# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 5 Future Works  
Finally, this review article is furnished via our understudy theoretical strategy for system identification. This strategy followed the Grey box approach while utilizing the differentiator observer theory [162]. We proposed a sliding mode-based system identification that utilizes the robust and accurate nature of sliding mode observer and flatness property. The proposed technique is briefly discussed in this section. The motivation for the use of the aforementioned technique is its inherent robustness in the face of uncertain conditions. In this work, we also relax the identifiability condition [163]. At this point, the following assumptions are furnished.  
1. It is assumed that the control input derivatives are known and certain.
2. The system's stability derivatives are assumed to be unknown and separable.
3. The states of the system are observable.
4. The system under study must satisfy the flatness property [164].  
Before proceeding to the stability derivative estimation, the observability and separability conditions are checked offline. The flatness property plays a significant role in this strategy based on which parameters are extracted. The controller used in the closed-loop estimation is the one designed via sliding mode control strategy [165]. The identification strategy flowchart is shown in Figure 7. At the first step, the mathematical model of the system is developed and some parameters are marked as unknown in an uncertain environment. Then, by utilizing the flatness property, these parameters are extracted and are further estimated by invoking the known data. The mathematical model is finalized for control design purpose by using these estimated parameters. Therefore, we can consider our strategy as the parameter identification of the flight dynamics of the FWMAVs.  
**Author Contributions:** All authors have equally contributed to the review. Initial draft-review, Q.K., writing-editing, analysis and review, R.A. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** No new data were created in this study.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Abbreviations**  
\((X_{l}:\ Y_{l},\ Z_{l})\) Inertial reference frame  
\((x_{b},\ y_{b},\ z_{b})\) Body reference Frame  
\((\overrightarrow{i},\ \overrightarrow{j},\ k)\) Unit vectors in the \((x\ y\ z)\) axes  
\((\overrightarrow{x}\ \overrightarrow{y}\ \overrightarrow{z})\) Orthonormal axes  
\(\overrightarrow{i}_{b}\) Unit vector along \(\overrightarrow{x}_{b}\)  
\(I_{i}\) Principal moment of inertia in the \(\overrightarrow{i}\) body axis  
\(I_{ij}\) Product of inertia for the \(\overrightarrow{i}\) and \(\overrightarrow{j}\) body axis  
\(m\) Mass of the system  
\(\overrightarrow{W}_{LR}\) Left-to-Right wing vector that connects the wing markers  
\(\phi,\psi,\ \theta\) Euler angles  
\(\alpha\) Angle of attack  
\(\beta\) Side slip angle  
\(\delta_{e}\) Elevator input angle  
\(\delta_{f}\) Flapping frequency  
\(\delta_{r}\) Rudder input angle  
\(\overrightarrow{\omega}\) Angular velocity vector \((p,\ q,\ r)\)  
\(\dot{\omega}\) Angular acceleration vector \((\dot{p},\ \dot{q},\ r)\)  
\((\phi_{r}\,\psi_{r},\ \theta_{r})\) Attitude angles (roll, pitch, yaw)  
Figure 7: The proposed system identification approach in stability derivative estimation.