Vertical Dynamics of Flapping-Wing Flying Robot Facing Wind Disturbance: State-Dependent Riccati Equation and Equivalent Dynamics

Flapping-wing flying robots (FWFRs) are becoming a trend case study in the control field. The model of an FWFR in the gliding phase of flight is similar to an unmanned lightweight aircraft. By actuating the wings (flapping), a periodic motion disturbs the dynamics and, additionally, generates the lift and thrust forces. The actuation makes the traditional analytical dynamics complex and computationally heavy for simulations of control algorithms. In this work, the vertical dynamic of the FWFR is presented using the equivalent dynamic approach as forced base excitation. Then, a wind disturbance model is implemented to study the effect of wind gusts. The state-dependent Riccati equation (SDRE) method is applied to control the model for height regulation, exploiting its nonlinear-optimal capabilities on the nonlinear FWFR model and evaluating the system response to the wind disturbance. The SDRE results were compared with the linear quadratic regulator (LQR) controller. The SDRE mimics the LQR design and delivers a nonlinear version; hence, the LQR is a good candidate for comparing the results.