1987 Harashima - Tracking Control of Robot Manipulators Using Sliding Mode.pdf

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174 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. PE-2, NO. 2, APRIL 1987 (a) . (a) r2: (n/s) t~~~~. ir (m/s) 1 (sec) ~~~~~~0. 3 06 .9(sec) WS)~~~~~~~~~~~~~~~~~~~~~~~~~~~b 0.5 1.0 1. (sec) 0 (b) Fig. 4. Motion pattern I of manipulator's end. (a) Acceleration. (b) Ve- Fig. 6. Motion pattern two of manipulator's end (higher speed motion). locity. (a) Acceleration. (b) Velocity. 0~ ~ ~~~~~~O (me ter ) (N *m) 0.01 30 (a) (a) -01(X 0.5 1.0 1.5 (sec) 0~ ~~ ~~~~~~~~~~~3 (meter) 0.01 30 |\ ' _ @~~~~~~~~~~ Torque due to gravity 0 .2 Q Total torque 0 0.45 0.9 (sec) ® Torque due to coupling inertia (i Torque due to effective inertia (d3 Torque due to centrifugal and Coriolis forces -0.01 '.. . 0 0.5 1.0 1.5 (sec) Fig. 7. Torque components of link'3. Payload: 4 kg. (Motion pattern two.) (b) Fig. 5. Tracking error of manipulator's end in work space (motion pattern byteculniera)ndhefth(usdycntfone). (a) Payload variation: 0 kg. (b) Payload variation: 4 kg. gal and Coriolis forces) cannot be neglected compared with other terms. In this case the tracking responses of pattern with a maximum value of 7.5 m/s2, and Fig. the three joints to the desired trajectories and the corre- 6(b) is the velocity pattern with a maximum value of 2.1 sponding input torques resulting from sliding mode conrn/s. The torque components of link 3 with a 4-kg pay- trol are shown in Figs. 8, 9, and 10, respectively. load variation in motion pattern two are shown in Fig. 7. As shown in these figures, the manipulator shows per- Due to the direct-drive manipulator, the influences of fect tracking capability as there are almost no tracking nonlinear coupling terms such as the third term (caused errors visible between the desired trajectories and the sys-
HARASHIMA et al.: TRACKING CONTROL OF ROBOT MANIPULATORS 175 (rad) 3 t (rad) 3 03d 2 2 \ 0D3 1 / 1 1 t (sec) 0 3 0.6 0.9 0.3 0.6 0.3 0.6 0.9 0 .9 t (sec) (a) (N m) (N m) (a) 600 300 300- ttsec) 150- t(sec) 0 .3 - 30 -600 -300 0.6 0.9 -150 0.3 0.6 0 .9 (b) (b) Fig. 8. Tracking response of first joint to desired trajectory. Payload vari- Fig. 10. Tracking response of third joint to desired trajectory. Payload ation: 4 kg. (a) Tracking motion. (b) Input torque. variations: 4 kg. (a) Tracking motion. (b) Input torque. (rad) servo sampling period is equal to 5 ms. The sensor reso- 3 lution is assumed to be infinite. 2 2 902d CONCLUSION The algorithm presented in this paper is for the accurate 02 t (sec) tracking control of robotic manipulators. By using the im- 0 0.3 proved sliding mode control law, the nonlinear dynamic 0 . 3 0.6 0 . 9 interactions of the manipulator joints are effectively sup- -1 pressed, and the system is insensitive to the physical parameter variations. The simulation results demonstrate the (N.m) (a) perfect tracking property of a robotic manipulator with three degrees of freedom. The nonlinear coupled manipulator dynamics show well-behaved linear uncoupled 300 characteristics in high-speed motion. In addition, the de- 150 t (sec) sign of the sliding mode controller needs less a priori in- -150 0.43 0.609PI formation about the parameter changes owing to the fact -300 that control gains need only to satisfy some inequality 300 f conditions associated with parameter bounds. Since the (b) variations of the control gains are determined according Fig. 9. Tracking response of second joint to desired trajectory. Payload to simple switching logic, computation for completing variation: 4 kg. (a) Tracking motion. (b) Input torque. control inputs can be reduced to the degree that real-time tracking control is realizable. As for measuring practical signals, the sensor resolution is always finite and gives tem's, i.e., the developed control system isin every way rise to the problem of affecting the actual control chatterrobust in high-speed motion even with the existence of ing frequency. Therefore, in future research we will take unknown parametric variations, Due to the actuator dynamics a simulation has been performed by introducing first-order filters between each controller output and the corresponding manipulator input into account the limitations of sensor resolution. REFERENCES toqe Th rnfrfnto fec itri hrce- ( 1] V. I. Utkin, "Variable structure system with sliding modes," lEEE ized by 1 /(1 + ris). T1 = 20mis, T2 = 15 ins, and 73 = Trans. Automat. Contr., vol. AC-22, pp. 212-222, Apr. 1977. 10 ms with respect to joints 1, 2, and 3, respectively. The [2] D. E. Whitney, "4Resolved rate control of manipulators and human
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1987 Harashima - Tracking Control of Robot Manipulators Using Sliding Mode.pdf

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