## 1 Introduction  
Since the research initiation of the micro aerial vehicle (MAV) from the defense advanced research projects agency (DARPA) program [1], increasing attention has been paid to the design of bio-inspired flapping wing MAV, and in particular, the study of aerodynamics [2; 3; 4]. [PERSON] et al. [5] designed a stable 21 g insect-like tailless flapping wing micro air vehicle (FWMAV) with proportion-differentiation (PD) feedback control. By undertaking several flight tests, they demonstrated that the tailless FWMAV could perform a vertical climb, then hover and loiter, within a 0.3 m ground radius, with small variations in pitch and roll body angles. [PERSON] et al. [6] developed an ultra-light FWMAV named Golden Snitch with only 8 g weight and 20 cm wingspan. By mounting a commercial infrared (IR) transmission module on the vehicle, they realized that altitude control of the FWMAV by a modified proportional feedback algorithm. The validity of their approach is demonstrated in both numerical simulations and flight tests. [PERSON] et al. [7] designed a scalable, controllable, miniature flapping wing robot. They manufactured a working prototype and conducted FEM analysis for their airframe design to ensure its strength. A scaling law, based on momentum theory, was proposed to predict the lift/weight ratio versus the flapping wing robot's size. [PERSON] et al. [8] proposed a nonlinear unsteady aerodynamic model for insect-like flapping wings, based on potential flow theory, and validated their model against existing experimental data. Very good agreement is found in flow field representation and force prediction in the experiments. [PERSON] et al. [9] also conducted experimental measurements for a flapping wing flight, ranging from \(Re=500\) to 15,000. They studied the behaviour of the leading-edge vortex based on these Reynolds numbers and verified the presence of Kelvin-Helmholtz instability, observed at a higher Reynolds number in computational fluid dynamics calculations. Regarding the MAV power, the electric motor is the most commonly used actuation source for bio-inspired flapping-wing MAV (FWMAVs). However, constrained by the rotational inertial force, the change rate of the electric motor's rotation speed is limited and power-consuming. [PERSON] and [PERSON] developed a piezoelectric actuator and multi-bar of flexure hinges to drive flapping-wing and a novel flapping wing rotor (FWR) [10; 11; 12]. [PERSON] and [PERSON] [13] designed an insect-type flapping wing MAV which utilizes piezoelectric transmission wings with flexure hinges to replace the motorized transmission. [PERSON] improved the piezoelectric transmission wings by designing and developing a flapping wing MAV, known as LionFly [14; 15]. [PERSON] et al. [16] designed and fabricated an 80-milligram, insect-scale, flapping-wing robot, which used a four-bar linkage to amplify the piezoelectric flight muscle's displacement and generate the wing-flapping motion. The common advantages of these piezoelectric transmissions are that they are small, light mass, simple structure, have superb accuracy, no gears, and low inertial effects. These advantages make piezoelectric transmission suited for nano- to pico-scale unmanned aerial vehicles (UAVs). Different from mimicking the insect-like wings, a novel flapping wing rotor, with combined rotary and flapping motion, was proposed by the author [17]. The FWR has the advantages of significant higher aerodynamic efficiency and lift coefficient than insect-like wings, in the range of Reynolds number from 2600 to 5000, and ideal Strouhal number around 0.3 [18; 19]. In order to evaluate the FWR aerodynamic performance, numerical and experimental studies have been conducted [12; 17]. [PERSON] et al. [10] designed a piezoelectric actuated flapping wing rotor model and analyzed the aerodynamic performance of the model with two-dimensional (2-D) CFD numerical simulation. Very good agreement is shown by comparing the experimental and simulation results.