertantes.

4 Jont Error Fg.7 Smulaton result max. jont error June 2-5, KINTEX, Gyeongg-Do, Korea uncertantes. In case of CTM and DFF controller, however, parameter uncertantes make the jont error larger n proporton to the magntude of the uncertantes. It s because the gap between model and real robot make a wrong compensaton torque and t causes bad performance. Especally n case of CTM, as the change of load mass become large, the controller performance becomes worse rapdly. So the accurate parameters are necessary for dynamc control. Trajectory Error Fg.8 Smulaton result max. trajectory error 4.2 Robustness to the parameter uncertantes In applcatons of robot control algorthm, one of the most mportant problems s handlng the parameter uncertantes. In ths paper, we evaluate the controller robustness by makng uncertan the payload mass from -50% to 20% of nomnal one. 5. HyRoHILS system 5. EXPERIMENT We use the HyRoHILS(Hyunda Robot Hardware In the Loop Smulaton) system, as shown n Fg.0 and Fg., for expermental verfcaton. The HyRoHILS system s rapd prototyper that makes effcent development of control algorthm. It conssts of a host staton, a prototypng devce(dspace equpment), drve unts and a 4-D.O.F. artculated manpulator. Now we explan the HyRoHILS system as followng functonal components. Fg.0 HyRoHILS system Fg.9 Smulaton result parameter uncertanty Fg.9 shows controller characterstcs accordng to the parameter uncertanty. In case of PPI controller, the jont error decrease lttle by lttle accordng the load mass decreases. So the robustness of PPI controller has no concern wth parameter Fg. Setup of HyRoHILS system 5.. Controller desgn tool The desgn and smulaton of an algorthm s performed on the host staton usng control desgn tool, the MATLAB and Smulnk. The host staton s a standard Intel-processor-based PC wth dual montors for effcency of dsplayng the operatonal condtons and expermental results. And the operatng system s Wndows Owng to the block dagram methods, the Smulnk makes t easy to desgn and modfy the control algorthm. For the mplementaton of some excessvely complcated parts or functonal parts for the dentty wth commercal controller such as dynamc parameter calculaton, encoder nterface and come sequences, the C-language-based S-functon can be used for makng these parts to the Smulnk blocks wth small modfcaton of the custom code.

5 5..2 Prototypng tool For the hgh-speed prototypng, mmedate mplementaton on drvng controller, we use the dspace DS03. The DS03 s a sngle-board hardware sutable for development of robot control algorthms. To control a robot manpulator t should have enough calculaton capacty, encoder nterfaces and enough dgtal and analog I/Os. And there s an experment and valdaton software envronment, after mmedate mplementaton, whch runs the mplemented real-tme control algorthm and gathers expermental results. Ths envronment s the ControlDesk that s provded by dspace. The ControlDesk makes t easy to desgn and confgure vrtual nstrument panels va drag & drop. Accessng all the model varables wthout nterruptng the experment s possble too. Tunng gans and recordng sgnal n real-tme s also avalable Manpulator The manpulator for the HyRoHILS system s a four degree-of-freedom artculated robot. Ths robot s able to handle up to 5kg-payload. Each axs s drven by AC servomotor, and ts reducer s all-n-one type Harmonc Drve that ncludes reducer tself, bearngs and case. The shape and structure of the arm s smply desgned for easy changng of mass propertes such as mass, center of gravty and moment of nerta. Postonal sensors for jonts are 7-bt absolute encoders. Absolute poston values are receved once through RS232 network when the system s ntally actvated. The controller receves only ncremental encoder data after ntalzaton of absolute poston. 5.2 Path trackng performance For evaluatng the performance of each controller, we compared some expermental data, such as jont errors and trajectory errors. June 2-5, KINTEX, Gyeongg-Do, Korea n whch dynamc characterstcs are well appear. Trajectory on the X-Y plane s shown n Fg.4. Dynamc controllers such as CTM and DFF controller track the reference trajectory better than PPI controller Poston (X-Y) Poston (X-Y) Poston (X-Y) PPI DFF CTM Desred Poston (X-Y) Fg.4 HyRoHILS experment result close-up corner 5.3 Robustness to the parameter uncertantes We evaluate the robustness aganst the wrong nformaton of robot dynamcs such as the change of load. The change of load makes a large uncertanty n mass, center of mass and nerta. Fg.5 shows the varaton of maxmum jont error when the load of robot, whose nomnal payload s 5kg, s changed from kg to 6kg by kg. And P, N, N2, N3 and N4 n ths graph mean 6kg, 4kg, 3kg, 2kg and kg respectvely. The result s smlar to that of smulaton. Jont Error Fg.2 HyRoHILS experment result max. jont error Trajectory Error Fg.3 HyRoHILS experment result max. trajectory error Fg.2 shows the jont error of each jont when the robot tracked the rectangular trajectory. Because of the modelng error n the dynamc model and frcton force, the jont errors n the experment are larger than those n the smulaton. Fg.3 shows the trajectory error. And next, we close up the corner of rectangular trajectory

