Rock and roll: how flies control their flight [with video]
Flies stabilize themselves during flight using a control reflex that is among the fastest in the animal kingdom. The findings described below are important for the basic understanding of animal locomotion and for the development of tiny flapping robots.
HFSP Cross-Disciplinary Fellow Tsevi Beatus and colleaguesauthored on Mon, 05 October 2015
The flight of flapping insects is a complex process that is beautiful to watch. One of the reasons flapping flight is so intriguing is that it is inherently unstable: similar to balancing a stick on one's fingertip, flapping flight is subject to rapid instabilities that must be constantly controlled to allow stable flight. For flies, the most unstable motions are rotation about their long body axis, called roll, and rotation consisting of “nose up” or “nose down” motion, called pitch. If a fly did not control its roll or pitch angles, it would tumble and crash within just a few wing-beats. Yet, flies manage to control this rapid instability and even perform extreme maneuvers, better than any man-made flying device.
Figure: Roll perturbation and correction. Images from three orthogonal fast cameras of a roll correction maneuver. The three-dimensional-rendered fly represents the measured body and wing motion. A 2mm magnetic pin was glued on the fly’s back, allowing us to use a magnetic field to “trip” the fly in mid-air. The pin added about 20 percent to the fly’s mass and did not interfere with its normal flight. The pin is best seen in the side-view images on the back “wall” of the illustration. The location of the fly during the 5ms magnetic perturbation (red line) is shown on the fly’s center-of-mass trajectory (green). In the second snapshot, the fly is rolled 60 degrees to its left. The fly fully corrected its body roll angle within eight wing beats (35ms) from the onset of the perturbation. The fly responded to the perturbation within 5ms, placing the fly’s roll-control response among the fastest reflexes in the animal kingdom.
To study the mechanism insects use to control their unstable roll and pitch angles we use common fruit flies as a model system. We developed a method to “trip” the flies in mid-air and film how they recover from these stumbles. Specifically, we glue a tiny magnet to the back of each fly and use a magnetic pulse to rotate it in mid-air either along its roll or pitch angles. We filmed the fly’s correction maneuvers using three high-speed cameras and developed an image analysis method to measure the intricate motion of the wings during the recovery maneuvers.
We found that flies manage to correct for impulsive perturbations along their roll angle that rotate them up to 100 degrees within 30 milliseconds; in a blink of an eye, the fly can perform this entire correction maneuver 10 times. The flies start to respond to the perturbation within 5ms, or a single wing-beat, which puts the roll correction reflex among the fastest in the animal kingdom .
Flies perform the maneuver by flapping one wing harder than the other for between two and five wing beats, and the resulting left-right force imbalance leads to corrective torque. We quantified the asymmetric wing amplitudes using a linear controller model called proportional-integral controller, that is mathematically similar to those used in cruise-control systems. However, when flies were perturbed along two axes – roll and yaw (rotation about the vertical axis that determines the fly’s heading) – at the same time, they corrected their roll angle but did not fully correct the yaw deflection, which is typically corrected in yaw-only perturbation. These observations suggest the overarching control architecture of the fly may include nonlinear coupling of different body angles. To further test the roll control mechanism, we challenged the flies by applying a series of perturbation pulses and rolling them right over in full turns. Surprisingly, the flies managed to recover from this extreme perturbation very quickly, within a few wing-beats .
To study how flies control the second unstable angle, body pitch, we performed a similar set of experiments, in which we exerted pitch up and pitch down deflections of up to 40 degrees. The flies corrected for these perturbations within 30 milliseconds by symmetrically modulating the front position where the wings flip between a forward and back stroke. Flies initiate this corrective reflex 10 milliseconds, or two wing beats, after the perturbation onset. Analysis and numerical simulations show that, as for roll, the pitch response can be well-described by a linear proportional-integral controller. Remarkably, flies can also correct for very large-amplitude pitch perturbations, greater than 150 degrees, providing a regime in which to probe the limits of the linear-response framework .
During pitch and roll correction responses flies mostly modulate their stroke angle of each wing, which describes the back and forth motion of the wing in the horizontal stroke plane. Deeper examination of the roll correction maneuvers revealed asymmetric changes also in the wing-pitch angles, which describe rotation about the wing long axis. This angle directly determines the wing’s angle of attack – the angle at which the wing “cuts through the air”. Similarly to changing the angle of your hand as you stick it out the window driving on the highway and feeling the different aerodynamic forces, the angle of attack is a key parameter in governing the magnitude and direction of the aerodynamic force generated by the wing. The intricate wing-pitch motion arises from the intricate mechanism of the fly’s wing hinge, which is among the most complicated joints in the animal kingdom, as well as the complexity of the interaction between the flapping wing and its own unsteady flow field. Hence, the complexity of the wing pitch motion is akin to a flapping-flag whose motion changes the surrounding air flow that, in turn, affects the flag, forming a complex feedback loop. To understand the wing-pitch motion we used a simplified approach and modeled the torques exerted by the wing hinge as a damped spring and described the air flows using a simplified quasi-static aerodynamic force model. Numerical simulations suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters, in particular the damping coefficient. These results propose a mechanism for wing-pitch control on a sub-wing-beat timescale via modulating the spring parameters on slower time scales. Moreover, these results raise new questions, such as what physiological mechanisms correspond to the simplified spring model, how the spring parameters are modulated, and whether such a semi-passive control scheme can be applied in insect-like flying robots .
To summarize, we used mid-air perturbations and simplified models to quantify the fast flight control reflexes fruit flies use to mitigate the rapid instabilities inherent to their flight. Moreover, the striking success in which flies recover from extreme perturbations highlights the robustness of their control mechanism, and may inspire scientists and engineers who develop insect-like flying robots. Although these tiny insects are common and often a nuisance, we now have a greater appreciation for what amazing fliers they are.
Movie 1: Roll correction maneuver
Movie 2: Extreme roll perturbation
Movie 3: Pitch correction maneuver
 Controlling roll perturbations in fruit flies. Tsevi Beatus, John Guckenheimer and Itai Cohen, Journal of the Royal Society Interface, 12: 20150075 (2015)
 Pitch perfect: How fruit flies control their body pitch angle. Samuel C. Whitehead*, Tsevi Beatus*, Luca Canale and Itai Cohen, The Journal of Experimental Biology 2015 Sep 18. pii: jeb.122622. [Epub ahead of print]
 Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring. Tsevi Beatus and Itai Cohen, Physical Review E 92, 022712 (2015)