EXPERIMENTAL RESULTS

In order to achieve desire motion specification and avoid the collision in the motion environment, the trajectory planning is required for the robotic motion control, and an appropriate controller is designed to monitor the end-effector motion trajectory. The multi axis manipulator is planned to execute point to point (PTP) motion or trajectory tracking control purpose in this study. The trapezoid speed curve motion trajectory is planned for PTP motion. Since the SOPC system is employed to implement this robotic servo control system, the control system cannot provide large computation ability for the model-based controller. Here, a model-free 1D fuzzy sliding mode controller is designed for each joint with gain scheduling scheme to control this Mitsubishi RV-M2 five DOF robotic system described in Section III. In order to evaluate the transient and steady sate control performances, the following experiments were performed. The sampling frequency in the experiments was 200 Hz. Since the sliding variable is divided into 11 fuzzy subsets from -1 to +1 with equal interval 0.2, a parameter is used to regulate the sliding variables into that range. A parameter was used to adjust the control input. The choice of these parameters is not sensitive to controller implementation. Their gain scheduling variation is designed as Fig. 4 and Table 3. If these parameters are varied within 50% and 200% of the original specified values, the

control system performance is not changed significantly. In order to display the outstanding performance of this intelligent novel controller, its dynamic responses are compared with that of a gain scheduling self-organizing fuzzy controller.

s gs

gu

Case (A): Each joint step response and working space PTP control

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In order to evaluate the transient and steady state responses of the proposed fuzzy intelligent controllers, each joint has

back and forth step motion is planned. The dynamic responses of each joint by using gain scheduling self-organizing fuzzy controller(SOFC) and fuzzy sliding mode controller (FSMC) are shown in Fig. 5(a) and 5(b), respectively for comparison. It can be observed that the dynamic response of FSMC has overshoot less than and steady state error less than . It is obviously less than the corresponding values, and of that of SOFC. In addition, the FSMC control strategy is employed to monitor the robot to move from a point to another point. The planning trajectory for the robotic end-effector is a trapezoid speed curve with a constant acceleration and deceleration for each joint, and it is moving from (0, 500, 200) mm to (400, 0, 300) mm in Cartesian space with 4 sec total motion time. The maximum angular acceleration of each joint is limited to . The motion trajectory in Cartesian space and the position error in each coordinate axis are shown in Fig. 6(a) and 6(b), respectively. The maximum angular tracking errors of each joint is less than . The overall position trajectory tracking error is less than 1.5 mm. The destination steady state position error is 0.03mm. Those data is obviously les than that of SOFC , 2.0mm and 0.1 mm. It is accurate enough for industrial applications.

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Case (B) Trajectory tracking of end-effector moving in Cartesian space

In order to evaluate the trajectory tracking control accuracy by using this model-free FSMC intelligent controller, one straight line from (400, 0, 300)mm to (350, 100, 300) mm and one circle with radius 60mm and center (410, 0, 400)mm in X-Y plane of Cartesian space are planned for trajectory tracking experimental investigation. The position responses in Cartesian space and the position errors in X, Y and Z directions and contouring error of straight line trajectory are shown in Fig.

7(a) and (b), respectively. The position responses in Cartesian space and the position errors in X, Y and Z directions and contouring error of circular trajectory are shown in Fig. 8(a) and 8(b), respectively. The maximum angular tracking errors of each joint is less than . The contouring tracking error in Cartesian space is always less than 0.5 mm except the motion direction change position and the position tracking error in each coordinate is less than 0.5mm. These data are less than

, 1.5mm and 1 mm of that of using SOFC.

It can be concluded that the proposed novel intelligent FSMC controller has simple control structure and excellent

4 Copyright © 2010 by ASME

[8] Shiuh-Jer Huang and Ji-Shin Lee, “A Stable Self-organizing Fuzzy Controller for Robotic Motion Control,” IEEE Transaction on Industrial Electronics, Vol. 47, No. 2, pp.

421-428, 2000.

transient and steady state responses. It can be implemented on robotic system for industrial PTP and trajectory tracking control applications.

[9] Shiuh-Jer Huang and Wei-Cheng Lin, 2003, “Adaptive Fuzzy Controller with Sliding Surface for Vehicle Suspension Control,” IEEE Transactions on Fuzzy Systems, Vol. 11, No. 4, pp. 550-559.

6. CONCLUSION

A SOPC control structure is implemented on a retrofitted Mitsubishi 5 DOF robot for motion control. The model-free fuzzy sliding mode controller was developed for each joint and coded inside the FPGA chip for each joint motion control of this robot. This control strategy has model-free and gain scheduling advantages for achieving good transient and steady state responses. The controller is easy to design and implement.

