## 4 Results and Discussion
In addition, the results in Figure 9b show the error in the rotational motion made by the AGV throughout the motion. According to these results, a maximum error of 0.06 rad was observed in the rotational motion along the entire route, and the average rotational error of the AGV is calculated to be 0.0228 rad. According to these results, it can be said that the AGV successfully follows the reference route both in translation and rotation with little error. These results can also be supported by linear velocities in the x and y directions. Figure 9c,d show the time variation of the instantaneous and reference linear velocities of the AGV in the x and y directions for the movement along the spiral route. As can be seen from the figures, errors are reduced in following the reference linear velocities calculated based on the reference orbit. Another indicator of successful tracking performance and the power consumed while achieving this tracking performance is the angular rotational speed of the wheels. The angular rotational speeds of the wheels are obtained by feeding DC motors from DC/DC converters. These voltage values are determined by the optimal PID controllers calculated by Optimizer-1, which provides angular velocity-based route control, and are obtained from the outputs of DC/DC converters, similar to reference voltages as much as possible, in line with the optimal parameters determined by Optimizer-2. For this reason, it is very important for low power consumption and successful path-tracking performance that the errors in the changes in the angular velocity of the wheels are low because these angular velocities sent to the wheels via the motors are determined by both optimizers on the basis of the lowest possible power consumption and maximum track performance. Figure 10 shows the reference angular velocities for all four Mecanum  
Figure 9: (**a**) The translational motion errors of the AGV at X and Y axis during the spiral path. (**b**) The rotational motion error of the AGV. (**c**) The reference and actual linear velocity of the AGV along X axis. (**d**) The reference and actual linear velocity of the AGV along Y axis. wheels, the instantaneous angular velocities of the AGV wheels along the route and the errors between these two speeds. The results show that the actual angular velocities shown with the red line successfully follow the reference angular velocities shown with the blue line for all four wheels. The variable structure observed in the instantaneous angular velocities in the figures is due to the voltage values from the DC/DC converters and the generation of these instantaneous wheel speeds because DC/DC buck converters use switching while reducing the high voltage value from the fuel cell to the specified reference voltage value, and this switching is performed with the PWM signal with a switching frequency (f\({}_{\text{s}}\) = 10,000 Hz). Therefore, the reference angular velocity values have a flatter variation as calculated with kinematic equations, while the actual velocity values have more noise-like additives. When the results are examined, it is observed that the errors in wheel angular velocities generally vary between +0.02 and \(-\)0.02 rad/s for each wheel. In addition, when the average angular velocity errors are calculated for each wheel during the movement, it is seen that the values of 2.6578 \(\times\) 10\({}^{-5}\), 6.7423 \(\times\) 10\({}^{-5}\), 6.9445 \(\times\) 10\({}^{-4}\) and 2.6578 \(\times\) 10\({}^{-5}\) rad/s are obtained for each wheel. These results show that the developed control strategies both improve route-tracking performance and reduce power consumption as much as possible, and this is successfully implemented by the entire system. In the previous figure, the importance of the voltage-tracking performance of the DC/DC converter is mentioned. The reference voltages from the PID controllers that control the trajectory tracking are provided by DC/DC converters by reducing the high voltage from the fuel cell, which is the system supply.