Sideways maneuvers enable narrow aperture negotiation by free-flying hummingbirds

Many birds, bats and insects fly near and within dense vegetation when foraging, nesting, evading predators or engaging in aerial chases. Successfully negotiating cluttered environments requires maneuvering through narrow constrictions between obstacles, which some birds accomplish by a pause in flapping, with their wings either held at the top of the upstroke or folded at the wrist so as to reduce their effective size (Schiffner et al., 2014; Williams and Biewener, 2015). For birds that cannot hover for prolonged periods but must instead maintain a minimum forward speed, flight through obstacle fields above a critical density guarantees a collision (Karaman and Frazzoli et al., 2012). Because of delays associated with visual processing (∼50 ms; Ros and Biewener, 2016; Cheng et al., 2016a) and maneuver initiation (∼20 ms; Cheng et al., 2016a), a bird moving at 1 m s⁻¹ (relatively slow for non-hovering birds) will fly about 7 cm before it can respond to new information and change course. Although faster flight may enhance escape from predators, flight at slower speeds (and the ability to hover in particular) likely improves visual assessment of upcoming obstacles and reduces the consequences of mistakes. In addition to their well-known ability to hover, hummingbirds are highly maneuverable along multiple axes; they can fly sideways and backwards through rapid adjustments of wing stroke patterns (Sapir and Dudley, 2012; Cheng et al., 2016a). Together, these abilities may enable hummingbirds to negotiate densely cluttered environments that are inaccessible to other birds. However, one consequence of the wing mass reductions that enable hovering in hummingbirds is that they exhibit only limited wing flexion during flight, and maintain (as do their sister group, the swifts) a span ratio close to 100% during the wingbeat (Greenewalt, 1960; Hedrick et al., 2012). Unless hummingbirds implement distinctive strategies to transit narrow apertures, they may be unable to enter gaps less than one wingspan in diameter. Thus, it is unknown how the notable agility of hummingbirds also enables flight within structurally complex environments such as tropical rainforests; the extent to which aperture negotiation occurs in the real world is as yet also unstudied.

Here, we show that Anna's hummingbirds, Calypte anna, aerially negotiate structural constrictions less than one wingspan in diameter using previously undescribed strategies that do not involve wing flexion about either the elbow or the wrist. Instead, hummingbirds use maneuvers along a spectrum of control strategies characterized by two well-defined extremes, which we refer to as asymmetric and swept strategies. In the asymmetric strategy, birds performed a sideways flight maneuver that incorporated continuous, bilaterally asymmetric wing motions. In the swept strategy, birds performed a ballistic maneuver characterized by tucked, non-flapping wings. After characterizing these strategies, we hypothesized that both aperture geometry and choice of maneuvering technique would have important consequences for the overall flight trajectory. Specifically, we hypothesized that birds would alter their transit strategy over time and in response to aperture geometry. We also hypothesized that large variation in overall flight trajectories observed among apertures and over repeated trials was mediated in part by choice of transit strategy. We predicted that the asymmetric technique would be associated with less downward acceleration because it allowed for continuous flapping during transit. To test these hypotheses, we examined the relationships among flight speed, vertical acceleration and transit strategy after correcting for (i.e. conditioned on) aperture size and experience.

Four adult male Anna's hummingbirds (Lesson 1829) (mean±s.d. body mass: 4.34±0.14, 4.25±0.12, 4.58±0.15 and 4.49±0.12 g; wingspan: 12.1, 12.0, 12.1 and 12.0 cm for the four birds, respectively) were obtained from the wild in June–August 2013 using a recessed acrylic window drop-trap. Hummingbirds were housed in separate 1×1×1 m mesh cages, each containing four 10 ml syringes filled daily with nectar solution (Nektar-Plus, Nekton GmbH). The room containing the mesh cages was held at approximately 22°C and was on a 12 h light:12 h dark cycle. After 2–3 days of habituation, hummingbirds were trained to fly between two feeders positioned within a flight arena (Fig. 1B) consisting of two 60×75×100 cm volumes separated by a partition. Various apertures (Fig. 1C) were inserted into a 16×16 cm square cutout within the partition and positioned such that their centers were 30 cm below the arena ceiling to minimize aerodynamic effects of the ceiling (Leishman, 2006). Partition walls were made of white pegboard to provide depth cues during flight. The enclosure was lit from above with two 750 W tungsten lights positioned 1 m above an acrylic ceiling, which was covered with white paper to diffuse light. Although lighting was kept constant throughout all experiments, interior illumination of the arena ranged from 700 to 900 lx depending on position.

