Equilibrium State for a Tailless Flapping Wing Micro Air Vehicle in Forward Flight

Flapping wing Micro Air Vehicles (FWMAVs) hold great potential for real-world applications but are currently still hard to model. In this article, a simplified analysis of the equilibrium state of a tailless FWMAV in forward flight is presented. The definition of the equilibrium state complements previous dynamic and stability analysis, adding new information about the flight behavior of FWMAVs. A new aerodynamic decoupled model has been used for the analysis, considering separately the thrust force generated by the flapping movement and the lift and drag caused by the forward velocity. The aerodynamic forces are included in a dynamic model of the FWMAV, and the equilibrium state is derived. The formulation obtained is explicit in terms of the pitch actuator deflection, thus allowing its use for control corrections, and provides an estimation of the flight velocity. The thrust needed to maintain height is also formulated, demonstrating that forward flight is more efficient than hovering. The results are validated experimentally for the pitch angle, showing good agreement with the analytical results. Then, the dynamics of the FWMAV are simulated, comparing the results with experiments where the FWMAV goes from hovering to a specific pitch reference while maintaining its height. Additional simulations are performed with basic control considerations, showing how considering the equilibrium state for a feed-forward control significantly improves the flight behavior compared to PI and PID controllers, reducing the convergence time.