## 4 Discussion and Conclusions  
This paper proposes a general procedure to evaluate and correct the systematic odometry errors of a real three-wheeled omnidirectional mobile robot (1.760 m, 30 kg) designed as a versatile personal assistant tool. This procedure is based on the definition of 36 representative straight and curved calibration trajectories which together depict a characteristic flower-shaped figure.  
The odometry and ground truth trajectories measured while performing each one of these calibration trajectories are measured and registered for later offline fitting of the kinematic parameters of the mobile robot in order to match these two trajectories. This paper has evaluated the use of different trajectory subsets and the use of two iterative matching strategies based on gradient search minimization and genetic algorithms. The best matching between odometry and ground truth trajectories has been obtained using genetic algorithms and five repetitions of all calibration trajectories. The fitting of the kinematic parameters has shown differences higher than 10% in the distance from the wheels to the center of the mobile robot \((R_{a},R_{b},R_{c})\), and between 2 and 5% in the radii of the wheels \((r_{a},r_{b},r_{c})\). This approach has the advantage of the feasible physical interpretation of the fitting results in the omnidirectional mobile robot.  
The fitting results have been validated with five new additional repetitions of all these measured trajectories, providing an average improvement of 82% in the evaluation of the multivariable cost function that compares the final position and orientation of the mobile robot. The best performances of the genetic algorithm agree with the results of [PERSON] et al. [15], and confirm that the mutation and combinations generated during the search based on genetic algorithms has the best chance to detect the global minimum of the multivariate function that summarizes the differences between the odometry and ground truth trajectories of the mobile robot. In this case, the genetic algorithm search (strategy STE-GA5) required 187 iterations and 37.545 function counts to meet the stopping criteria.  
The final conclusion of the comparative calibration analysis performed in this work is that the use of curved calibration trajectories is more representative to calibrate the  
Figure 10: Planned trajectory (back dotted line) zoomed at the planned ending position and orientation of the mobile robot (black point and line); measured ground truth trajectories (orange dotted line) detailing the final position and orientation of the mobile robot (orange circle and line); and odometry trajectories measured after calibration (green dotted line) detailing the ending position and orientation of the mobile robot (green circle and line).  
kinematic parameters of an omnidirectional mobile robot. This conclusion agrees with [PERSON] et al. [17], who proposed the use of four curved trajectories for general omnidirectional mobile robot calibration, and with [PERSON] et al. [11], who concluded that the performance of a calibration procedure depends on the type of trajectory analyzed.  
Future works will analyze the application of this procedure to different units of the same mobile robot type in order to validate its application in a general manufacturing stage.  
Conceptualization, J.P.; Investigation, E.R. and E.C.; Methodology, J.P. and E.R.; Software, E.C.; Writing--original draft, E.R.; Writing--review & editing, J.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare that they have no conflict of interest.  
[TABLE:A1.T1][ENDT  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Trajectory**} & \multicolumn{4}{c}{**Motion Command**} & \multicolumn{4}{c}{**Target Angular Velocities (tpm)**} \\ \cline{2-7}  & \(\mathbf{v}\) **(m/s)** & \(\mathbf{a}\)(\({}^{*}\)) & \(\mathbf{\omega}\)**(rad/s)** & \(\mathbf{d}\)**(m)** &