## 5 Results and Discussion
### Evaluation of Two UAV Path Following Algorithms  
The following sharp maneuvers guarantees the ability of the flight control system to achieve different missions. This section highlights the ability of carrot chasing and PLOS path following methods to track the predetermined path. As aforementioned, MNLDI is accepted in tracking performance while guaranteeing robustness against external disturbances in addition to it is non-sensitive to the uncertainties. Therefore, MNLDI flight control system was used as the inner control loop for the outermost guidance loop. For carrot chasing algorithm, the optimal weighting values for the control gain \(k\) and the VTP distance \(\delta\) were chosen on the trial and error basis. The selection of VTP distance \(\delta\) controls the performance of the UAV following the desired path. If \(\delta\) is small, the UAV oscillates around the desired path, thus increasing the cross-track error distance, which prevents the UAV from riding the path early. By increasing the value of \(\delta\), the UAV quickly rides the desired path. The maximum value of \(\delta\) is constrained by the value of cross-track error. Consequently, \(\delta\) is increased until a certain point, beyond which the cross-track error increases again and UAV fluctuates around the desired path. For PLOS path following guidance algorithm, the advantages of the combination of two guidance laws are exploited; one keeps the LOS angle while the other minimizes the cross-track error distance. If the pursuit guidance gain \(k_{1}\) in Equation (2) is a small positive number, then the UAV oscillates around the desired path. The proposed sequence of the desired waypoints highlights the ability of the UAV to follow abrupt maneuvers with different LOS angles starting from acute angles to obtuse angles \(\theta=10\):\(180\) [deg] passing through sharp change square LOS angle \(\theta=90\) [deg] excluding the transient errors from the turns. The critical practical problem is associated with the flight control system with external wind disturbances, however using the geometric path following algorithm with the robust MNLDI guarantees a stable platform that meets the desired performance criteria. In the following analysis, the effect of constant west wind with a speed half the Tiger-Trainer UAV cruise speed was introduced. Figure 22: Attitude angle error for outer side-slip angle excitation with wind and uncertainties. In each scenario, just touching a circumferential circle around the desired waypoint with radius \(r=130\) [m] was required. In Figure 23, a comparison between carrot chasing and PLOS guidance method for following a predetermined path is illustrated. The cross-track error and LOS angles are compensated by generating bank angle commands based on the position of the UAV to the desired waypoint. After touching the circle centered by the desired waypoint location, the algorithm switches to the next desired waypoint. Figure 24 illustrates the robustness of the proposed flight control model against wind disturbance. With constant altitude, the pitch channel control law regulates the desired trim altitude for the Tiger-Trainer UAV \(h=200\) [m]. Meanwhile, the roll channel control law responds to the desired bank angle to achieve required turning. The altitude hold control loop keeps the altitude constant despite the sharp change of the bank angles to turn in responding to different sharp maneuvers, as shown in Figure 25. Similarly, the velocity maintains the UAV on the desired position along the given path, as shown in Figure 26.  
Figure 24: Straight line path following with wind. Figure 23: Straight line path following without wind. The cross track error shown in Figure 27 confirms that the PLOS path following guidance law is more robust against wind disturbances than the carrot chasing path following guidance law. Since PLOS is a combination of two guidance laws, controlling the cross-track error is a main part of the generated guidance law that leads to a rapid decreasing of the error.