6 Fg.5 HyRoHILS experment result parameter uncertanty 6. CONCLUSIONS AND FUTURE WORK In order to accomplsh good path-trackng performance of ndustral robots, we studed the practcal ssues for the development of nverse dynamc controllers such as dynamc modelng, calculaton, structure and robustness. We bult two well-known nverse dynamc controllers, one s the DFF(Dynamc FeedForward) control method and the other s the CTM(Computed Torque Method). And we evaluated the control performance and robustness of the controller by smulaton and experments. For the smulaton, we used an evaluaton model from the Matlab/SmMechancs, and for expermental evaluaton, we used a rapd control prototyper, the HyRoHILS(Hyunda Robot Hardware In the Loop Smulaton) system, whch has a 4-DOF seral manpulator. We tested a rectangular-path trackng performance and the performance varaton due to perturbatons on the payload. The results showed that the desgned controllers are effectve and practcally useful. Partcularly for the movements along the corner, whch are typcally affected by the dynamc force, they showed better path accuracy than the conventonal PID controller. For some extent of system parameter uncertantes, the effectveness of dynamcs based model s stll superor to the conventonal one. But for the best performance, exact nformaton of system parameters s requred. For the future work, we have a plan to develop a robust controller that has robust stablty and performance n spte of the parameter uncertanty. A canddate s a nonlnear H-nfnty control algorthm proposed n [2]. June 2-5, KINTEX, Gyeongg-Do, Korea Transactons on Robotcs and Automaton, vol. 4, no., pp , 998. [7] L. A. Nguyen, I. D. Walker, and R. J. P. Defgueredo, "Dynamc Control of Flexble, Knematcally Redundant Robot Manpulators", IEEE Transactons on Robotcs and Automaton, vol. 8, no. 6, pp , 992. [8] C. H. An, C. G. Atkeson, J. D. Grffths, and J. M. Hollerbach, Expermental Evaluaton of Feedforward and Computed Torque Control, Proc. IEEE Int. Conf. Robotcs and Automaton, 987. [9] C. H. An, C. G. Atkeson, and J. M. Hollerbach, Expermental Determnaton of the Effect of Feedforward control on Trajectory Trackng Errors, Proc. IEEE Conf. on Robotcs and Automaton, 986. [0] C. H. An, C. G. Atkeson, and J. M. Hollerbach, "Model-based Control of a Robot Manpulator", The MIT Press, 988. [] F. Brun, F. Caccavale, C. Natale, and L. Vllan, "Experments of Impedance Control on an Industral Robot Manpulator wth Jont Frcton", Proc. IEEE Conf. on Control Applcaton, 996. [2] T. Wk, C. -M. Fransson, and B. Lennartsson, "Feedforward Feedback Controller Desgn for Uncertan Systems", Proc. IEEE Conf. on Decson and Control, [3] S. Jagannathan, Control of a Multple Lnk Robot Arm at Very Hgh Speeds for an Industral Applcaton", Proc. Amercan Control Conf, 200. [4] S. Lm, and K. Chan, Coordnated Feedforward and Feedback Control for Fast Repostonng of Uncertan Flexble Systems", Proc. Amercan Control Conf, [5] B. Armstrong, O. Khatb, and J. Burdck, "The Explct Dynamc Model and Inertal Parameters of PUMA 560 Arm", IEEE, 986. REFERENCES [] Y. J. Cho and W. K. Chung, "Performance and H- optmalty of PID Trajectory Trackng Controller for Lagrangan Systems", IEEE Transactons on Robotcs and Automaton, vol. 7, no. 6, pp , 200. [2] J. Ym and J. H. Park, "Robust Control of Robot Manpulator wth Actuators", KSME Internatonal Journal, vol. 5, no. 3, pp , 200. [3] C. -H. Cho and N. Kwak, "Robust Control of Robot Manpulator by Model Based Dsturbance Attenuaton", IEEE/ASME Tranjactons on Mechatroncs, vol. 8, no. 4, pp. 5-53, [4] B. K. Km, S. Park, W. K. Chung and Y. youm, "Robust Controller Desgn for PTP Moton of Vertcal XY Postonng Systems wth a Flexble Beam", IEEE/ASME Transactons on Mechatroncs, vol 8, no., pp. 93-0, [5] A. Vsol, and G. Legnan, "On the trajectory control of ndustral SCARA robot manpulators", IEEE Transactons on Industral Electroncs, vol. 49, no., pp , [6] F. Ln and R. D. Brandt, "An Optmal Control Approach to Robust Control of Robot Manpulators", IEEE

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