## 4 Experimental Results
### Wall-Following Control of a Mobile Robot  
Reinforcement learning was used to achieve wall-following control of a mobile robot. A complex system need not be used to design the control rules of mobile robots. Figure 16 depicts the block diagram of the entire system. Only an appropriate fitness function should be defined to assess the effectiveness of mobile robots in a training setting. The IT2 FNN had four input signals (\(ps_{0}\), \(ps_{1}\), \(ps_{2}\), \(ps_{3}\)), and two output signals (\(V_{L}\), \(V_{R}\)). The input signal \(ps_{i}\) was the infrared sensing distance of the mobile robot, and the output signal was the turning speed of the left and right wheels of the mobile robot. Straight lines, right angles, smooth curves, and U-shaped curves were set as the training setting to verify the response of the mobile robot to various situations in uncertain environments. The size of the training setting was 2.1 (m) \(\times\) 2 (m), as depicted in Figure 17.  
Three termination conditions were set for the mobile robot to ensure wall-following without collision or moving away from walls during the experiment. 1. The mobile robot moves more distance in the training setting than the distance of a circle around the training setting (only one circle of the training setting), indicating that the mobile robot successfully circled the training setting. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fitness**} & **Algorithm** & \multirow{2}{*}{**DGCPSO**} & **DE [24]** & **PSO [25]** & **QPSO [26]** & **CPSO [27]** \\ \hline Best & 0.990 & 0.987 & 0.981 & 0.984 & 0.983 \\ Worst & 0.987 & 0.979 & 0.962 & 0.960 & 0.952 \\ Average & 0.984 & 0.980 & 0.973 & 0.974 & 0.972 \\ SD & 0.004 & 0.006 & 0.005 & 0.006 & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Chaotic time-series performance of various algorithms. Figure 16: Block diagram of the system. Figure 15: Results after adding noise for (**a**) Type-1 and (**b**) Type-2. 2. One sensor of the mobile robot measures a distance of less than 1 cm. Figure 18a illustrates a collision between the mobile robot and the wall. 3. A sensor \(S_{2}\) to the side of the mobile robot detects a distance greater than 6 cm, indicating that the mobile robot has deviated from the wall, as depicted in Figure 18b. Each individual represents a solution of an IT2 FNN controller, and the controller controls the mobile robot to achieve the wall-following movement in the training setting. After movement, the mobile robot is returned to the initial position. The robot repeats this movement until it reaches a termination condition. The fitness function was used to assess the effectiveness of the mobile robot in the learning process. The fitness function has three subfitness parameters, namely the total distance the mobile robot moved (\(SF_{1}\)), the distance the mobile robot maintained from the wall (\(SF_{2}\)), and the degree of parallelism between the mobile robot and the wall (\(SF_{3}\)). 1. Total distance the mobile robot moved: The closer the moving distance \(R_{dis}\) of the mobile robot is to the predefined value \(R_{stop}\), the closer the mobile robot is to completing one circle around the training setting. \[SF_{1}=R_{stop}-R_{dis}\] (23) If \(R_{dis}>R_{stop}\), then the mobile robot successfully circumvents the training setting under all conditions. If \(R_{stop}=R_{dis}\), then the fitness function \(SF_{1}\) is zero. 2. The distance the mobile robot maintained from the wall: The fitness function \(SF_{2}\) is the average value of \(WD(t)\) during the moving time. The aim is to maintain a fixed distance between the mobile robot and the wall. In each time step, the distance \(WD(t)\) between the side of the mobile robot and the wall is calculated as follows: \[WD(t)=\left|S_{2}(t)-d_{wall}\right|\] (24)  
Figure 17: Training setting for wall-following control. Figure 18: (**a**) Collision between the mobile robot and the wall; (**b**) the mobile robot deviated wall.