## 4 Results
### Validation of the Omnidirectional and Translation Capabilities
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multirow{2}{*}{
\begin{tabular}{c} **Motion Command** \\ **(\(v\),\(\alpha\),\(\omega\),\(t\)) (m/s\({}^{\circ}\),rad/s,s)** \\ \end{tabular} } & \multicolumn{2}{c}{**Motion Required**} & \multicolumn{2}{c}{**Final Position**} \\ \cline{2-5}  & & **Translation** & **Rotation** & **(\(x_{f},y_{f},\theta_{f}\)) (\(m\),\(m\),\({}^{\circ}\))** \\ \hline E1 & \((0.1,0,0,10)\) & X & - & \((1,0,0)\) \\ E2 & \((0.1,90,0,10)\) & X & - & \((0,1,0)\) \\ E3 & \((0.1,45,0,14.14)\) & X & - & \((1,1,0)\) \\ E4 & \((0.1,0,0.15,14)\) & X & X & \((0.58,1.00,120.32)\) \\ E5 & \((0.1,90,-0.15,14)\) & X & X & \((1.00,0.58,-120.32)\) \\ E6 & \((0,0,0.15,10.5)\) & - & X & \((0,0,90.24)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Definition of the motion commands used in the validation experiments. Figure 6: Trajectories of the motion commands defined in Table 7. Yellow circles represent the final positions of the platform after implementing each motion, and blue lines represent the final orientation of the platform. The green circles and the red lines depict intermediate positions of the mobile platform along the trajectory simulated. defined in Table 7 and Figure 6. The result of each validation experiment is labeled as OK in the case where the final position reached by the mobile platform differs less than 0.01 m from the expected destination, and as FAILED if it differs more. Additionally, Tables 8 and 9 provide a summary of the trajectories simulated. In these images, a yellow circle depicts that the mobile platform has reached the expected final position within the distance threshold of 0.01 m while an empty circle depicts that the final position has not been reached. The parameter OMD summarizes the omnidirectional capabilities of the mobile platform obtained by simulation: labeled as YES in the case that the mobile platform is able to successfully execute all trajectories requiring a rotation (E4, E5, and E6), and NO otherwise. Similarly, the parameter T summarizes the translational capabilities of each mobile platform: labeled as YES in the case that the mobile platform is able to successfully execute all trajectories requiring only translation (E1, E2, and E3), and NO otherwise. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Platform**} & \multicolumn{6}{c}{**Experiment (Type of Motion Required)**} & \multicolumn{6}{c}{**Summary of the Simulations**} \\ \cline{2-10}  & **E1 (T)** & **E2 (T)** & **E3 (T)** & **E4 (T+R)** & **E5 (T+R)** & **E6 (R)** & **OMD** & **T** & Trajectories \\ \hline
3A & & & & & & & & & \\
1A-2B & & & & & & & & & \\
1A-2C & & & & & & & & & \\
1A-1B-1C & & & & & & & & & \\
1A-1B-1D & & & & & & & & & \\
3E & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the validation experiments of the mobile platforms identified as omnidirectional. OK means that the trajectory has been successfully executed by the platform (it has arrived at the planned destination). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Platform**} & \multicolumn{6}{c}{**Experiment (Type of Motion Required)**} & \multicolumn{6}{c}{**Summary of the Simulations**} \\ \cline{2-10}  & **E1 (T)** & **E2 (T)** & **E3 (T)** & **E4 (T+R)** & **E5 (T+R)** & **E6 (R)** & **OMD** & **T** & Trajectories \\ \hline
3B & & & & & & & & & \\
0K & OK & OK & FAILED & FAILED & FAILED  
The simulation results displayed in Table 8 show that the mobile platforms identified as omnidirectional by the procedure proposed in this paper are able to execute successfully all the validation trajectories. Alternatively, the simulation results displayed in Table 9 show that the mobile platforms identified as non-omnidirectional are not able to execute successfully all the validation trajectories.