Vibrational control is an open loop stabilization technique via the application of highamplitude,
high-frequency oscillatory inputs. The averaging theory has been the standard
technique for designing vibrational control systems. However, it stipulates too high oscillation
frequency that may not be practically feasible. Therefore, although vibrational
control is very robust and elegant (stabilization without feedback), it is rarely used in
practical applications. The only well-known example is the Kapitza pendulum; an inverted
pendulum shose 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 paper, 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.
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Vibrational Control in Flapping-Wing Micro-Air-Vehicles
Flapping-Wing Micro-Air-Vehicles (FWMAVs) are
bio-inspired air vehicles that mimic insect and bird flight. The
dynamic behavior of these systems is typically described by a
multi-body, multi-time-scale, nonlinear, time-varying dynamical
system. Interestingly, this rich dynamics lead to unconventional
stabilization mechanisms whose study essentially necessitates a
mathematically rigorous analysis. In this paper, we use higherorder
averaging, which is based on chronological calculus, to
show that insects and their man-made counterparts (FWMAVs)
exploit vibrational control to stabilize their body pitching angle.
Such an unconventional stabilization cannot be captured by
direct averaging. We also experimentally demonstrate such a
phenomenon by constructing an experimental setup that allows
for two degrees of freedom for the body; forward motion
and pitching motion. We measure the response of the body
pitching angle using a digital camera and an image processing
algorithm at different flapping frequencies. It is found that
there is a flapping frequency threshold beyond which the body
pitching response is naturally (without feedback) stabilized,
which conforms with the vibrational control concept. Moreover,
we also construct a replica of the experimental setup with the
FWMAV being replaced by a propeller revolving at constant
speed, which results in a constant aerodynamic force, leaving
no room for vibrational control. The response of the propellersetup
is unstable at all frequencies, which also corroborates
the fact that the observed stabilization of the FWMAV-setup at
high frequencies is a vibrational stabilization phenomenon.
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- Award ID(s):
- 1709746
- PAR ID:
- 10081739
- Date Published:
- Journal Name:
- American Control Conference
- Page Range / eLocation ID:
- 6445-6450
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Flapping flight dynamics is quite an intricate problem that is typically represented by a multi-body, multi-scale, nonlinear, time-varying dynamical system. The unduly simple modeling and analysis of such dynamics in the literature has long obstructed the discovery of some of the fascinating mechanisms that these flapping-wing creatures possess. Neglecting the wing inertial effects and directly averaging the dynamics over the flapping cycle are two major simplifying assumptions that have been extensively used in the literature of flapping flight balance and stability analysis. By relaxing these assumptions and formulating the multi-body dynamics of flapping-wing microair- vehicles in a differential-geometric-control framework, we reveal a vibrational stabilization mechanism that greatly contributes to the body pitch stabilization. The discovered vibrational stabilization mechanism is induced by the interaction between the fast oscillatory aerodynamic loads on the wings and the relatively slow body motion. This stabilizationmechanism provides an artificial stiffness (i.e., spring action) to the body rotation around its pitch axis. Such a spring action is similar to that of Kapitsa pendulum where the unstable inverted pendulum is stabilized through applying fast-enough periodic forcing. Such a phenomenon cannot be captured using the overly simplified modeling and analysis of flapping flight dynamics.more » « less
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Abstract A limiting factor in the design of smaller size uncrewed aerial vehicles is their inability to navigate through gust-laden environments. As a result, engineers have turned towards bio-inspired engineering approaches for gust mitigation techniques. In this study, the aerodynamics of a red-tailed hawk’s response to variable-magnitude discrete transverse gusts was investigated. The hawk was flown in an indoor flight arena instrumented by multiple high-speed cameras to quantify the 3D motion of the bird as it navigated through the gust. The hawk maintained its flapping motion across the gust in all runs; however, it encountered the gust at different points in the flapping pattern depending on the run and gust magnitude. The hawk responded with a downwards pitching motion of the wing, decreasing the wing pitch angle to between −20∘and −5∘, and remained in this configuration until gust exit. The wing pitch data was then applied to a lower-order aerodynamic model that estimated lift coefficients across the wing. In gusts slower than the forward flight velocity (low gust ratio), the lift coefficient increases at a low-rate, to a maximum of around 2–2.5. In gusts faster than the forward flight velocity (high gust ratio), the lift coefficient initially increased rapidly, before increasing at a low-rate to a value around 4–5. In both regimes, the hawk’s observed height change due to gust interaction was similar (and small), despite larger estimated lift coefficients over the high gust regime. This suggests another mitigation factor apart from the wing response is present. One potential factor is the tail pitching response observed here, which prior work has shown serves to mitigate pitch disturbances from gusts.
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Accepted Manuscript1.0
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