Edited by John G. Hildebrand, University of Arizona, Tucson, AZ, and approved September 24, 2013 (received for review July 31, 2013)
In this study, we investigate the cues that honey bees use to land on vertical surfaces. We show that bees use the apparent rate of expansion of the image generated by the surface to smoothly reduce their speed when landing. From our results, we develop a mathematical model for visually guided landing that, unlike all current engineering-based methods, does not require knowledge about either the distance to the surface or the speed at which it is approached. This strategy is not only specific to landings on vertical surfaces or to honey bees but represents a universal strategy that any flying agent (animal or machine) could use to land safely on surfaces of any orientation.
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. How do honey bees control speed when landing on surfaces that have different orientations? To answer this, we analyze the trajectories of honey bees landing on a vertical surface that produces various patterns of motion. We find that landing honey bees control their speed by holding the rate of expansion of the image constant. We then test and confirm this hypothesis rigorously by analyzing landings when the apparent rate of expansion generated by the surface is manipulated artificially. This strategy ensures that speed is reduced, gradually and automatically, as the surface is approached. We then develop a mathematical model of this strategy and show that it can effectively be used to guide smooth landings on surfaces of any orientation, including horizontal surfaces. 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.
Author contributions: E.B., M.R.I., and M.V.S. designed research; E.B. performed research; N.B. and M.R.I. contributed new methods; E.B. analyzed data; and E.B., N.B., and M.V.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1314311110/-/DCSupplemental.
