1. Science and Information Conference 2015
An Optimal Defuzzification Method For
Interval Type-2 Fuzzy Logic Control Scheme
Presented By:
Ziyad T. Allawi
University of Baghdad, Iraq
Science and Information Conference 2015
July 28-30, 2015 | London UK

2. Introduction:
Karnik and Mendel (1998) were the first who introduced the Type-2 Fuzzy Logic Sets.
They introduced “Type-Reduction” to convert the type-2 fuzzy sets into type-1 fuzzy sets.
Bio-inspired Optimization methods are widely used in optimizing the shapes of fuzzy sets in the universe of discourse.
Interval Type-2 Fuzzy Logic Controllers (IT2 FLC’s) can handle uncertainties but could not eliminate their effects.

3. Introduction:
The optimization method can help in choosing the best value of fuzzy system output for better response.
Artificial Bee Colony (ABC) algorithm which was introduced by Karaboga (2005) will be used for optimizing the IT2 FLC.
The controller will be used to optimize the path of nonholonomic DDMR in a 2D unknown environment.

4. Theoretical Background: T2 Fuzzy

5. Theoretical Background: T2 Fuzzy
The Type-2 Fuzzy Logic Set can be defined as follows:
The Defuzzification output of T2 FLS is:

6. Theoretical Background:
The IT2 FLS contains five components: fuzzifier, rule base, inference system, type-reducer and defzzifier.
Type-reducer may use the conventional Karnik-Mendel Algorithm or the fast Enhanced Iterative Algorithm with Stop Condition (EIASC).
EIASC was introduced by Wu and Nie (2011) which saves time in about 70%.

7. Design Procedure: DDMR

8. Design Procedure: DDMR Model
The design procedure will depend on the Lagrange-Euler differential equation of dynamics:
The dynamics model above was used in the design of the DDMR whose equation is as below.

9. Design Procedure: DDMR Model
Parameter
Symbol
Value
Unit
Robot Heading Velocity v
[-1, 1]
m/s
Robot Steering Velocity ω
[-10, 10]
rad/s
Wheels Rotating Velocity
ωr, ωl
[-20, 20]
Robot Wheel Radius r
0.05 m
Semi-length of Wheel Axle l
0.1
Total Robot Mass MR 2 Kg
Total Robot Moment of Inertia IR
0.02
Kg.m2
Total Wheel Moment of Inertia IW
0.0005
Wheel Viscous Friction c
0.06
Kg.m2/s
Gain Factor k -

10. Design Procedure: DDMR Model

11. Design Procedure: Fuzzy Control
The OA controller accepts three inputs, which are LD, FD and RD. The TR controller accepts four inputs, which are the same as OA controller along with the Target Heading Angle (TA).
FLS Input Variables
Real Values
Normalized Values
Scale Factor
Front Distance (FD)
0 – 50 cm
0 – 1
0.02
Left Distance (LD)
Right Distance (RD)
Target Angle (TA)
-π/2 – π/2
-0.5 – 0.5
1/π

12. Design Procedure: Fuzzy Control
Type-1 Fuzzy Input Variables
Interval Type-2 Fuzzy Input Variables

13. Design Procedure: Fuzzy Control
Type-1 Fuzzy Input Variables
Interval Type-2 Fuzzy Input Variables

14. Design Procedure: Fuzzy Control
The two FLCs generate two outputs, which are the Left Wheel Speed (LW) and the Right Wheel Speed (RW).
FLS Output Variables
Normalized Values
Real Values
Scale Factor
Right Wheel Speed (RW)
-1 – 1
-20 – 20 rad/s 20
Left Wheel Speed (LW)

15. Design Procedure: Fuzzy Control
Type-1 Fuzzy Output Variables
Interval Type-2 Fuzzy output Variables

16. Design Procedure: Fuzzy Control
Switching Condition
Optimal Defuzzification

17. Optimal Defuzzification:
In the optimal-defuzzified IT2 FLC, the defuzzification stage is replaced by an optimization algorithm.
Instead of averaging type-reduced set as in normal Defuzzification stage, the optimization algorithm chooses a population of solutions from these bounds, optimizes these solutions using a given objective function, and then uses the optimum solution (velocity) to motivate the DDMR in the next period.
The optimization algorithm used in this article is the ABC algorithm.

18. Results and Discussions:
In the simulation phase of this paper, a nonholonomic DDMR was placed in an unknown environment with many obstacles. The DDMR starts from an initial position (0, 0) towards a target positioned at (800, 600) pixels.
The simulation was performed using the DDMR dynamic model in three cases: the first was performed by using T1 FLC, the second by using IT2 FLC in normal defuzzification (ND), and the third by using IT2 FLC in optimal defuzzification (OD).

19. Results and Discussions:
The three cases were performed under uncertainties in proximity sensor reading in about ±20% and for two sensor ranges: 20 and 50 pixels.
The fitness function used in optimal defuzzification is as below, where v and v* represent the current and preferred velocity of the robot, respectively:

20. Results and Discussions: T1 FLC
Robot path for the T1 FLC and 20 pixels
Robot path for the T1 FLC and 50 pixels

21. Results and Discussions: ND IT2FLC
Robot path for the ND IT2 FLC, 20 pixels
Robot path for the ND IT2 FLC, 50 pixels

22. Results and Discussions: OD IT2FLC
Robot path for the OD IT2 FLC, 20 pixels
Robot path for the OD IT2 FLC, 50 pixels

23. Results and Discussions:
Simulation Results of the Odometry in Pixels
Simulation Results of Travelling Time in Seconds
Sensor Range
T1 FLC
ND IT2 FLC
OD IT2 FLC 20
1280
1241
1129 50
1338
1360
1174
Sensor Range
T1 FLC
ND IT2 FLC
OD IT2 FLC 20
15.7 s
13.7 s
11.7 s 50
17.0 s
15.4 s
12.8 s

24. Results and Discussions:
The results of the T1 FLC were the worst results. The controller could not hold the sensor uncertainties, the path was rougher and longer, whereas the time was also longer.
The results of the ND IT2 FLC were better than the former controller. The path was smoother with some irregularities because the controller minimize the effect of the uncertainties but does not remove them completely. The path and time were shorter.

25. Results and Discussions:
The results of the OD IT2 FLC were better than the two controllers. The robot path was smoother; the effect of uncertainties was removed completely.
The distance and time values approach the ideal values for obstacle- free navigation, which are 1000 pixels and 10 seconds.
It can be found that the results of the 20 pixel method is better than the results of the 50 pixel one. The small proximity range allows the robot to be closer to the obstacle than the large one.

26. Conclusions:
The OD IT2 FLC improved the control system performance compared with the ND IT2 FLC and T1 FLC systems.
Using smaller sensor pixel length has aided in making travel distance shorter.
Although the OD IT2 FLC consumes time longer than the normal one that only needs averaging the interval, but this is not a big problem when considering the high-speed microcontrollers that are widely used in this recent time for control systems.

27. Contact Ziyad Allawi + 964 770 270 6108 ziyad.allawi
twitter.com/ZiyadAllawi
facebook.com/ziyad.allawi.80

28. Thank You…