## 1 Introduction
In [24], flying with damaged wings is achieved by a hybrid controller combined with the adaptive controller and sliding mode control. However, these adaptive controllers do not include a reference generator that will provide a reasonable trajectory of setpoint which can reduce the overshoot of the control result and faster the convergence of adaptive parameters. In our previous works [25], we have designed a model-based Active Disturbance Rejection Controller (ADRC) for altitude control of the FMAV with internal and external disturbances. It showed that the ADRC can not only reduce the influence of weight change on altitude control but also has a good ability to suppress external disturbance. The ADRC with the Extended States Observer (ESO) was also applied to maintain the stable attitude of a bird-like flapping wing robot [26] during the automatic landing. However, the flapping wing produces large-amplitude, low-frequency vibration, which will introduce a lot of noise to the state measurement, especially to the attitude state perception. Thus, the selection of ESO bandwidth needs to reach a compromise between the tracking speed and signal-to-noise ratio of the estimators, which poses a great challenge for the application of ADRC controller on attitude control of the FMAV [27; 28]. In addition to the lack of accurate model information, strong-coupling dynamics between attitude axes are the other significant feature. Although the decoupling of control torque and force between each axis is taken into consideration as much as possible during the mechanism design, there still exists coupling due to the limitation of the actuators' number and the complexity of the air force. In most of the above literature, the input of each actuator was assigned as a linear addition of the relevant controllers' output [15; 16]. This approach is based on the assumption that the cross-axis coupling effect is not significant near the trim condition of the hovering FMAV. Although this method is more convenient for implementation, a reasonable control allocation based on the model is needed to obtain a larger domain of controllable flights. In this paper, we concentrate on the control of a FMAV capable of hovering with unknown or time-varying model parameters relying on onboard sensors alone, the detailed hardware scheme is presented. Additionally, an adaptive controller designed by the backstepping method and a reasonable control allocation are proposed. To reduce the overshoot of the states controlled, a Tracking Differential (TD) is included as the reference regulator. The effectiveness of the proposed controller is validated through the real flight with multi-axes motion control. The main contributions are as follows: (1) A tailless FMAV capable of hovering with the attitude and altitude control relying on onboard sensors alone is proposed, which relies on onboard sensors alone. (2) An adaptive controller combined with the reference regulator is proposed and verified by the flight tests. (3) For the four-wing FMAV controlled by tilting the flapping plane, a reasonable control allocation is proposed. The rest of the article is organized as follows. Section 2 introduces the detailed design of the tailless FMAV and establishes the rotational and altitude model. Based on this model, we derive the control allocation. Section 3 discusses the control problem of the FMAV and designs the adaptive controller based on the backstepping method. In Section 4, the effectiveness of the proposed controller is verified by the simulation and flight test. Section 5 summarizes this work.