# BIZON-UGV for Airport Pavement Testing: Mechanics and Control
## 3 Modelling and Control
### Experiment and Measurement
\begin{bmatrix}0&0&0&0&0\end{bmatrix} ^{T}\) and \(\dot{\mathbf{q}}(0)= \begin{bmatrix}0&0&0&0\end{bmatrix} ^{T}\). At each waypoint, the initials were zeroing the whole tracking process. Results of numerical simulations are presented in Figure 12. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Point nr.**} & \multicolumn{2}{c}{**Geographic Coordinates**} & \multicolumn{2}{c}{**Distance between Points [m]**} & \multicolumn{1}{c}{**Heading Angle**} \\ \cline{2-5}  & **Latitude** & **Longitude** & **Points [m]** & [\({}^{\circ}\)] \\ \hline
1 & \(52^{\circ}26^{\circ}59.461^{\prime\prime}\) N & \(20^{\circ}40^{\prime}25.917^{\prime\prime}\) E & - & 63.2 \\ \hline
2 & \(52^{\circ}27^{\prime}0.2500^{\prime\prime}\) N & \(20^{\circ}40^{\prime}28.467^{\prime\prime}\) E & 54.4 & 151.0 \\ \hline
3 & \(52^{\circ}26^{\circ}59.449^{\prime\prime}\) N & \(20^{\circ}40^{\prime}29.201^{\prime\prime}\) E & 28.6 & 248.6 \\ \hline
4 & \(52^{\circ}26^{\circ}58.849^{\prime\prime}\) N & \(20^{\circ}40^{\prime}26.691^{\prime\prime}\) E & 51.0 & 140.7 \\ \hline
5 & \(52^{\circ}26^{\circ}58.446^{\prime\prime}\) N & \(20^{\circ}40^{\prime}27.240^{\prime\prime}\) E & 16.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Trajectory coordinates. Figure 11: Reference waypoint trajectory: (**a**) view with numbered waypoints, (**b**) zoomed-in view. The mobile platform realized the defined waypoint trajectory, shown in Figure 11, with the desired cruise speed of 5 km/h. The tightening function was also activated to compare with classic PID-FF control. Figure 13 shows the trajectory performance of the UGV when the tightening function was deactivated. The numbers denote following trajectory waypoints. Figure 14 shows the realized waypoint trajectory by UGV with an activated tightening function. Figure 12: Simulation result of performed trajectory. Figure 13: UGV trajectory without tightening (red line—reference path, black line—platform path). Realized cases can be compared and shown in one common picture for a better view. Figure 15 presents the two cases: PID-FF and PID-FF with activated tightening function. The difference is clearly visible and similarly as in Figure 13, numbers denote following trajectory waypoints. The PID-FF (proportional-integral-derivative with feedforward)-based control algorithm enables the unmanned ground vehicle (UGV) to accurately follow a path delineated by a series of trajectory points, herein referred to as waypoints. This way, the course path consists of line sections that connect indicated waypoints. Hence, based on the current platform position, the platform moves to the destination point (waypoint) with the desired driving course obtained from heading angle computation. This means that as a result, the platform does not realize the course by the line between waypoints, only by being next to or along it. The situation is different when the tightening function is activated. Then, with the actual platform position and orientation, i.e., the distance between the platform and the path line, a course correction is computed and added to the control. This way, the platform can move precisely along the line section determined from the two indicated waypoints. The performed tests proved the usefulness and effectiveness of the implemented control and navigation algorithms in the autopilot subsystem. Considering RTK correction in the navigation system GNSS RTK/INS, the accuracy of tracking in the context of geographic coordination did not exceed 0.1 m. Still, in the case of relative position, the accuracy was lower than 0.01 m. Neglecting the RTK correction, the autopilot system realized a trajectory with an accuracy of about 0.4 m. Therefore, a measurement system based on GNSS RTK was employed to achieve precision in deviation angle, position, and speed. This sensor is a component of an advanced state observer.