A. A. KHALATE ET AL.

Copyright © 2011 SciRes. ICA

370

trol scheme is effective in reducing chattering in torque

control signal and simultaneously control effort is less in

comparison to the results in [2].

the system response of a two-link robot manipulator based

on nonlinear saturation controller [2] and proposed adap-

tive fuzzy controller (15) for two cases while the robot

manipulator is (i) unloaded (ii) loaded. Results are pre-

sented in the following sequences in the figures: joint

positions (joint-1 (1), joint-2 (2)), tracking errors (1

and 2), and input torques (1

q qq

q

and 2

) respectively. It

may be mentioned that the robot manipulator is loaded at

time 2 sec. i.e. the second link lifts some mass due to

which the parameter of the robot changes as given in

(38).

7. References

[1] J. J. E. Slotine and W. Li, “On the Adaptive Control of

Robotic Manipulators,” International Journal of Robotics

Research, Vol. 6, No. 3, 1987, pp. 49-59.

doi:10.1177/027836498700600303

[2] M. W. Spong, “On the Robust Control of Robot Manipu-

lators,” IEEE Transactions on Automatic Control, Vol.

37, No. 11, 1992, pp. 1782-1786. doi:10.1109/9.173151

The results of the proposed adaptive fuzzy controller

are compared with that of [2] (see (12)) where fixed PD

controller gains are considered as and

. In both the methods, it is observed that

the tracking error responses remain almost the same or-

der and insensitive irrespective of the payload variation.

Further it has been observed through simulation studies

that the proposed technique effectively alleviates or re-

duces the chattering effect in control signals. A signifi-

cant chattering in the control signal is noticed while a

robot arm takes a sharp turn under loaded condition.

Simulation result shows that the proposed controller ef-

fectively reduces the magnitude of input torque or in

other words effectively reduces the control effort com-

pared to the method discussed in [2]. It may be further

observed from the figures ((see Figures 4(g)-(h) and

Figures 6(g)-(h)) how the diagonal elements of gain

matrix

diag75 50K[3] A. B. Sharkawy, M. M. Othman and A. M. A. Khalil, “A

Robust Fuzzy Tracking Control Scheme for Robotic Ma-

nipulators with Experimental Verification,” Intelligent Con-

trol and Automation, Vol. 2, No. 2, 2011, pp. 100-111.

doi:10.4236/ica.2011.22012

diag40 15

(11 22

,

K) of PD controller are updated adap-

tively.

[4] M. Galicki, “An Adaptive Regulator of Robotic Manipu-

lators in the Task Space,” IEEE Transactions on Auto-

matic Control, Vol. 53, No. 4, 2008, pp. 1058-1062.

doi:10.1109/TAC.2008.921022

[5] M. W. Spong, S. Hutchinson and M. Vidyasagar, “Robot

Modeling and Control,” John Wiley & Sons Inc., New

York, 2006.

[6] C. C. Cheah, C. Liu and J. J. E. Soltine, “Adaptive Track-

ing Control for Robots with Unknown Kinematics and

Dynamic Uncertainty,” International Journal of Robotics

Research, Vol. 25, No. 3, 2006, pp. 283-296.

doi:10.1177/0278364906063830

[7] T. H. S. Li and Y. C. Huang, “MIMO Adaptive Fuzzy

Terminal Sliding-Mode Controller for Robotic Manipu-

lators,” Information Sciences, Vol. 180, No. 23, 2010, pp.

4641-4660. doi:10.1016/j.ins.2010.08.009

6. Conclusions

[8] Z. Bingul and O. karahan, “A Fuzzy Logic Controller

Tuned with PSO for 2 DOF Robot Trajectory Control,”

Expert Systems with Applications, Vol. 38, No. 1, 2011,

pp. 1017-1031. doi:10.1016/j.eswa.2010.07.131

In this paper, an adaptive fuzzy control law is proposed

for trajectory tracking of robot manipulator with a view

to reduce the chattering effect in torque control signal.

The advantages of fuzzy and adaptive control strategies

are combined and subsequently the stability condition of

robot manipulator is derived based on Lyapunov theorem.

The implementation of proposed controller is very

straightforward due to the use of simple fuzzy rules and

control strategies. The gain of PD term is updated

with time and hence proposed adaptive control scheme

removes the disadvantage of using fixed large gain val-

ues in [2]. Simulation results show that the present con-

K

[9] L.-X. Wang, “Stable Adaptive Fuzzy Control of Nonlin-

ear Systems,” IEEE Transactions on Fuzzy Systems, Vol.

1, No. 2, 1993, pp. 146-155.

[10] G. Feng, “A Survey on Analysis and Design of Model-

Based Fuzzy Control Systems,” IEEE Transactions on

Fuzzy Systems, Vol. 14, No. 5, 2006, pp. 676-697.

[11] M. W. Spong and M. Vidyasagar, “Robot Dynamics and

Control,” Wiely, New York, 1989.

[12] L. X. Wang, “A Course in Fuzzy Systems and Control,”

Prentice-Hall, Englewood Cliffs, 1997.