## 4 Experimental Validation
### Experimental Results: Control Scenario II  
The second test was implemented in the Girona500 AUV at the port of Sant Feliu de Guixols (Girona, Spain), as shown in Figure 13. The implementation consists of a path-following of a predefined coverage planar area keeping a constant depth for the heave motion equal to 4 meters. The path-following experiments were performed successfully  
Figure 11: AUV tracking trajectory for the simulation model in NED coordinate system: (**a**) North, East, and Down, (**b**) Yaw.  
Figure 12: AUV errors at the LOS-based, path-following algorithm in Control scenario I, including the respective waypoints marked with their order number: (**a**) Cross-track error [m], (**b**) Yaw orientation error [deg].  
with the proposed GNC approach, as illustrated in Figure 14, where the red and blue solid lines are the coverage and actual AUV paths, respectively. In this control scenario, there was no current affecting the AUV, and the vehicle was located inside the harbor with good weather conditions and without the presence of significant waves during the field tests.  
Figure 15 shows the input control values for the position PID controllers in the NED coordinate system. The implementation of the path-following algorithm performed correctly, reaching the ending waypoint of the coverage path. Nonetheless, there are differences between control scenario I and control scenario II, such as the total time of the test and behavior in the steady-state at yaw motion. These discrepancies are related to the reduced-order model and the non-inclusion of Coriolis and cross-terms of the dynamic matrices. Furthermore, the standalone ROS-node generated by MATLAB-Simulink can affect the results, as the simulation compiler differs slightly from the auto-generated C++ code.  
Based on the cross-track error \(e(t)\), three non-dimensional indicators measure the performance for the LOS-based, path-following algorithm: root-mean-square error (RMSE), mean absolute error (MAE), and standard deviation (SD). Table 4 includes these non-dimensional indicators showing the numeric values for control scenario II. Furthermore, Figure 16a illustrates the cross-track error \(e(t)\) for the LOS-based, path-following algorithm in the sea implementation. Even though the LOS-based, path-following performance is correct, there are oscillations in the yaw motion, as shown in Figure 16b, which need to decrease. As mentioned in Section 3, the PID controller parameters are estimated from the MATLAB-Simulink control toolbox, showing a great performance in the simulation environment; however, there is an oscillation in the yaw angle at steady-state for the implementation in the open environment at sea. A more accurate tuning of the PID parameters is required to reduce the oscillations in the yaw motion, including the integral parameter increase in the LOS PID controller to reduce the steady-state cross-track error.  
Figure 14: AUV tracking trajectory for the sea trials in NED coordinate system: (**a**) 3D view, (**b**) 2D view.  
Figure 13: Girona500 AUV during the implementation of the path following algorithm at the harbor of Sant Feliu de Guixols (Girona, Spain).