# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 4 Conclusions  
A comprehensive review on system identification and mathematical modeling of flapping wing micro-aerial vehicles has been presented. The details were provided for tailless and tailed natural fliers and micro-aerial vehicles such as _Drosophila_, hawk ornithopter, RoboBee, KUBette, and Delfly-II as well as the Delfly Nimble. The outcomes of the system identification approaches in all reviewed articles were satisfactory in general. The obtained models were validated to predict and/or estimate the dynamics of the plants used, and they could achieve reasonable accuracies. The identification strategies that have been used were top-down Grey box approaches. These include the extended Kalman Filter, linear regression and least square estimation, frequency-based identification, and computational fluid dynamic based system identification. Most of the approaches were used to estimate model parameters that are related to aerodynamics and result in standard aircraft mathematical models or equations of motion, which are adopted with or without modifications. The modifications were based on a priori knowledge of the natural fliers' aerodynamics and engineering insights. The final models typically involve decoupling of the longitudinal and lateral dynamics. Additionally, wind tunnel or CFD-based system identification has been mostly performed to determine the stability derivatives, which were then again used together with the conventional aircraft equations of motion. CFD-based procedures were performed on the tested MAVs, while they were either mounted on a fixed platform or were tethered, thus, the natural flight motions of the vehicles were constrained, and this would change the aerodynamics during the flight. The final mathematical model would be either a full-model or a reduced model, in which insignificant stability derivatives were removed. Moreover, we found that a more complete system identification process aimed for design decision and controller development was presented in [159], in which a simplified linear damping model of the Delfly Nimble was obtained. This review has shown that system identification approaches have a promising potential to uncover many unanswered questions in generating valid mathematical models of FWMAVs that can capture the overall FWMAVs' complex flight dynamics. From the review, we conclude that system identification approaches have not been used to their maximum advantage for modeling FWMAVs at the present stage. The approaches were mostly used to obtain the aerodynamic parameters of certain FWMAVs for hovering and/or steady flight, linear regression and least square estimation were mostly used, and the acquired models were mostly linear. Thus, they are valid only for particular flight modes. There are still questions on the fidelity of the models obtained, particularly those for various maneuvers. Better outcomes of system identification and modeling complex systems such as FWMAVs can be achieved with detailed analyses done before the start of the identification that lead to appropriate model selection. Such analysis will be critical to determine the optimized model structure and model order where a priori knowledge and engineering insights are combined with formal properties of models. In addition, it is imperative to have clear objectives of the system identification to be performed, for example, system identification for design decision, simulation or validation, and/or for flight control design. Therefore, specific experimental data, efficient model selection, and structure as well as identification approach can be determined accordingly. Many nonlinear system identification approaches that are known for their powerful capabilities in dealing with nonlinear dynamical systems such as the unscented Kalman filter (UKF) and nonlinear autoregressive moving average model with exogenous inputs (NARMAX) have not been considered to solve the modeling problems of FWMAVs.