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Meeting	ACGS Committee Meeting 122 - Savannah, GA - October 2018
Agenda Location	8 SUBCOMMITTEE D – Dynamics, Computations and Analysis 8.1 Vibrational Control: Mysterious Stabilization Mechanism in Insect Flight
Title	Vibrational Control: Mysterious Stabilization Mechanism in Insect Flight
Presenter	Haithem Taha
Affiliation	UCI
Available Downloads*	presentation
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Abstract	Vibrational control is an open loop stabilization technique via the application of high-amplitude, high-frequency oscillatory inputs. The averaging theory has been the standard technique for designing vibrational control systems. One of the most well-known examples is the Kapitza pendulum: an inverted pendulum whose pivot is subject to vertical oscillation. the unstable equilibrium of the inverted pendulum gains asymptotic stability due to the high-frequency oscillation of the pivot. In this presentation, we provide a new vibrational control system from Nature: flapping flight dynamics. Flapping flight is a rich dynamical system as a representative model will typically be nonlinear, time-varying, multi-body, multi-time-scale dynamical system. Over the last two decades, using direct averaging, there has been consensus in the flapping flight dynamics community that insects are unstable at the hovering equilibrium due to the lack of pitch stiffness. In this work, we perform higher-order averaging of the time-periodic dynamics of flapping flight to show a vibrational control mechanism due to the oscillation of the driving aerodynamic forces. We also experimentally demonstrate such a phenomenon on a flapping apparatus that has two degrees of freedom: forward translation and pitching motion. It is found that the time-periodic dynamics of the flapping micro-air-vehicle is naturally (without feedback) stabilized beyond a certain threshold. Moreover, if the averaged aerodynamic thrust force is produced by a propeller revolving at a constant speed while maintaining the wings stationary at their mean positions, no stabilization is observed. Hence, it is concluded that the observed stabilization in the flapping system at high frequencies is due to the oscillation of the driving aerodynamic force and, as such, flapping flight indeed enjoys vibrational stabilization. We also show the underpinning physics behind this phenomenon. It is found that vibrational stabilization in flapping flight is mainly due to interactions between the wing motion and body dynamics; more specifically due to synchronization between the flapping waveform and the oscillatory response of the body horizontal speed due to pitch disturbances. Finally, a real moth experiment is considered where the moth is disturbed in pitch while recording body and wing motion via a motion capture system. These motions are then fed to an aerodynamic model that determines the pitching moment and, hence pitch stiffness. It is found that the contributions from the oscillatory, zero-mean component of the body motion (i.e., vibrational effects) are always stabilizing and dominate feedback effects. Moreover, he contributions from the averaged body motion are always destabilizing (i.e., resulting in negative stiffness).