In this work, a multi-objective optimization framework is developed for optimizing low Reynolds number ([Formula: see text]) hovering flight. This framework is then applied to compare the efficiency of rigid revolving and flapping wings with rectangular shape under varying [Formula: see text] and Rossby number ([Formula: see text], or aspect ratio). The proposed framework is capable of generating sets of optimal solutions and Pareto fronts for maximizing the lift coefficient and minimizing the power coefficient in dimensionless space, explicitly revealing the trade-off between lift generation and power consumption. The results indicate that revolving wings are more efficient when the required average lift coefficient [Formula: see text] is low (<1 for [Formula: see text] and <1.6 for [Formula: see text]), while flapping wings are more efficient in achieving higher [Formula: see text]. With the dimensionless power loading as the single-objective performance measure to be maximized, rotary flight is more efficient than flapping wings for [Formula: see text] regardless of the amount of energy storage assumed in the flapping wing actuation mechanism, while flapping flight is more efficient for [Formula: see text]. It is observed that wings with low [Formula: see text] perform better when higher [Formula: see text] is needed, whereas higher [Formula: see text] cases are more efficient at [Formula: see text] regions. However, for the selected geometry and [Formula: see text], the efficiency is weakly dependent on [Formula: see text] when the dimensionless power loading is maximized.
Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.
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