- Award ID(s):
- 1709746
- PAR ID:
- 10081740
- Date Published:
- Journal Name:
- AIAA SciTech
- 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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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.more » « less
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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.
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Abstract 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.
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Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta , we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flapping flyers.more » « less