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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Thrust enhancement and degradation mechanisms due to self-induced vibrations in bio-inspired flying robots
Bio-inspired flying robots (BIFRs) which fly by flapping their wings experience continuously oscillating aerodynamic forces. These oscillations in the driving force cause vibrations in the motion of the body around the mean trajectory. In other words, a hovering BIFR does not remain fixed in space; instead, it undergoes oscillatory motion in almost all directions around the stationary point. These oscillations affect the aerodynamic performance of the flier. Assessing the effect of these oscillations, particularly on thrust generation in two-winged and four-winged BIFRs, is the main objective of this work. To achieve such a goal, two experimental setups were considered to measure the average thrust for the two BIFRs. The average thrust is measured over the flapping cycle of the BIFRs. In the first experimental setup, the BIFR is installed at the end of a pendulum rod, in place of the pendulum mass. While flapping, the model creates a thrust force that raises the model along the circular trajectory of the pendulum mass to a certain angular position, which is an equilibrium point and is also stable. Measuring the weight of the BIFR and the equilibrium angle it obtains, it is straightforward to estimate the average thrust, by moment balance about the pendulum hinge. This pendulum setup allows the BIFR model to freely oscillate back and forth along the circular trajectory about the equilibrium position. As such, the estimated average thrust includes the effects of these self-induced vibrations. In contrast, we use another setup with a load cell to measure thrust where the model is completely fixed. The thrust measurement revealed that the load cell or the fixed test leads to a higher thrust than the pendulum or the oscillatory test for the two-winged model, showing the opposite behavior for the four-winged model. That is, self-induced vibrations have different effects on the two BIFR models. We felt that this observation is worth further investigation. It is important to mention that aerodynamic mechanisms for thrust generation in the two and four-winged models are different. A two-winged BIFR generates thrust through traditional flapping mechanisms whereas a four-winged model enjoys a clapping effect, which results from wing-wing interaction. In the present work, we use a motion capture system, aerodynamic modeling, and flow visualization to study the underlying physics of the observed different behaviors of the two flapping models. The study revealed that the interaction of the vortices with the flapping wing robots may play a role in the observed aerodynamic behavior of the two BIFRs.
more » « less- Award ID(s):
- 1846308
- PAR ID:
- 10470717
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 13
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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