# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 1 Introduction  
The fascination toward the flight of natural fliers has inspired the development of flapping-wing micro air vehicles (FWMAVs). Natural fliers, particularly of insect types, offer interesting flight mechanisms and aerodynamics that have not been completely understood until today. The currently estimated more than ten million insect's species [1] include flies, which change their flight conditions based on some specific arrangements of their wing strokes [2, 3], offer different adjustments of the wings that make the insects capable of flying with extreme maneuverability and impressive stability [1, 4, 5] compared to the conventional fixed wing aircrafts [6, 7]. Some characteristics like their dexterity, broad flight envelope, robust behaviors in different situations at very low Reynolds numbers, hovering ability, the ability of quick transition to forward flight, abrupt maneuvers, make FWMAVs potentially beneficial in this era. Insect fliers generally use elastic elements in their flight muscles as energy storage and thus, minimize their inertial power, thus enhancing their power loading [8]. This results in a more efficient flight, which is another advantage of flapping-wing flight over rotary wings [9]. Exhaustive applications of such MAVs can be found, for example, as a reconnaissance platform for search and rescue as well as military operations. Fitted with a camera, FWMAVs can be deployed in risky and hazardous conditions such as after natural catastrophes to quickly determine and monitor the situation, for finding routes, identify potential dangers, and patrol border lines for security purposes as well as for civil applications such as the remote inspection ofpipes and power lines, inspection of crop fields, and the conditions for fertilization and harvesting [10; 11; 12; 13]. Based on the current trends, it is envisioned that FWMAVs will dwell in the gaps between the rotary and fixed wing aircraft because of their aforementioned appealing characteristics. In this context, micro- and nano-flapping wing fliers [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20] are also believed to provide a wide number of advantages with considerably low cost and flight efficiency. As shown in [21], insect flights show higher power loading than multi-rotor drones. However, for FWMAVs, the small size of the sensors and mass restricts the onboard processing. Furthermore, depending on the overall size of the MAVs, the limited choice of small size onboard power supplies often means that the flight duration is a relatively short period in comparison with other types of aircraft. Thus, at the present stage of development, such efficiency has yet to be achieved. Therefore, energy efficient flight, attitude determination, and flight control of FWMAVs are still the main focus of researchers, scientists, and engineers [13; 16]. FWMAVs are primarily recognized and developed into two classes (i.e., tailless and tailed). The tailless designs usually mimic the insects, which, consequently, provide high dynamic maneuvers. These configurations, in general, require active stabilization because they can be found passively unstable in forward flight and hovering [22]. In such developments, the nano-hummingbird [7] and robotic bee, known as RoboBee [10], have shown actual flight stability. On the other hand, the tailed design is found to be similar to configurations in birds, which are known for being passively stable, and therefore do not require active stabilization [15; 23]. This kind of configuration provides the ease to develop and implement higher-level problems like altitude stabilization [24; 25] and obstacle avoidance [25; 26; 27]. Figure 1 displays some of the well-known flapping-wing micro air vehicles that have been developed to date. It is witnessed in Figure 1 that these FWMAVs differ in design as well as in its flying mechanism. The FWMAVs (Figure 1a,b,f,h) follow very similar flight mechanics as birds. This class utilizes the surface control mechanism for different maneuvers like pitching, rolling, yawing, and hovering.