The fast flight stabilization strategy in flying insects

• A PD-based control model is developed to solve the closed-loop dynamics of insect flight. • Our results show that insects achieve fast flight stabilization by minimizing restoring time. • We demonstrate that passive aerodynamic damping plays a critical role in stabilizing flight. • This strategy provides valuable insights for flight controller design in bioinspired flying robots. Flying insects demonstrate remarkable control over their body movements and orientation, enabling them to perform rapid maneuvers and withstand external disturbances in just a few wing beats. This fast flight stabilization mechanism has captured the interest of biologists and engineers, driving the exploration of flapping-wing flight control systems and their potential applications in bioinspired flying robots. While many control models have been developed within a rigorous mathematical framework using linear feedback systems, such as proportional (P), integral (I), and derivative (D)-based controllers, the exact mechanisms by which insects achieve the fastest stabilization—despite constraints such as passive aerodynamic damping and feedback delay—remain unclear. In this study, we demonstrate that flying insects employ a novel strategy for fast flight stabilization by minimizing the restoration time under external perturbations. We introduce a versatile PD-based control model that solves the closed-loop dynamics of insect flight and optimizes flight stabilization within a mathematical framework. Our findings reveal that passive aerodynamic damping plays a crucial role in stabilizing flight, acting as derivative feedback without delay, whereas feedback delay hinders stabilization. Additionally, we show that minimizing the restoring time leads to the fastest flight stabilization. Hovering flight analyses of fruit flies, honeybees, hawkmoths, and hummingbirds suggest that restoring time minimization through dynamic oscillatory modes rather than closed-loop time constants is a common strategy among small bioflies for effective maneuvering against disturbances. This strategy, which spans a broad range of Reynolds numbers (on the order of 10 2 to 10 4 ), could offer valuable insights for designing flight controllers in bioinspired flying robots.