Robustness analysis of minimally-actuated flapping wing systems due to aerodynamic modeling uncertainty

In this paper, we study the robustness of minimally-actuated 3D flapping wing hovering systems under aerodynamic modeling uncertainties. Our goal is to evaluate and compare the vehicles’ robustness under commonly used control scheme and provide guidelines for control design stage. For this purpose, we first develop a 3D flapping wing dynamical model and find a desired hovering flight mode based on the nominal estimate of the aerodynamic characteristics. Then, we parameterize the wing kinematics in a novel way to allow the system to generate recovering aerodynamic forces. Using this parameterization, the control inputs are defined as the variable-time segments of the wingbeat cycle. We use the discrete LQR framework to design three controllers, each focused on a different objective: i) least control input change, ii) fast convergence rate and iii) least state residue. To study the robustness, we apply the controllers to the nonlinear system with aerodynamic uncertainty and through exhaustive simulations, we find the range of uncertainties that lead to stable response. The results show that controller (i) has the largest tolerance for drag and lift coefficient uncertainties. Moreover, this controller is robust on the uncertainties from lift offset phase over a wide range (up to 90 degrees) but has narrower tolerance to drag offset phase changes, especially towards the positive offset angles. Considering inherent uncertainty associated with the quasi-steady models, the results suggest to use a slightly larger than nominal value (upper bound) aerodynamic coefficients for control design to enjoy a greater tolerance (more robustness). This is true for both the magnitudes as well as the offset angles used in lift and drag functions.