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Fig. 4 PID and Fuzzy Control System

3.1 PID Controller

In this paper, in order for the Humanoid robot to carry

an object with stability, the chest of the robot was set as

the basis, and the errors of the direction and the speed

from the objects horizontal and perpendicular

components were corrected by PID controller. Thereason for using PID controller is assumption that the

surface the robot was moving on was flat, and the safety

of the object is decided according to the motion of therobot and the movement difference among other robots.

Therefore, the result of PID controller of a robots

motion with stable regularity was shown with betterefficiency than that of other controllers. PID controller

can be expressed as Formula (3).

ut (3)In formula (3), e(t) is the amount of error between the

standard input r and the controller output y, and this can

be expressed as the following:

et rt yt (4)In formula (3), K is the profit of ratio-integral

calculus-differentiation, respectively. These result was

from Ziegler-Nichols method, which is formula (5).

0.6 , , ( is Critical Gain,is Oscillation Period) (5)The oscillation period, the reaction from robots

motion, was set as approximately 7 seconds. Critical

Gain was calculated with a set of the absolute maximum

of errors of position and speed when any correctionswere not made, and recalculated in the range that would

not affect the robots motion. Table 2 illustrates the

profit values in order to correct the errors of horizontalposition, perpendicular position, and speed respectively.

Table 2 Profit values using Ziegler-Nichols formula

Element Horizontal

Position Error

102.00 5.14 5.25

Horizontal

Speed Error

174.00 1.71 4.25

Perpendicular

Position Error

174.00 49.71 152.25

Perpendicular

Location Error

66.00 18.85 57.75

3.2 Fuzzy Controller

Comparing to the regular motion with fixed period of

steps of other robots, the motion of humanoid robot for

carrying an object is irregular. Therefore, this problemwas solved by the Fuzzy controller and corrected by

making the robots position parallel to the object when

the robot is carrying the object. The Fuzzy membership

function of the Fuzzy controller is depicted on Fig 5. As

shown in the picture, the used function has 3 sections:

Slow, Medium and Fast, and each section presented howthe robot has started comparing to other robot did. Table

3 illustrates the Fuzzy Rule for correcting the speed.

Because the objects are carried by 2 of the humanoid

robots, a total of two inputs and 2 outputs will be

resulted. Moreover, since the classification of Master

and Slave should be applied in order to control themovements and speed of the robot, the Master robots

started off beforehand in the simulation exercise.

Fig. 5 Speed of Humanoid Robot Fuzzy Function

Table 3 Fuzzy rule to correct speed

Slave

Master

Slow Medium Fast

Slow Medium Slow Slow

Medium Fast Medium Slow

Fast Fast Fast Medium

4 Simulation Results

Simulation results were confirmed by using the

controller and the simulation environment that was

previously explained. Fig. 6 depicted a graph of the

errors of objects horizontal position, perpendicular

position, and speed. The motions of actual robots were

applied directly through the simulation, and the object

was assumed to be aluminum panels. According to Fig.

6, the Fuzzy controller corrects the error of the initial

starting time. The graph of Fig 6 also shows the positionerrors of perpendicular element are all 0 except for the

initial value. However, as seen in (a) of Fig. 6, the

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position errors of horizontal elements were not

corrected properly, and the reaction occurred when therobot has moved. Such result came out because the

correction value was decreased in order to prevent the

robot from falling when the PID controller forcibly

corrects the objects horizontal element of position

errors.

(a)

(b)

Fig. 6 Perpendicular, Horizontal Position and Speed

Error of Element ((a) : Horizontal, (b) : Perpendicular)

5. Conclusion

The current discussion based on the robots chest in

order for the Humanoid robots to safely move the

objects co-operatively, The simulations with PID and

Fuzzy controller to correct the position and speed of two

robots were performed. By developing this research

further, the results of this study could be used for

developing the algorithm for robot to carry objects

safely on various surfaces from flat to a slope or

irregular surface.

REFERENCES

[1] K. Hirai, Current and Future Perspective ofHonda Humanoid Robot, Proc. IEEE/RSJ Int.

Conference on Intelligent Robots and Systems,pp. 500-508, 1997.

[2] K. Yokoyama, J. Meada, T. Isozumi, and K.Kaneko, Application of Humanoid Robots for

Cooperative Tasks in the Outdoors, Proc. Int.Conference on Intelligent Robots and Systems,Workshop2, 2001.

[3] K. Harada, S. Kajita, H. Saito, M. Morisawa, F.Kenehiro, K. Fujiwara, K. Kaneko, and H.Hirukawa, A Humanoid Robot Carrying a

Heavy Object, Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1712-1717,2005.

[4] Jung-Yup Kim, Ill-Woo Park and Jun-Ho Oh,Realization of Dynamics Stair Climbing forBiped Humanoid Robot Using Force/TorqueSensors, Journal of Intelligent Robot System.pp. 389-423, 2009.

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