## 5 Verification Tests of the Control Algorithm
### Verification Test 2 (Intelligent Control)  
The arrangement of the graphs showing the waveforms of individual motion parameters, errors, and control signals in Figure 10 corresponds to that in Figure 9. Additionally, Figure 10 shows the waveforms of the control signals generated by the NN (Figure 10f) and the waveforms of the total control signals (Figure 10g). The waveforms of the NN output weights are presented for the first wheel in Figure 10h. The diagram of the desired and implemented motion path is shown in Figure 10i. The waveforms of the realized motion parameters and control signals presented in Figure 10 had a shape similar to the waveforms obtained in the simulation tests. The tracking error values were slightly higher, which was confirmed by the values of the determined quality indicators. It may have been a result of the occurrence of unmodeled phenomena and disturbances during motion. The tracking errors were the highest in the initial phase of the movement, and then they were minimized to a range close to zero, which resulted from the presence of an adaptive element in the control system in the form of an NN. Such a phenomenon did not occur when only the PD controller had been used in the control system, as in Verification Test 1. The values of the NN weights from zero initial values changed their values during the adaptation process and stabilized at certain values. The comparison of the desired and realized trajectory of the selected WMR point indicated the high accuracy of the tracking and mapping of the desired trajectory. The quality indicators obtained as a result of the verification are presented in Table 4.  
The values of the quality indicators obtained during verification with the use of the neural control algorithm indicated significantly improved accuracy of the tracking, as compared to the use of the PD controller alone. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Indicator** & **e\({}_{\text{max}}\) [rad]** & \(\hat{\textbf{e}}_{\text{max}}\) [rad/s] & \(\varepsilon_{\text{i}}\) [rad] & \(\hat{\textbf{\emph{i}}}_{\text{i}}\) [rad/s] & \(\textbf{d}_{\text{max}}\) [m] & \(\textbf{d}_{\text{n}}\) [m] & \(\rho\) \\ \hline wheel 1, i = 1 & 0.7718 & 4.1174 & 0.1371 & 0.3763 & & & \\ wheel 2, i = 2 & 0.7149 & 3.8033 & 0.2099 & 0.4677 & & & \\ wheel 3, i = 3 & 0.9735 & 4.8162 & 0.1834 & 0.4891 & 0.0846 & 0.0319 & 0.0278 \\ wheel 4, i = 4 & 1.1244 & 4.0510 & 0.2383 & 0.4718 & & & \\ mean value & 0.8961 & 4.1970 & 0.1922 & 0.4512 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Quality indicators for neural control verification. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Indicator** & **e\({}_{\text{max}}\) [rad]** & \(\hat{\textbf{e}}_{\text{max}}\) [rad/s] & \(\varepsilon_{\text{i}}\) [rad] & \(\hat{\textbf{\emph{i}}}_{\text{i}}\) [rad/s] & \(\textbf{d}_{\text{max}}\) [m] & \(\textbf{d}_{\text{n}}\) [m] & \(\rho\) \\ \hline wheel 1, i = 1 & 5.1201 & 3.1432 & 2.8616 & 1.3841 & & & \\ wheel 2, i = 2 & 4.6355 & 3.0982 & 2.1873 & 1.4994 & & & \\ wheel 3, i = 3 & 4.6579 & 3.0943 & 2.1949 & 1.4994 & 0.3751 & 0.0124 & 0.2606 \\ wheel 4, i = 4 & 5.1606 & 3.2050 & 2.8842 & 1.3841 & & & \\ mean value & 4.8935 & 3.1352 & 2.5320 & 1.4380 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quality indicators for PD control verification.