# Modifications to ArduSub That Improve BlueROV SITL Accuracy and Design of Hybrid Autopilot
## 6 Conclusions and Future Work
The immediate next steps for this project are having live AR pilots interact with the hybrid autopilot in SITL and real water dives. Future work in gathering experimental data to model roll and pitch hydrodynamics of the BROV2 is also planned. Conducting tests similar to the ones in this study and tow tank tests in the real world could assist in this process of refining the hydrodynamic model used to calculate PD gains. Improving the accuracy of the hydrodynamic model will reduce errors and speed up convergence in practical applications and increase the value of SITL testing and improve the hybridautopilot to better assist pilots. Some updates to the SITL model are unique to our particular vehicle, but many fundamental errors were corrected in this work. Readers are encouraged to adopt our methodologies and use our results as reference points for their own vehicles. Moving forward, as our ArduSub SITL model of the BROV2 Heavy continually improves, exploration of complicated topics like motor saturation, other nonlinear strategies, and fully autonomous operations are more worthwhile to conduct in simulation and now have a way to be implemented thanks to our updates to ArduSub that unlock quantitative control. Conceptualization, P.N. and M.K. ; methodology, P.N. and M.K. ; software, P.N. ; validation, P.N. ; formal analysis, P.N. and M.K. ; investigation, P.N. ; resources, P.N. ; data curation, P.N. ; writing--original draft preparation, P.N. ; writing--review and editing, P.N. and M.K. ; visualization, P.N. ; supervision, M.K. ; project administration, M.K. ; funding acquisition, M.K. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Science Foundation (NSF) grant number 2128924. Not applicable. The raw data supporting the conclusions of this article will be made available by the authors on request. Thanks to University of Florida (UF) collaborators [PERSON] and [PERSON] for the test trajectories simulating an AR piloted dive, and for consultation on controller strategy. ChatGPT and Github Copilot assisted with coding tasks associated with this work. The authors declare no conflicts of interest. The simulation code uses a classic drag model for calculating the drag forces or torques acting on the vehicle, which for any single degree of freedom is  
\[\tau_{d}=-\frac{1}{2}V|V|C_{d}S\rho, \tag{1}\]  
where \(\tau_{d}\) is the drag force or torque, \(V\) is the signed linear or angular velocity to preserve the direction of movement, \(C_{d}\) is the drag coefficient, \(S\) is the wetted area, and \(\rho\) is the density of the surrounding fluid. The original code approximated the vehicle as a sphere to determine \(S\), chose arbitrary \(C_{d}\), and applied Equation (1) to calculate instances of linear drag. However, for drag torque the value of \(\tau_{d}\) was then multiplied by an approximate equivalent sphere radius. Depending on if the drag being calculated is a force or torque, \(C_{d}\) will be dimensionless for force or have units of meters for torque; in the case of angular drag torques, by multiplying \(\tau_{d}\) by a radius an additional length dimension multiplies the torque, producing major errors. To fix the erroneous implementation and improve accuracy, a different model with values backed by the research literature is proposed to replace the Equation (1) model. Research conducted by [PERSON] in Sandey (2018) characterized a smaller version of the BlueROV named uDrone. The uDrone had only five thrusters and could not be controlled in the roll and pitch degrees of freedom, so only the yaw direction was analyzed. Researchers had exerted constant moments at various torques and recorded the angular velocity of the vehicle at those points; then, a least squares curve fit was used to find  
\[N_{D}=N_{r}r+N_{r|r}r|r| \tag{2}\]  
where \(N_{D}\) is the viscous torque due to drag in the yaw direction, \(N_{r}\) is the linear damping coefficient, \(N_{r|r}\) is the quadratic damping coefficient, and \(r\) is the signed yaw velocity.