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: A hidden stabilization mechanism in insect flight
It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.
more » « less- Award ID(s):
- 1846308
- PAR ID:
- 10195864
- Publisher / Repository:
- American Association for the Advancement of Science (AAAS)
- Date Published:
- Journal Name:
- Science Robotics
- Volume:
- 5
- Issue:
- 46
- ISSN:
- 2470-9476
- Page Range / eLocation ID:
- Article No. eabb1502
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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