Passive pitch rotation enables optimal vibrational stabilization in hawkmoth forward flight

Flying insects maintain stable flight through both active control and passive mechanisms that exploit natural wing and body vibrations. One such mechanism, vibrational stabilization, uses high-frequency wing vibrations to create a virtual spring effect that helps insects like hawkmoths stay stable during hovering. In addition, the flexible musculoskeletal system contributes pitch stiffness to add a stabilizing effect that may vary with forward flight speed but has not been fully explored. This study develops a fluid-structure interaction model that integrates the dynamics of an elastic wing hinge with unsteady flapping aerodynamics. We introduce a vibrational stabilization framework to investigate the passive stability of the hawkmoth Manduca sexta across a broad range of forward flight velocities. The framework reveals that natural wing vibrations enhance flight stability at all speeds. At low speeds, vibrational stiffness generates a restorative pitching moment, while at higher speeds, damping effects from wing vibrations dominate. The model shows that biologically realistic hinge stiffness values optimize vibrational stabilization throughout the flight envelope. This flexible-vibrational mechanism significantly improves robustness against external pitch disturbances, reducing reliance on active neural control. These findings offer useful design principles for biomimetic flying robots, potentially simplifying their control architectures.