## 5 Simulation Studies
### Results of Simulation Studies
In particular, the driving torques obtain high values all the time during turning, which is related to the lateral forces acting on the wheels for this type of kinematic structure of the robot. Therefore, the driving torques during turning have the greatest impact on energy consumption, as can be seen from the time histories of the electrical power for the robot's drive units (Figure 8f). Figure 7: Time histories of the desired motion parameters for cases 1 and 3.  
the pose controller, while minimizing pose errors, must modify the original values of the robot's desired generalized velocities, i.e., \({}^{\mathcal{O}}\!v_{Rd}\) (m/s) and \({}^{\mathcal{O}}\!\omega_{0 zd}\) (rad/s). The obtained time histories of wheel spin angular velocities (Figure 9c) are the result of many factors, including the operation of the wheels' controller and the pose controller, the properties of the drive units, and the occurring wheel slips. As for the issue of driving torques and electrical power for the robot's drive units, their time histories are similar to those obtained when only the wheels' controller is used (compare Figure 8e,f with Figure 9e,f). The key conclusion is, therefore, that adding a pose controller does not significantly affect the robot's energy efficiency. In the second stage of simulation studies, the influence of the wheel track \(W\) (m) on the accuracy of tracking control and energy efficiency was analyzed. As a consequence,  
Figure 9: Robot motion simulation results with wheels’ controller and pose controller for cases 1 and 3.  
the ratio of the wheel track to the distance of the front wheel axle from the rear wheel axle \(W/(2L)\) (-) is also analyzed. The research results at this stage are presented for the control system with the wheels' controller only in Table 2, and for the control system with an added pose controller in Table 3.  
In both cases, the results are presented in the form of quality indices obtained for various wheel track values and for the analyzed cases of the desired motion trajectories. In the case of the wheels' controller, changing the wheel track does not significantly affect the quality indices related to the wheel angular velocity errors, which reach slightly higher values for a larger wheel track (see Table 2). Increasing the wheel track, however, has a positive effect on the robot's pose errors, as can be seen from the quality indices associated with them--some of which decrease even twice. Increasing the wheel track also significantly reduces the maximum demand for electrical power of the drives, but the savings on the overall demand for electrical energy are not as large. This is due to the fact that the greatest demand for electrical power is when the robot is turning, when the greatest driving torques occur. Since turning is only one phase of the robot's movement, in general, it does not significantly affect the demand for electrical energy in the considered motion scenario. Partially similar conclusions as in the case of the research for the wheels' controller can be reached for the control system with an additional pose controller (see Table 3). In particular, it can be seen that the quality indices related to the errors of the angular velocities of the wheels, as well as the electrical power and the electrical energy of the drives, reach  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case No. **} & **W** & **W/(2L)** & **e\({}_{\text{unmax}}\)** & **E\({}_{\text{e}}\)** & **R\({}_{\text{demar}}\)** & **E\({}_{d}\)** & **R\({}_{\text{demar}}\)** & **E\({}_{\text{  
similar values (compare Tables 2 and 3). In turn, the quality indices related to pose errors change only slightly with the change in wheel track. However, when comparing the quality indices related to pose errors for the control system with the wheels' controller and with the additional pose controller, it can be noticed that, this time, they reach values lower by an order of magnitude.