## 5 Experimental Verification
### Offset Running  
When the IRW enters the steady convergent process, the dynamic oscillations are suppressed by the yaw suspensions, and the IRW only presents offset running, as described by Equations (45)-(47) in Section 2.5. Here, we applied some instantaneous lateral disturbances in sequence on the traction plate. The process of each disturbance input is shown in Figure 30.  
Considering the IRW being installed on an IRW bogie, the traction plate shown in Figures 22d and 30 can be regarded as the \"bogie frame\". When disturbance force is applied on the bogie frame, the bogie's heading angle will change, leading to yaw angle variations in the IRW. Because of the relation between the longitudinal creep forces and the yaw angular velocity \(\dot{\psi}\) of the IRW in the wheel rotational direction, as demonstrated in Equations (30) and (31) in Section 2.4, the rotational angular accelerations of the two wheels, \(\dot{\omega}_{\mathrm{L}}\) and \(\dot{\omega}_{\mathrm{R}}\), will change. When the disturbance force is removed, because the longitudinal creep forces also relate to the lateral displacement \(y\), the rotational speeds of the two wheels will continuously vary with \(y\). The regulation law can be inferred as follows  
Figure 30: Apply instantaneous lateral disturbance force after the IRW enters the steady convergent process. (**a**) Before disturbance; (**b**) under disturbance; (**c**) after disturbance. Figure 29: Experiment results of the IRW with yaw suspensions at average rotational speed \(620\ \mathrm{r}/\mathrm{min}\). (**a**) Lateral displacement; (**b**) yaw angle; (**c**) differential wheel rotational speed; (**d**) \(y-\psi\) phase diagram. \[\left\{ \begin{array}{l}y\uparrow,\dot{\omega}_{\rm L}>0,\dot{\omega}_{\rm R}<0, \omega_{\rm L}\uparrow,\omega_{\rm R}\downarrow\\ y\downarrow,\dot{\omega}_{\rm L}<0,\dot{\omega}_{\rm R}>0,\omega_{\rm L} \downarrow,\omega_{\rm R}\uparrow\end{array} \right. \tag{49}\]  
Then, the IRW will eventually reach another steady state with another \((y,\omega_{\rm L},\omega_{\rm R})\). As shown in Figure 31, several instantaneous lateral disturbances act on the IRW every 10 s. Because the disturbances are instantaneous and the longitudinal creep forces vary simultaneously, the whole stabilization process is too short to be detected in detail. The lateral displacement \(y\) and the differential wheel rotational speed \(\Delta\omega\) both change after each disturbance, and almost remain unchanged during the intervals of the adjacent two disturbance inputs. The yaw angle sensor is installed on the yaw joint shown in Figures 22a and 30, so only the yaw angle to the traction plate can be measured. Under the suppression effects of the yaw suspensions, the yaw angle to the traction plate is almost unchanged during the stabilization process of each disturbance. That is why the curve of \(\psi\) in Figure 31 stays around \(0^{\circ}\) just with the sensor noise during the 120 s experiment. The average lateral displacement \(y\) and average differential wheel rotational speed \(\Delta\omega\) can be calculated in every interval of the adjacent two disturbances. The linear regression results of these data points are demonstrated in Figure 32, which shows a positive linear relation between \(\Delta\omega\) and \(y\). According to Equation (47) in Section 2.5, the theoretical slope of this line is 301.1, which means that the relative error is 9.4%. These experimental results also demonstrate that the IRW should have many steady states, which shows the exact characteristic of the offset running. That is, after the oscillation has been suppressed, the states on the straight line described by Equation (47) all become steady states. They finally converge to 0, but the steady convergent process is too long in practice, which means they can be treated as steady states and lead to the IRW's offset running. These features are in accordance with the analysis in Section 2.5 and previous simulation results in Section 4.2.