## 4 Application
### Control Implementation and Test Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Desired Course** & **Average Velocity** & **Stabilized Interval** & **Stabilized Interval** \\  & **Angle (\({}^{\circ}\))** & **(m/s)** & **(s), (with the EKF)** & **(s), (with the UKF)** \\ \hline
1 & 010 & 0.5 & 7.1 & 6.4 \\
2 & 010 & 1.5 & 5.7 & 5.2 \\
3 & 020 & 0.5 & 7.6 & 7.1 \\
4 \({}^{\star}\) & 020 & 1.5 & 6.9 & 6.2 \\
5 & 030 & 0.5 & 9.3 & 8.8 \\
6 & 030 & 1.5 & 8.3 & 7.9 \\ \hline \hline \end{tabular} \({}^{\star}\) This test scenario corresponds to the simulation case shown in Figure 8.

\end{table} 
Table 4: Testing results for the course-tracking of the torpedo-shaped AUV. Figure 10: The AUV reached and followed a desired rectangle-shaped trajectory: (**a**) with the extended Kalman filter (EKF) algorithm; (**b**) with the unscented Kalman filter (UKF) algorithm. An assessment of the above-described AUV application using MBSE methodology combined with MDA components is described in Table 5. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Proposed Models** & **Advantages** & **Disadvantages** \\ \hline CIM & This model focuses on a global model of top level, which can combine discrete models and continuous models. & An implemented functional block diagram must be supplemented in the CIM to depict internal continuous behaviors for the control system developed. \\ \hline PIM & The PIM–PSM separation and its model transformation allow the designed control elements to be customizable and reusable for various kinds of AUVs. & This can influence the performance effort of projects. \\ \hline PSM & The control capsules can be transformed into various PSM IDEs (e.g., Java, Net, or Ada IDEs).Arduino microcontrollers are used to deploy the real-time and embedded control system using open-source solutions. & Within the OMG, the XML Metadata Interchange (XMI) specification [103] supports the exchange of model data when using an MOF-based language such as real-time UML/SysML. However, development engineers may need training to develop the required skills in different IDEs. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Assessment of the torpedo-shaped AUV control application of model-based systems engineering (MBSE) methodology combined with the model-driven architecture (MDA). CIM, computation-independent model; PIM, platform-independent model; PSM, platform-specific model; IDE, implementation development environments; OMG, Object Management Group; XML, extensible markup language; MOF, Meta Object Facility; UML, unified modeling language; SysML, systems modeling language. Figure 11: The AUV reached and followed a desired triangle-shaped trajectory: (**a**) with the EKF algorithm; (**b**) with the UKF algorithm. ## 5 Conclusions and Future Work

This paper introduced an application of MBSE methodology to intensively deploy controllers for AUVs whose dynamics can be considered an HDS. This application model is based on the MBSE methodology, combined with MDA concepts, real-time UML/SysML, EKF/UKF algorithms, and HA to systematically realize the controller. The dynamic models and control structure of AUV were first used for control combined with MDA components such as the CIM, PIM, and PSM. In the CIM, the use case model was defined with continuous behaviors, EKF/UKF algorithms, and HA to closely control the requirements. The PIM was established to establish the design model by constructing a real-time capsule pattern. This pattern can be customized and reused in new AUV control applications (Table 2). The PIM designed was then converted into the PSM through round-trip engineering of the intermediate C++ codes to form an AUV controller with suitable microcontrollers. On the basis of the proposed model, a planar trajectory-tracking controller of a miniature torpedo-shaped AUV running on the free surface was implemented and evaluated using the ATMEGA U2 and STM32-Cortex-M4 microcontrollers.