# Modifications to ArduSub That Improve BlueROV SITL Accuracy and Design of Hybrid Autopilot
## 3 Open-Loop Experimental Testing and Hydrodynamic Characterization  
In this section, a description of the open-loop yaw torque experimental testing that was performed to determine the yaw hydrodynamic coefficients for hybrid autopilot model and ArduSub SITL shall be covered. This round of testing was necessitated because initial trials of the autopilot described in the following sections produced inadequate performance due to discrepancies in the models available from other works and the actual BROV2 used in this work. The yaw degree of freedom isolated from the full hydrodynamic model in Appendix B is  
\[N=(I_{z}+N_{r})\dot{r}+N_{r}r+N_{r|r|}r^{2} \tag{10}\]  
where \(N\) is the external yaw torque acting on the BROV2, \(I_{z}\) is the moment of inertia in yaw, \(N_{r}\dot{r}\) is the added mass in yaw, \(N_{r}\) is the linear viscous damping in yaw, \(N_{r|r|}\) is the quadratic damping in yaw, \(r\) is the vehicle's yaw velocity, and \(\dot{r}\) is the vehicle's yaw acceleration.  
Control gains were calculated using this strategy, initially based on hydrodynamic coefficients found in [16; 38] for vehicles similar to the BROV2. Using the hydrodynamic coefficients found in the literature, initial results of real-world testing of the yaw step response produced large discrepancies between the settling times predicted by SITL, where actual settling times were much longer. Therefore, a preliminary round of water tank testing for system identification was performed that determined a more accurate model for simulations and the hybrid autopilot.  
Open-loop testing of the yaw degree of freedom of the BROV2 Heavy was performed in a water tank (Figure 7). During this, six different yaw torques were applied to the  
Figure 7: Real-world testing was performed in a small tank approximately two meters in diameter and a meter and a half in depth.  
BROV2 and the resulting yaw velocities were measured, with at least five trials performed per torque tested. These tests were intended to observe inertia and drag behavior. The particular BROV2 Heavy used in these experiments had additional ballast in the form of metal washers attached to the front corners of the vehicle to level out its resting floating state. It was slightly positively buoyant, and before each trial was allowed to come to rest near the surface of the water, mostly submerged so that less than a quarter inch of the buoyancy floats was exposed. An experimenter also held the vehicle's tether above and out of the way, careful not to disturb the vehicle. At the start of each trial at time \(t=0\), a fixed yaw torque input command was sent to the vehicle and held constant. Data collection recorded yaw velocity \(r\) for times \(t\geq 0\). Yaw torques were held constant for several seconds to give the velocity output ample time to stabilize before ceasing the trial. Each open-loop response had two distinct regions of the velocity output: an initial unsteady region while the vehicle was accelerating from rest and a steady-state region where the vehicle was no longer accelerating and maintained a constant velocity \(r_{f}\). The unsteady region of the velocity output of the open-loop response was analyzed to determine inertia characteristics and the steady-state region to determine drag characteristics.