Researchers develop model for stable flapping flight of robots

A research team at Cornell University has developed a computer model that maps the complex physical influences on the stable flight of birds and insects. The model can be used to build flapping robots that exhibit similarly stable flight characteristics to their biological role models. Furthermore, it can be used to understand and research the evolution of flapping birds and insects.

Building bird- or insect-like robots that can fly stably powered by flapping is not trivial. The difficulty lies in the morphology of birds and insects. The body structure plays a crucial role in stabilization during flight, as the researchers write in the study “Stable flapping flight in morphological space: Model, simulation, and explicit stability criteria,” which was published in Proceedings of the National Academy of Sciences (PNAS).

Zheng Jane Wang, Professor of Physics and Mechanical Engineering and lead author of the study, had already investigated about ten years ago how the neural circuits of fruit flies evolved to improve their flight stability. Wang and her research team discovered at the time, using a 3D computer simulation, that fruit flies can sense and stabilize their body position in space with each wingbeat, which occurs approximately every 4 ms.

However, this finding cannot be applied to all insects. Accordingly, a simulation would need to be developed that is capable of mapping the flight of various different insects. Other scientific studies on the topic are also limited to models of individual real insects. This means that research misses out on all other possible flight combinations, explains Wang.

Calculations in “five-dimensional morphological and kinematic space”

The team at Cornell University has therefore chosen a different approach in their latest research. The scientists reduced the 3D model in such a way that the crucial physical principles of body-wing coupling and unsteady aerodynamics (time-dependent air flows where pressure and forces are not constant) are retained. From the new model, the researchers derived equations from which they could deduce the crucial physical parameters: the ratio of wing to body mass, the wing loading, the position of the wing joint, and the flapping frequency and amplitude of the wing movement. The scientists refer to this as “five-dimensional morphological and kinematic space.”

“The power of this model is to give us something much more explicit than what we had before,” says Wang. “We knew the fundamental physics. By capturing the essential physics in the new model, we can understand each piece conceptually as well as facilitate computation to explore a large parameter space.”

The analysis of the results of the calculations in the “five-dimensional” space yielded two explicit formulas that provided criteria for the often-neglected coupling between wing inertia and body. This essentially involves the interplay of flapping frequency, joint position, and the ratio of wing to body mass. If everything works together in the right proportion, a kind of anti-resonance state is achieved, which allows the bird or insect to control its body vibrations to achieve passive, stable flight. Passive stable flight means flight that is stable despite air disturbances that would normally cause the bird or insect to tumble.

The scientists realized that many different forms of flapping can exhibit passive stability. Previous studies had shown that most insects are passively unstable and therefore use neural circuits for their flight control.

Assistance in constructing flapping robots

With knowledge of the stability limit, the researchers can now derive a concrete design principle for the stable flapping of robots.

“In principle, this opens up a completely new path for the development of a flapping robot,” says Wang. “Instead of relying on extensive feedback control, which is only partially successful, our results suggest that we can adjust the shape and frequency of the flapping organs so that the flying devices are already passively stable according to these two rules. This would significantly simplify flight control.”

The model developed by the researchers can now be used to perform simpler calculations for the construction of flapping robots. It can also be used to model stability characteristics that enable the evolution of winged animals and insects to be understood and researched.

“During evolution, various traits are selected, but we don't have much idea about what they are, let alone understand why they are being selected and how they evolve, apart from a very few examples, such as an eye,” says Wang. “This project brings new quantitative methods to study these very big questions in both biology and robotics. Mathematical modeling allows us to go beyond our ideas and preconceptions to tackle these large questions.”

(olb)