It’s easy to take for granted the sight of a bee landing on a picnic table, wall or ceiling. For many of us, our first thought is to shoo it away. When you think about what’s involved from an engineering standpoint, though, it’s really quite remarkable. Landing on a window requires the insect to see the window, decelerate, turn its whole body, and grip the smooth surface. Try writing software to make a radio-controlled helicopter or drone do that. The scientific and mathematical knowledge required is daunting, but a fly or bee does it with ease.

Figuring that there must be a simple rule in the process somewhere, Emily Baird of Lund University and three German and Australian colleagues watched bees land. The research was reported by the University of Queensland, and on The Conversation. Here was the question on their minds, from their paper in PNAS:

Landing is a challenging aspect of flight because, to land safely, speed must be decreased to a value close to zero at touchdown. The mechanisms by which animals achieve this remain unclear. When landing on horizontal surfaces, honey bees control their speed by holding constant the rate of front-to-back image motion (optic flow) generated by the surface as they reduce altitude. As inclination increases, however, this simple pattern of optic flow becomes increasingly complex. (Emphasis added.)

They watched and measured the trajectories of bees landing on vertical surfaces. Enough observation generated a testable model: "We find that landing honey bees control their speed by holding the rate of expansion of the image constant" — not the expansion itself, but the rate of expansion. Obviously the image of the surface spreads as you approach it. The rate of spread, though, is the secret: hold that rate constant, and the landing becomes much simpler.

The team developed a model based on that rule and rigorously tested it. Sure enough, "it can effectively be used to guide smooth landings on surfaces of any orientation, including horizontal surfaces." Nature had provided a shortcut to the solution of a real-world problem:

This biological strategy for guiding landings does not require knowledge about either the distance to the surface or the speed at which it is approached. The simplicity and generality of this landing strategy suggests that it is likely to be exploited by other flying animals and makes it ideal for implementation in the guidance systems of flying robots.

This strategy, they said, was "unlike all current engineering-based methods" for landing a robot. An engineer might have assumed that it is necessary to constantly track the distance to the surface and the flying speed. That can work, but it is "computationally demanding," the scientists realized. How can insects, with small brains and fixed-focus eyes unsuited for stereoscopic measurement, do it? The "biological strategy" they uncovered works so well because of its "simplicity and generality."

They knew that landing on a horizontal surface is the simplest case. To land on a tabletop, all the insect has to do is measure optic flow (the speed of image motion on the retina) and hold it constant. Consequently, just prior to touchdown, flight speed decreases to near zero — no crash landings result. Landing in other orientations, though, requires additional vector calculus, yet angled landings are the most common kind for honeybees.

It is important, therefore, to ask whether bees — and flying animals in general — possess a universal landing strategy that can operate in a variety of circumstances, including approaches to horizontal, vertical, and oblique surfaces, as well as small, raised objects such as flowers.

And so the hunt for the design solution was on. As part of their experimental setup, they prepared a target on which they could artificially manipulate the apparent rate of image expansion, using spirals and other patterns they could rotate in either direction. To visualize the challenge, "play bee" for a moment and picture yourself in a flight simulator with rotating patterns out the window. Your job is to land on that artificially manipulated surface. Once you learn the secret, you could do it again and again as the operator tries to trip you up.

If their hypothesis was true, they could predict the bees’ approach. They graphed their predictions, and found that, even with the rotating pattern producing expanding or contracting spirals, it was hard to fool the bees: "The large difference between this theoretical curve and the angular velocities that the honey bees actually experience during the landing indicates that, for each speed of spiral expansion, the bees are doing a very good job of adjusting their approach speed to maintain a constant rate of image expansion throughout the landing," they said.

This surprisingly elegant strategy for guiding landings does not require knowledge of the distance to the surface, or of the speed of approach — it only requires measurement of the rate of expansion of the image of the surface. Because image expansion is the only cue that is required, an added advantage of this strategy is that it does not require a constant attitude in pitch, roll, or yaw.

Though simple, clearly there is a lot more going on. In the bees’ world, flat vertical surfaces are rare. Additional calculations must factor into their mechanisms for sensing and landing on dynamic and rounded surfaces, like flower petals moving in a breeze. They also need to operate their landing gear on a variety of textures. Imagine the challenge of landing upside down on a glass ceiling! Nonetheless, the research team made a significant discovery for this one aspect of the bees’ landing skill, providing a take-home message for robot designers on how to safely land a craft with less on-board computation.

Conclusions

Once again, intelligent design is the key to the story. The authors had no need of Darwinism; in fact, they never mentioned evolution, even in passing. They knew, rather, that they were dealing with an engineering problem — one that transcends the biological world: "Orchestrating a safe landing is one of the greatest challenges for flying animals and airborne vehicles alike" was their first sentence.

Aware that flight engineers face exactly the same challenges as do insects, birds and bats, they looked to nature for inspiration. Everyone knows that flying animals rarely make mistakes when landing. It’s only natural, therefore, that these researchers thought they could learn something from a successful case. It doesn’t really matter that it was a honeybee. If they had captured a drone from China that could land on a vertical surface, don’t you think they would study it in much the same way? Whether a flying machine is made of cells or metal, it has to solve problems of physics and mathematics. In our universal experience, the ones that succeed at complex engineering problems are products of intelligent design.