## 1 Introduction  
The fascination toward excellent flying skill of natural fliers has inspired the development of Flapping-wing Micro Aerial Vehicle (FMAV). Researchers have been trying to uncover the secrets behind its high-lift characteristics by analyzing the aerodynamical and flow dynamic [1, 2, 3, 4]. With the continuous progress and development of manufacturing technology, it offers us the opportunity to design FMAV to mimic and learn from natural fliers. The research object of this paper is the tailless FMAV weighing less than 30 g. From the perspective of flight control mode, this kind of FMAV is more similar to insects in nature, and 15 g\(\sim\)30 g is the minimum weight range that would make it possible for the FMAV to fly for more than four minutes with the propulsion system, sensor system, battery, and some mission payloads onboard. However, due to the lack of tail, the inherent instability of the FMAV makes it more difficult to control. As of now, some flapping wing robots capable of hovering have been designed. The first ornithopter to achieve stable hovering flight is the two-wing FMAV developed by the Defense Advanced Research Projects Agency (DARPA) [5] of the United States. The control torque is generated by adjusting the trailing edge. It realizes the stable flight and the wireless transmission of images using the onboard camera. The two-wing FMAVs with similar control method include the 22 g Colibri robot [6] and the 21 g KUBeetle [7, 8, 9]. Among them, KUBeetle-S [10] generates the control torque by adjusting the stroke plane. In this way, the direction of the average thrust is changed and the required control torque is generated. Moreover, there are also some direct-drive, two-wing FMAVs, such as the 20.4 g hummingbird robot [11; 12; 13; 14] and 80 mg Robbee [15], generating the three-axis torque through wing kinematics modulation. In addition, another category is four-wing FMAV. Although the four-wing flapping robot is not as closely related to insects as the two-wing FMAV, it can utilize the clap-and-fling effect to improve aerodynamic efficiency, such as DelFly series [16; 17; 18]. Most of above FMAVs can achieve stable flight with onboard batteries, control, and attitude sensing systems, but few have more sensors on board to sense states other than posture due to weight and power constraints. Only with the help of the external motion capture system, the stable control of 3D position can be implemented [19; 20]. The FMAV designed in this paper is a four-wing FMAV equipped with a laser sensor and a barometer, which can rely only on its sensors to achieve altitude and attitude control. From the control perspective, since most FMAVs are custom designed and manufactured, assembly errors and manufacturing imperfections are unavoidable. Moreover, depending on the mission requirements, the FMAV will carry different mission payloads, such as cameras, to accomplish specific tasks sometimes. All of these will make a difference between the actual model parameters of the FMAV and the theoretical model parameters, which poses a challenge to the control of the FMAV. Thus, many scholars have tried different controllers to solve these problems. In terms of attitude stability control, the most popular controller is the PID controller. In [21], a loop shaping compensator is designed and added to the PD controller to improve the low frequency gain while sustaining the stability margin. In [22], the attitude stability is achieved by the PD controller with a reference generator. It seems that a model-free PID controller can achieve attitude stability of the most FMAV, but when the model parameters of the vehicle change, the controller whose parameters have been tuned before may not work or has a limited stability margin. To avoid this problem, many nonlinear controllers have been proposed. In [23], an adaptive controller was proposed to achieve attitude control with unknown model parameters.