## 5 Results  
### Local Models and PI Controllers  
Initially, a code for open-loop tests was implemented in the ESP32 microcontroller code with the purpose of performing data acquisition for the entire PWM range applied to the motor input. Figures 11 and 12 present the acquired data and the validation of the models obtained for ranges from 30% to 100% for the PWM of the right and left wheel motors, respectively, in the positive direction of the trajectory: that is, considering that the robot is moving forward. It is noted that the motors are coupled to the wheels, and in the positive direction, they have an open-  
Figure 15 shows the behavior of the time constant: that is, its evolution for each operating range of the mathematical models that were obtained to implement the controllers in this work. In this way, an adaptive control by gain scheduling and a fuzzy multimodel intelligent control were used so that the speeds of the robots' wheels tracked a certain reference, allowing the robot to track a certain trajectory. To achieve this, the adjustments of each local controller occur according to the speeds of the motors for each PWM range.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{6}{c}{**Positive Direction**} \\ \hline
**PWM Step (\%)** & **RW Model** & **Kp** & **Ki** & **LW Model** & **Kp** & **Ki** \\ \hline
30 & \(\frac{13.70}{0.74s+1}\) & 0.754 & 4.85 & \(\frac{15.84}{0.73s+1}\) & 0.643 & 4.14 \\
40 & \(\frac{16.12}{0.53s+1}\) & 0.446 & 2.98 & \(\frac{16.64}{0.47s+1}\) & 0.377 & 2.56 \\
50 & \(\frac{15.94}{0.42s+1}\) & 0.340 & 2.36 & \(\frac{15.84}{0.39s+1}\) & 0.313 & 2.20 \\
60 & \(\frac{14.94}{0.34s+1}\) & 0.280 & 2.04 & \(\frac{14.96}{0.33s+1}\) & 0.269 & 1.97 \\
70 & \(\frac{13.79}{0.29s+1}\) & 0.248 & 1.88 & \(\frac{13.60}{0.28s+1}\) & 0.240 & 1.84 \\
80 & \(\frac{12.69}{0.24s+1}\) & 0.215 & 1.72 & \(\frac{12.39}{0.23s+1}\) & 0.208 & 1.69 \\
90 & \(\frac{11.70}{0.21s+1}\) & 0.194 & 1.64 & \(\frac{11.29}{0.21s+1}\) & 0.194 & 1.66 \\
100 & \(\frac{11.12}{0.18s+1}\) & 0.156 & 1.44 & \(\frac{10.69}{0.17s+1}\) & 0.147 & 1.41 \\ \hline \multicolumn{6}{c}{**Negative Direction**} \\ \hline
**PWM Step (\%)** & **RW Model** & **Kp** & **Ki** & **LW Model** & **Kp** & **Ki** \\ \hline
30 & \(\frac{15.54}{0.67s+1}\) & 0.680 & 3.19 & \(\frac{14.29}{0.70s+1}\) & 0.643 & 3.62 \\
40 & \(\frac{16.62}{0.47s+1}\) & 0.377 & 2.11 & \(\frac{16.43}{0.49s+1}\) & 0.400 & 2.22 \\
50 & \(\frac{15.81}{0.37s+1}\) & 0.2 Table 2 represents the speed of each operating point, which is used in the selection structures and was obtained through tachometer measurements.  
The work was carried out in two stages: the first in a Simulink environment--a tool for modeling, simulating, and analyzing dynamic systems. Using the models and controllers developed and validated in the simulation environment, the second stage carried out a practical application on the robots.  
The following subsections describe the responses obtained in the practical application. The results aim to represent the robot's response to different speed references applied to it as well as the control signals applied to the motors. Various system performance criteria are adopted to define the best strategy to be employed.  
Throughout the results, positive and negative references are depicted to represent the robot's movement. In Figure 1, a positive reference corresponds to the robot's forward movement towards the ball, while a negative reference represents its backward movement in the opposite direction of the ball. Furthermore, when performing an analysis between the results, it is observed that the control signals for the left and right wheels sometimes differ significantly. This occurs due to the presence of gearboxes in the motors, which demand higher control signals for the right wheel.