It can reduce the computing time and data base for onboard system consideration. The experimental results show that this FSMC intelligent control system can effectively monitor the robotic end-effector to track various trajectories planned in Cartesian space with good control accuracy. This SOPC+FSMC control structure can be employed in pick-and-place, assembly and trajectory flowing operations.

[10] L.T. Wang and C.C. Chen, “A Combined optimization Method for Solving the Inverse Kinematics Problem of Mechanical Manipulator,” IEEE Trans. On Robotics and Automation Vol.7, N0.4, 1991.

[11] K. Kazerounian, “On the Numerical Inverse Kinematics of Robotic Manipulator,” AMSEJ of Mechanisms, Transmissions and Automation in Design, Vol.109, pp8-13，March 1987.

[12] Utkin V. I., “Variable structure systems with sliding modes,” IEEE Trans. On Automatic Control, Vol. AC-22, no. 2, pp 212-222, 1977.

[13] Slotine J-J. E., Applied nonlinear control, Prentice Hall, 1991.

ACKNOWLEDGEMENTS

The authors would like to thank the financial support of Taiwan National Science Council under the contract NSC-98-2221-E-011-079.

[14] Edwards Ch. And Spurgeon S. K., Sliding Mode Control – Theory and Applications, Taylor &Francis Ltd., London, Bristol, 1998.

[15] Hwang G. C. and Lin S. C., “A stability approach to fuzzy control design for nonlinear systems,” Fuzzy Sets Systems, Vel 48, pp.269-278,1992.

REFERENCES

[1] F. J. Lin, D. H. Wang and P. K. Huang, “FPGA- based Fuzzy Sliding-mode Control for a Linear Induction Motor Drive,” Proceedings of the IEEE Int. Conf. on Electrical Power Application, Vol. 152, No. 5, pp. 1137-11148, Sept.

2005.

Table 1 D-H parameters of Mitsumishi RVM2 robot

[2] Y. S. Kung and G. S. Shu, “Development of a FPGA-based Motion Control IC for Robot Arm,” Proceedings of the IEEE Int. Conf. on Industrial Technology, pp. 1397-1402, 2005.

[3] M. Okura and K. Murase, “Artificial Evolution of FPGA that Control a Miniature Mobile Robot Khepera,”

Proceedings of the Autonomous Minirobots for Research

and Edulainmente (AniiRE2003), pp. 103-111, 2003. Table 2 The parameters of MIMO trapezoid speed curve trajectory planning.

[4] Sprros Tzafestas and Leonidas Dristsas, ”Combined Computed Torque and Model Reference Adaptive Control of Robot System,” Journal of the Franklin Institute.Vol.327, No.2, pp. 273-294,1990.

[5] Ho-Hoon Lee and Fred E. Chlick, "Design of a Adaptive Control Law for Robotic Manipulator,”Journal of Robotic Systems, Vol.11, No.4, pp. 241-255,Jun.1994.

[6] Louis-A Dessaint; Marouf Sand; Bernard Hebert,"An Adaptive Controller for a Direct-drive SCARA Robot,”

IEEE Trans. On Industrial Electronics, Vol.39, No.2, pp.105-111, April.1995.

[7] Shiuh-Jer Huang and Ruey-Jing Lian, "A Hybrid Fuzzy Logic and Neural Network Algorithm for Robot Motion Control," IEEE Transaction on Industrial Electronics, Vol.

44, No. 3, pp. 408-417, 1997.

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Table 3 The fuzzy gain scheduling control parameters.

Fig. 4 Gain scheduling parameters variation of FSMC controller.

(a)

Fig. 1 SOPC Robotic control system structure.

(b)

Fig. 2 Fuzzy sliding mode control block diagram.

(a)

(b)

Fig. 5 Joints step responses by using gain scheduling (a) SOFC control algorithm (b) FSMC control strategy.

Fig. 3 (a) Sliding variables fuzzy membership functions (b) joints fuzzy control parameters and fuzzy control rules.

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(a) (a)

(b)

(b)

Fig. 6 (a) PTP motion response in Cartesian space and (b) Position tracking error in X, Y and Z directions and 3D contouring error.

(a)

Fig. 8 (a) A circular trajectory tracking in Cartesian space and (b) Position tracking error in X, Y and Z directions and 3D contouring error.

(b)

Fig. 7 (a) A straight line trajectory tracking in Cartesian space and (b) Position tracking error in X, Y and Z directions and 3D contouring error.

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