# Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles
## 2 Micro-Aerial Vehicle Flight  
Current developments in flapping wing MAVs, which are inspired by natural fliers, can be categorized into two classes: bird (or vertebrate) flight and insect flight [60]. Although in general, both types of natural fliers observe three types of flight, which are named as gliding flight (mostly found in vertebrate flight), forward flight, and hovering [12; 61; 62; 63; 64; 65; 66], there are differences in their aerodynamics (see Figure 3). In bird flight, the wings generally have two degrees of freedom (i.e., the flapping and symmetric twisting of the wings downward and upward, i.e., pronation and supination occur respectively) to change the angle of attack and the lift. However, in the second class, the wings follow three degrees of motion (i.e., the main flapping motion is defined along the body axis with a certain stroke plane, while flapping the wing exhibits pitching motion along its root and experiences deviation from the stroke plane). In other words, while flapping, the wings follow an eight like pattern, which is, by definition, a two-degree motion [52]. Consequently, a three degree of motion occurs. The wing strokes are divided into upstroke and downstroke that are further categorized into normal rotation, advanced rotation, and delayed rotation. The wing rotation is termed as normal if the rotation occurs at the end of each half stroke, the rotation is advanced if it occurs before the end of the half stroke and after the mid stroke, and delayed rotation occurs after the half stroke and before the mid stroke. Furthermore, the normal rotation is, once again, recognized as water treading and normal hovering (for more details see [60; 67; 68]). Detailed comparison between the vertebrate and insect flights can be found in [69; 70]. Figure 2: The system identification loop [54]. In the context of understanding the aerodynamics and wing kinematics, the lift and power requirement analysis related to hovering natural fliers (e.g., hummingbird and _Drosophila_ family) was conducted in seminal works [73, 74], which was further refined in the work of [PERSON] [75, 76, 77, 78, 30]. These pioneering works were further developed for other species, which include the design of some morphological parameters and wing kinematics (e.g., hawkmoths [80, 81], dragonflies [82, 83], bumblebee [84, 85], robotic bee [10, 20], and the beetle [11]. The flight characteristics are modeled in terms of aerodynamics and wing kinematic models. In the existing literature, two main strategies have been extensively studied for the development of the aerodynamic models (i.e., blade element methodology (BEM) and Navier-Stokes equation) through the computational fluid dynamics (CFD) strategy. The blade element strategy based aerodynamic models was developed in [61, 68], where they incorporated the unsteady and added mass effects. The progress in the aerodynamics modeling in the last decades is comprehensively presented in [86, 87, 88, 89, 90, 91, 92]. Figure 3: Wing kinematics and aerodynamics of (**a**) hummingbird (reprinted from [71] with permission from Elsevier) and (**b**) insect flight (adapted from [72]). In recent developments, [93; 94] tried to abridge the theoretical and experimental strategies and to develop a standard linear aerodynamic model for DeFlFly II. The developments were mainly based on the standard aircraft system identification techniques and their extension to FWMAVs, which can be further used for simulation and autonomous full flight envelope. In [95; 96], a two-dimensional flapping wing was considered, and the aerodynamic performance in asymmetric stroke in hovering and forward flight was numerically studied. In addition, the analysis of the effects of the asymmetry of the stroke on the aerodynamic forces and flow structures was carried out. The authors in [97] carried out a BEM for the development of the fluid-structure interaction model by synthesizing it with a structural model.