Vibrational Control: A Mysterious Stabilization Mechanism In Insect Flight

Insect flight has been a puzzle for aeronautical engineers and biologists for a century, particularly its flight stability. Over the past two decades, there has been a near-consensus among the biology and the engineering communities that insects are unstable at hover. This widely accepted result is based on direct averaging of the flight dynamics over the flapping cycle. From a different perspective, it is well-known to dynamicists that an oscillatory system (such as the inverted pendulum) may gain stability without feedback through a phenomenon called vibrational stabilization. In the honor of the 70th birthday of the great Pontryagain, Agrachev and Gamkrelidze developed a new calculus for time-varying systems: the chronological calculus. Using this less-known calculus, we showed a hidden passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. The oscillations of an insect’s body around the hovering equilibrium naturally stabilizes its flight dynamics, similar to the inverted pendulum. This stabilization technique cannot be captured using the direct averaging approach, commonly used in literature. It is a fascinating design by Nature where the flapping of the insect wings, that is inevitably needed to create an aerodynamic force for lifting, naturally provides stability for free without feedback.