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Researchers in the US have shed new light on the puzzling and complex flight physics of creatures such as hummingbirds, bumblebees and dragonflies that flap their wings to hover in place. According to an interdisciplinary team at the University of Cincinnati, the mechanism these animals deploy can be described by a very simple, computationally basic, stable and natural feedback mechanism that operates in real time. The work could aid the development of hovering robots, including those that could act as artificial pollinators for crops.
If you’ve ever watched a flapping insect or hummingbird hover in place – often while engaged in other activities such as feeding or even mating – you’ll appreciate how remarkable they are. To stay aloft and stable, these animals must constantly sense their position and motion and make corresponding adjustments to their wing flaps.
Feedback mechanism relies on two main components
Biophysicists have previously put forward many highly complex explanations for how they do this, but according to the Cincinnati team of Sameh Eisa and Ahmed Elgohary, some of this complexity is not necessary. Earlier this year, the pair developed their own mathematical and control theory based on a mechanism they call “extremum seeking for vibrational stabilization”.
Eisa describes this mechanism as “very natural” because it relies on just two main components. The first is the wing flapping motion itself, which he says is “naturally built in” for flapping creatures that use it to propel themselves. The second is a simple feedback mechanism involving sensations and measurements related to the altitude at which the creatures aim to stabilize their hovering.
The general principle, he continues, is that a system (in this case an insect or hummingbird) can steer itself towards a stable position by continuously adjusting a high-amplitude, high-frequency input control or signal (in this case, a flapping wing action). “This adjustment is simply based on the feedback of measurement (the insects’ perceptions) and stabilization (hovering) occurs when the system optimizes what it is measuring,” he says.
As well as being relatively easy to describe, Eisa tells Physics World that this mechanism is biologically plausible and computationally basic, dramatically simplifying the physics of hovering. “It is also categorically different from all available results and explanations in the literature for how stable hovering by insects and hummingbirds can be achieved,” he adds.
The researchers and colleagues. (Courtesy: S Eisa)
Interdisciplinary work
In the latest study, which is detailed in Physical Review E, the researchers compared their simulation results to reported biological data on a hummingbird and five flapping insects (a bumblebee, a cranefly, a dragonfly, a hawkmoth and a hoverfly). They found that their simulation fit the data very closely. They also ran an experiment on a flapping, light-sensing robot and observed that it behaved like a moth: it elevated itself to the level of the light source and then stabilized its hovering motion.
Eisa says he has always been fascinated by such optimized biological behaviours. “This is especially true for flyers, where mistakes in execution could potentially mean death,” he says. “The physics behind the way they do it is intriguing and it probably needs elegant and sophisticated mathematics to be described. However, the hovering creatures appear to be doing this very simply and I found discovering the secret of this puzzle very interesting and exciting.”
Eisa adds that this element of the work ended up being very interdisciplinary, and both his own PhD in applied mathematics and the aerospace engineering background of Elgohary came in very useful. “We also benefited from lengthy discussions with a biologist colleague who was a reviewer of our paper,” Eisa says. “Luckily, they recognized the value of our proposed technique and ended up providing us with very valuable inputs.”
Eisa thinks the work could open up new lines of research in several areas of science and engineering. “For example, it opens up new ideas in neuroscience and animal sensory mechanisms and could almost certainly be applied to the development of airborne robotics and perhaps even artificial pollinators,” he says. “The latter might come in useful in the future given the high rate of death many species of pollinating insects are encountering today.”
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