Visual guidance of honeybees approaching a vertical landing surface

ABSTRACT Landing is a critical phase for flying animals, whereby many rely on visual cues to perform controlled touchdown. Foraging honeybees rely on regular landings on flowers to collect food crucial for colony survival and reproduction. Here, we explored how honeybees utilize optical expansion cues to regulate approach flight speed when landing on vertical surfaces. Three sensory-motor control models have been proposed for landings of natural flyers. Landing honeybees maintain a constant optical expansion rate set-point, resulting in a gradual decrease in approach velocity and gentile touchdown. Bumblebees exhibit a similar strategy, but they regularly switch to a new constant optical expansion rate set-point. In contrast, landing birds fly at a constant time to contact to achieve faster landings. Here, we re-examined the landing strategy of honeybees by fitting the three models to individual approach flights of honeybees landing on platforms with varying optical expansion cues. Surprisingly, the landing model identified in bumblebees proved to be the most suitable for these honeybees. This reveals that honeybees adjust their optical expansion rate in a stepwise manner. Bees flying at low optical expansion rates tend to increase their set-point stepwise, while those flying at high optical expansion rates tend to decrease it stepwise. This modular landing control system enables honeybees to land rapidly and reliably under a wide range of initial flight conditions and visual landing platform patterns. The remarkable similarity between the landing strategies of honeybees and bumblebees suggests that this may also be prevalent among other flying insects. Furthermore, these findings hold promising potential for bioinspired guidance systems in flying robots.

).The similar results are observed for the travel time ∆t * .(B) The difference between the new and the current set-point ∆r * with the current set-point r * for different factors f (Equation S3: The dependence of the set-point r * on distance to the platform y * along with the effect of different landing patterns for different factors f (Equation S4:  2).
Table S1.The number of landing maneuvers and honeybees recorded in each tested treatment, and the number of landing maneuvers that are identified with constant-r segments for different values of factor f. Table S2.The analysis of distance covered and travel time of honeybees at different set-points of relative rate of expansion.The data is extracted from 359 constant-r segments in 227 landing maneuvers of honeybees (factor f = 1.5).The post-hoc tests compare differences between the mean distance covered (∆y * ) or the mean travel time (∆t * ) in three set-point regions: low (r * ≤ 2.58 s −1 ), medium (2.58 s −1 < r * ≤ 3.29 s −1 ) and high (r * > 3.29 s −1 ) (statistical model as given by Equation S2: Table S3.The analysis of transition between the set-points of relative rate of expansion observed in honeybees and bumblebees during their approach towards a landing surface.

Effect on ∆y
For honeybees, the data is extracted from 132 transitions in 100 landing maneuvers with more than one constant-r segments (factor f = 1.5).(statistical model as given by Equation S3:

Fixed effect
Fig.S1.The comparison of raw data with the low-pass filtered data.Approach velocity V and relative rate of expansion r with perpendicular distance to the landing platform y for a landing approach towards a checkerboard pattern (A), gray pattern (B), horizontally striped pattern (C) and random Julesz pattern (D).In each panel, the identified constant-r segments are highlighted in red and the raw data (black) is overlayed on the low-pass filtered data (orange).

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Fig. S2.The effect of factor f on the results.(A) The distance covered by honeybees ∆y * with three regions of optical expansion rate set-point r * for different factors f (Equation S2: ∆y* i,s,f ∼ N(α + αs + α f + β 1 MEDIUM i,s,f + β 2 HIGH i,s,f , σ 2 )).The similar results are observed for the travel time ∆t * .(B) The difference between the new and the current set-point ∆r * with the current set-point r * for different factors f (Equation S3:∆r * i,s,f ∼ N(α + αs + α f + β 1 r * i,s,f , σ 2 )).(C)The dependence of the set-point r * on distance to the platform y * along with the effect of different landing patterns for different factors f (Equation S4:log(r * i,s,f ) ∼ N(α + αs + α f + 9 j=1 β j PATTERN j,i,s,f + m log(y * i,s,f ), σ 2 )).(A-C)The vertical bars for each coefficient indicate 95% confidence intervals.
Fig. S3.The set-point of optical expansion rate r* with distance to the surface y* in the logarithmic domain as identified by the linear mixed-effects model in Equation S4 (Table2).
Movie 1.A honeybee landing on a checkerboard pattern, recorded using the top camera.Playback is slowed down 16 times.