# Gaze-Guided Control of an Autonomous Mobile Robot Using Type-2 Fuzzy Logic
## 2 Method of Gaze Guided System
### Interval Type2 Fuzzy Control System
#### 2.3.3 Type Reducer  
Type reducer creates a type-1 fuzzy set output which is then transformed into a crisp output through the defuzzifier that combines the outputs sets to acquire a single output using one of the existing type reduction methods. Type reducer was proposed by [PERSON] and [PERSON] [32; 34; 55]. In our experiments, we used the center of sets (cos) type reduction method. The expression of this method can be written in the following Equation (6).  
\[Y_{cos}(x)=[y_{l},\ y_{r}]=\int_{y^{1}\in[y_{l}^{1},y_{l}^{.1}]}\cdots\int_{y^ {1}\in[y_{l}^{M},y_{l}^{.M}]}\int_{f^{1}\in[f^{1},\bar{f}^{1}]}\cdots\int_{f^{ M}\in[f^{M},\bar{f}^{M}]}\Big{/}\frac{\sum_{i=1}^{M}f^{i}y^{i}}{\sum_{i=1}^{M}f^{i}}. \tag{6}\]  
The consequent set of the interval type-2 determined by two endpoints (\(y_{l},\ y_{r}\)). If the values of \(f_{i}\) and \(y_{i}\), which are associated with \(y_{l}\), are donated \(f^{i}\) and \(y_{l}^{i}\), respectively, and the values of \(f_{i}\) and \(y_{i}\) which are associated with \(y_{r}\) are donated \(f_{i}^{i}\) and \(y_{r}^{i}\) respectively, these points are given in Equations (7) and (8).  
\[y_{l}=\frac{\sum_{i=1}^{M}f^{i}y_{l}^{the simulation of the robot's initial and goal points is illustrated and robot motion data on this behavior is also shown in Table 3.  
The outcomes of the experiment and simulation are illustrated graphically and plotted separately to elucidate the effect of gaze based on the fuzzy type-2 rule set in Figures 14-19. In Table 3, it can be seen that robot wheel speeds are change according to the gaze coordinates. In this table, there are only a few examples. The details of these data are shown graphically below in Figures 15, 17, and 18. Various scenarios were performed to test the proposed method in a real environment. The experimental setup is shown in Figures 14 and 16. The adaptability, robustness, accuracy and efficiency of the proposed methods can be observed from these experimental results. The real experimental environment is shown in Figures 14 and 16. It includes the robot, obstacle and target token. Here are six different frames obtained from the experimental environment. The eye gaze data coordinates, robot path coordinates, and robot wheel speed are stored during the movement of the robot and this data is graphically illustrated. The affection of the relationship between robot speed and gaze point is illustrated in Figure 18. The effectiveness of the fuzzy rules and suitability of the fuzzy controller on collision-free behavior is shown in Figure 19.  
the robot is moving smoothly and without colliding. The real experimentation of this scenario is illustrated in Figure 14. The eye gaze coordination for this scenario is shown in Figure 15.  
In the second scenario, the user has directed the robot to the left side with the eye movements. It was seen that the mobile robot behaved similarly to its first scenario. The real experimental results are shown in Figure 16. The plot of this scenario is shown in Figure 17. The objective of this driving is to confirm the efficacy of the method in different cases. As can be seen from this case, the mobile robot navigates successfully around the obstacles without collision and reach the target.  
Figure 16: Experiment setup; 2. Scenario—robot motion control from start (1) and goal (6) position.  
Figure 14: Experimental setup; 1. Scenario—robot motion control from start (1) and goal (6) position.  
Figure 15: Eye gaze coordination for 1. Scenario (Figure 13) (2D line graph (**a**), scattered (**b**)).