The paper deals with the development of a bounded control law for Flappingwing Micro Aerial Vehicles (FMAVs) that mimics a strategy adopted by animal flapping flyers to stabilize their orientation. The control consists on generating torques about the body's principal axes by means of a modulation of the wing angle amplitudes. It is known that flapping flyers orient their body without any numerical computation or estimation of their current attitude. Therefore, the proposed control law is computed using the direct measurements of on-board sensors mimicking animal sensitive organs, more specifically the halteres, legs sensilla and magnetic sense. The technological equivalents of these biological sensors are respectively three rate gyros, a tri-axis accelerometer and a tri-axis magnetometer. Besides, the control signal is bounded to keep the wing angle amplitudes below the maximal values. Owing to its simplicity, this control law is suitable for applications where on-board computational resources are limited. The stability of the closed loop system is proved based on Lyapunov analysis and averaging theory. The effectiveness of the proposed control law is shown in simulations. The robustness with respect to external disturbances is also shown emphasizing the importance and need of the bounded control.