# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 1 Introduction
The surface motion control resembles the fixed wing aircraft strategies [7], whereas the FWMAVs in (Figure 1c,d,e,g) mimic the insects flying mechanism to experience different flight maneuvers [11; 14; 15; 16; 19; 20; 28; 29]. The autonomous flight of the first category is relatively easier compared to that of the second class of FWMAVs. A clear understanding of insect flight depends on subtle details that might be easily overlooked in otherwise thorough theoretical or experimental analyses. Recently, researchers have benefited greatly from the use of high-speed cameras for capturing wing kinematics, new strategies such as digital particle image velocimetry (DPIV) to quantify flows, and powerful computers for further computational analysis. With the help of these methodologies, one can develop more accurate and rigorous models of these insects while having a fewer number of assumptions in developing wing kinematics, aerodynamics, and flight dynamics. Despite the challenges faced in conducting experiments to quantify the wing motions of several flying insects due to their small size and high wing beat frequencies, insect fliers' flapping kinematics, particularly that of free hovering flight and free forward flight, have  
Figure 1: (**a**) Festo-smartbird, manufactured by Festo’s Bionic Learning Network (photo courtesy of Festo [14]); (**b**) AeroVironment Nano Hummingbird (photo courtesy of AeroVironment); (**c**) a four-winged robot that flies with a jellyfish-like motion (photo courtesy of [16]); (**d**) DelFly MAV (photo courtesy of Wikipedia-DelFly); (**e**) insect-scale flying robot (photo courtesy of Wyss Institute Harvard University); (**f**) big bird developed by University of Maryland (Photo courtesy of University of Maryland); (**g**) Beetle Mimicking Flapping MAV (Photo courtesy of [11]); (**h**) Flapping wing developed by Tamkang University (Photo courtesy of [29]). been well-researched for more than 50 years. Early attempts to capture free-flight wing kinematics such as [PERSON]'s comprehensive and influential survey [30] relied primarily on a single-image high-speed cine. Although quite informative, especially because digital imaging technology continues to offer exceptional spatial resolution, single-view techniques cannot provide an accurate time course of the angle of attack of the wings. More recent methods have employed high-speed videography [31], which offers greater light sensitivity and ease of use, albeit at the cost of image resolution. A further consideration is that insects rely extensively on visual feedback, and hence, care must be taken to ensure that lighting conditions do not significantly impair an insect's behavior. Even more challenging than capturing wing motions in 3-D is measuring the time course of aerodynamic forces during the stroke. At best, flight forces have been measured on the body of the insect rather than its wings, making it very difficult to separate the inertial forces from the aerodynamic forces generated by each wing [32; 33; 34; 35; 36]. In addition, unlike in free flight conditions, tethering can alter the wing motion, and thus, modify the generated forces. Researchers have overcome these limitations using two strategies. The first method involves constructing dynamically scaled models on which it is easier to directly measure aerodynamic forces and visualize flows [37; 38; 39; 40; 41; 42; 43]. A second approach is to construct computational fluid dynamic simulations of flapping wings [44; 45; 46; 47; 48]. The power of both approaches, however, depends critically on accurate knowledge of wing kinematics. In general, to understand the mechanics of flapping wing flight, three basic aspects need to be well understood: flapping kinematics, aerodynamics, and flight dynamics (a detailed summary can be found in [49; 50; 51]). Several attempts have been made to model FWMAVs based on the knowledge of those three aspects of natural fliers such as those in [52], which focused on the first principle approach of modeling that includes flight stability and control.