## 4 Results
### Validation of the Omnidirectional and Translation Capabilities  
This section presents the experiments conducted to validate the application of the procedure proposed for estimating the omnidirectional and translational capabilities of the mobile platforms described in Table 1. This validation is based on the simulation of the motion of the different omnidirectional platforms assessed. The simulator used in the paper is described in [50]. The simulator uses the information of the configuration of the wheels of the platform and the target velocity assigned to each wheel to compute the trajectory and displacement of the mobile platform. The simulator is limited to indoor conditions and no wheel slippage. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Configuration**} & \multirow{2}{*}{**Representation**} & \multicolumn{2}{c}{**Omnidirectional**} & \multicolumn{2}{c}{**Proposed Procedure**} \\ \cline{3-6}  & & **Rank (J), Full** & **[PERSON] et al. [17]** & **Omnidirectional** & **Translation** \\ \hline
3A & YES & YES & YES & YES & YES \\ \hline
1A-2B & YES & YES & YES & YES & YES \\ \hline
1A-2C & YES & YES & YES & YES & YES \\ \hline
1A-1B-1C & YES & YES & YES & YES & YES \\ \hline
1A-1B-1D & YES & YES & YES & YES & YES \\ \hline
3E & YES & YES & YES & YES & YES \\ \hline
3B & YES & NO & NO & NO & YES \\ \hline
2A-1B & YES & NO & NO & NO & NO \\ \hline
1B-2C & YES & NO & NO & NO & NO \\ \hline
1B-2D & YES & NO & NO & NO & NO \\ \hline
1A-2D & NO & NO & NO & NO & NO \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparative analysis of the omnidirectional capabilities of the platforms obtained with two state-of-the-art methods and the omnidirectional and translation capabilities obtained with the procedure proposed in this paper. The validation experiments consist of the definition of a set of trajectories and on the implementation of these trajectories by the mobile platforms assessed. The execution of the motion defined in these trajectories requires a combination of translation and rotation capabilities in the mobile platform. Table 7 details the experiments, the target motion command applied to each mobile platform, the translation or rotation capabilities required to execute the motion, and the expected final position of the platform after the motion \((x_{f},y_{f},\theta_{f})\). In all these experiments, the initial position of the mobile platform in the simulation \((x_{i},y_{i},\theta_{i})\) is the same: (0 m, 0 m, 0\({}^{\circ}\)). The last parameter \(t\) of the motion command \((v,\alpha,\omega,t)\) is the time defined to execute the motion in order to reach the final position of the motion \((x_{f},y_{f},\theta_{f})\). Additionally, Figure 6 shows the expected trajectory that must follow the mobile platform in case of executing the motion commands defined in Table 7. Trajectories E1 and E2 only require translational capabilities in the \(x_{s}\) and \(y_{s}\) axes of the world frame. Trajectory E3 requires a combination of translational capabilities in both axes in the world frame. Trajectories E4 and E5 require translation and rotation capabilities. Finally, trajectory E6 only requires rotation capabilities as it depicts a single rotation of approximately 90\({}^{\circ}\) to the left side of the mobile platform. Tables 8 and 9 summarize the results of the simulation experiments performed with all the mobile platforms assessed. Table 8 shows the results of the mobile platforms identified as omnidirectional in the previous analysis (provided in Table 6), while Table 9 shows the results of the mobile platforms identified as non-omnidirectional. Both tables show a CAD design of the mobile platform and the evaluation of the validation experiments