Elastic storage enables robustness of flapping wing dynamics

Flying insects could perform robust flapping-wing dynamics under various environments while minimizing the high energetic cost by using elastic flight muscles and motors. Here we propose a fluid-structure interaction model that couples unsteady flapping aerodynamics and three-torsional-spring-based elastic wing-hinge dynamics to determine passive and active mechanisms (PAM) in bumblebee hovering. The results show that a strategy of active-controlled stroke, passive-controlled wing pitch and deviation enables an optimal elastic storage. The flapping-wing dynamics is robust, which is characterized by dynamics-based passive elevation-rotation and aerodynamics-based passive feathering-rotation, capable of producing aerodynamic force while achieving high power efficiency over a broad range of wing-hinge stiffness. A force-impulse model further confirms the capability of external perturbation robustness under the PAM-based strategy.