## 4 Conclusions  
In this paper, we have introduced an approach for solving the Inverse Kinematics of the robotic arm of TIAGo using methods based on supervised Deep Learning algorithms  
Figure 15: Motion capture markers as detected by the system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Joint Reached** & \multicolumn{2}{c}{**FK (Joint Reached)**} & **Motion Capture Pose** \\ \hline \(\theta_{1}\) & 1.3631 & **X** & \(-\)0.1580 & \(-\)0.2065 \\ \(\theta_{2}\) & 0.4002 & **Y** & 0.1290 & 0.0203 \\ \(\theta_{3}\) & \(-\)0.5982 & **Z** & 0.5530 & 0.5239 \\ \(\theta_{4}\) & 0.1362 & **x** & \(-\)0.0805 & 0.7464 \\ \(\theta_{5}\) & 0.732 & **y** & 0.3326 & \(-\)0.6497 \\ \(\theta_{6}\) & 0.3666 & **z** & \(-\)0.1420 & \(-\)0.1098 \\ \(\theta_{7}\) & 1.5844 & **w** & 0.9288 & \(-\)0.0922 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Example of the values extracted after the sim2 real experiment. Values are in meters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mean Position** & **Standard** & \
\begin{tabular}{c} **Mean** \\ **Orientation** \\ **Error** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline
**Error 1** & 0.000093 & 0.000061 & 1.3049 & 0.3609 \\
**Error 2** & 0.1382 & 0.0733 & 1.4296 & 0.2276 \\
**Global** & 0.1382 & 0.0733 & 1.2765 & 0.3430 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Final errors for sim2 real experiment. (MLP, CNN, and RNN) and putting the focus on static transformations, setting aside joint velocities or trajectories. The complete pipeline has been presented, including data generation and preprocessing, training, and validation. The effect of orientation representation and data normalization has been studied, and different DNN models have been built and evaluated. Finally, the effect of curriculum learning on the training scheme has been studied. The evaluation of different orientation representations highlights the impact of incorporating orientation as an input to the IK problem to achieve higher precision. Among the methods tested, the quaternion-based definition proved to be the most effective. This approach stands out because it creates fewer input parameters than rotation matrices, while still delivering robust results. These findings suggest that quaternions are a promising and efficient option to represent orientation in DNN-based IK applications. Based on the findings of this study, it is evident that data normalization appears to play a crucial role in improving the performance of DNNs applied to the IK problem. Various normalization techniques were tested, and the results suggest that preprocessing can be an essential step in the training pipeline. Among the techniques evaluated, robust scaling yielded the best results, performing similarly to max-absolute normalization. This suggests that robust scaling is an effective choice for IK data preprocessing, as datasets representing poses in Cartesian space and joint space positions are prone to contain outliers or varying feature scales. The testing of various models indicates that even small and simple architectures can achieve position and orientation errors comparable to those of larger models after sufficient training. Notably, Recurrent Neural Networks (RNNs) were among the best-performing models, as they are capable of capturing the temporal dependencies and relationships between joint movements. This ability to consider the sequential nature of joint interactions likely contributes to their superior performance in the IK problem. However, the best performing model consisted of a feed-forward neural network which explicitly takes into account the dependencies between joints by using a subnet to represent each one. The outputs of the preceding subnet are fed as an input for each of these along with the target position and orientation. These findings hint at the importance of joint dependencies for the IK problem.