## 4 Conclusions  
In this paper, different learning methods based on Artificial Neural Networks (ANNs) have been examined to replace the default speed controller for high-precision position control and drift attenuation in robotic manipulators. ANN learning methods including Levenberg-Marquardt and Bayesian Regression have been implemented and compared using a UR5 robot with six degrees of freedom to improve the trajectory tracking and minimize the position error. Extensive simulation and experimental tests on the identification and control of the robot by means of the neural network controllers yielded comparable results with respect to the classical controller, showing the feasibility of the proposed approach. It can be noted that while we have not achieved improvement in the positional accuracy of the TCP using the NN-based control, the strength of the proposed approach lies rather in the power of generalization and adaptation. As the kinematic parameters of individual robot arms vary ever so slightly between different units, we expect the NN controller to compensate for these differences and perform without the need for tuning which \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{3}{c}{**Controller**} \\ \hline  & **PID** & **BR** & **LM** \\ \hline \(q_{1}\) & 0.0197 & 0.0221 & 0.0291 \\ \hline \(q_{2}\) & 0.0121 & 0.0177 & 0.0171 \\ \hline \(q_{3}\) & 0.0154 & 0.0213 & 0.0165 \\ \hline \(q_{4}\) & 0.0036 & 0.0051 & 0.0038 \\ \hline \(q_{5}\) & \(3.16\times 10^{-5}\) & \(5.72\times 10^{-5}\) & \(2.83\times 10^{-4}\) \\ \hline \(q_{6}\) & 0.0197 & 0.0225 & 0.0288 \\ \hline mean & 0.0117 & 0.0148 & 0.0159 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE of the position tracking for the compared controllers (in rad). \begin{table}
\begin{tabular}{l c c c} \hline \hline  & \multicolumn{3}{c}{**Controller**} \\ \hline  & **PID** & **BR** & **LM** \\ \hline \(\dot{q}_{1}\) & 0.0593 & 0.0597 & 0.0984 \\ \hline \(\dot{q}_{2}\) & 0.0398 & 0.0400 & 0.0505 \\ \hline \(\dot{q}_{3}\) & 0.0446 & 0.0413 & 0.0550 \\ \hline \(\dot{q}_{4}\) & 0.0135 & 0.0167 & 0.0175 \\ \hline \(\dot{q}_{5}\) & \(8 could be the case with the classical control scheme. We admit that such generalization can only be achieved with a large enough dataset, which will be our focus in our further work. We had noted no technical difficulties of implementing the ANN controller even in the prototype configuration based on Matlab. The implementation was able to match the hardware robot control cycle frequency of 125 Hz without issue. We expect that a more optimized implementation based on a performance-focused software platform will perform even better. However, further experiments are necessary to attest that the proposed control scheme will work well enough for the new versions of the UR robots incorporating a 500 Hz control cycle. In the future, we plan to compare the results of our approach with alternative models, as for instance, machine learning using classical methods. We will also investigate the possibility of applying ANN control to more complex robotics applications, as for instance in real collaborative tasks [28]. Furthermore, ANN control will be applied to address complex structural vibration problems in the case of lightweight and flexible robotic arms. Conceptualization, A.M.; methodology, A.W., A.M., L.S. and N.K. ; software, A.W. and N.K. ; validation, A.M., A.W. and M.S. ; formal analysis, A.M. and A.W. ; investigation, A.M., A.W., N.K. and L.S. ; resources, M.S. ; data curation, N.K. ; writing--original draft preparation, N.K. ; writing--review and editing, A.M., A.W. and L.S. ; visualization, N.K., A.M., A.W. and M.S. ; supervision, A.M. and L.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. This research was supported by the Bialystok University of Technology project (no: WZ/WE-IA/4/2023) financed by a subsidy provided by the Ministry of Science and Higher Education and by National Science Centre in Poland, grant No.