The Animal Care and Use Committee at the University of California, Berkeley, activities of which are mandated by the US Animal Welfare Act and Public Health Service Policy, approved all experimental procedures (protocol #AUP-2014-09-6676).

We motivated hummingbirds to transit between feeders using a custom-built nectar delivery system. Artificial feeders were positioned 30 cm below the ceiling at both ends of the flight arena, and were aligned with the aperture so that a line of sight ran through the aperture between the two feeders. Each feeder consisted of a plastic flower placed on a nectar reservoir adjacent to a photoresistor sensor, which detected the presence of a bird at the feeder. Each feeder reservoir provided only a small amount of nectar (10–40 µl), which we assumed hummingbirds consumed in a single visit. Feeders were automatically refilled by a servo valve controlled by an Arduino Uno microcontroller. Once a bird had visited a feeder, the nectar volume was not refreshed (via the servo valve) until the bird had been detected at the feeder on the other side of the partition. Thus, metered nectar rewards were alternately presented on opposite sides of the aperture, and hummingbirds volitionally and repeatedly shuttled between the two feeders.

Appropriate aperture sizes and training protocols were determined in a preliminary experiment using one additional hummingbird, which was not included in this study. Aperture width and height ranged between 0.5 and 1.0 wingspan in diameter (6–12 cm; Fig. 1C). To form the apertures, circular and elliptical shapes were cut out from the center of 16×16 cm squares of 3/8 inch (∼9.5 mm) thick white foamboard. White electrical tape was used to line the cut edges. Aperture dimensions were 6, 8 and 12 cm in both height and width (i.e. about 0.5–1.0 wingspan). Specific apertures [listed by height (cm)×width (cm)] were 12×12, 12×8, 8×12, 8×8, 12×6, 6×12 and 6×6. We also included one clover-shaped aperture, but only results from the circular and elliptical apertures are presented here.

We organized experimental trials into 10 sets of consecutively presented apertures. Each aperture was presented once within each set, during which the bird completed at least two transits (i.e. back and forth through the aperture). Apertures were ordered pseudorandomly within each experimental set, but the same sequence was used for all four birds. Over the course of 4–6 weeks, each bird completed 10 sets of eight apertures, for a total of at least 160 trials. The number of birds (n=4) was limited by availability, and the number of trials per aperture treatment (n=20 per bird) was chosen to (i) detect differences in behavior and performance among apertures, (ii) capture any learning that may occur over hundreds of trials, and (iii) sufficiently sample variation within each aperture size so that we could detect effects of behavior on performance after conditioning on aperture and experience variables.

Hummingbirds were first habituated to the flight arena and feeder system for 2 h, with no aperture present. All birds learned to use the feeder system during this 2 h habituation period. We then inserted an aperture and waited for the bird to transit back and forth, before replacing the aperture with a new one. Birds typically perched and occasionally re-checked the empty feeder between transits. Waiting time between transits ranged from a fraction of a second to 37 min between transits (when fitted with a log-normal distribution, the mean waiting time was 4 min and the mode was 13 s).

Birds landed on the aperture in 12 trials (one bird landed 10 times and two others landed once each). Landing trials were excluded from further analyses so that results reflect only flight behaviors. Frequently (592 of 1232 total transits), a transit was not filmed because it occurred during video downloading; in these cases, the aperture was removed and the bird was permitted to fly through the 16×16 cm square opening to the original side of the arena, at which point the original aperture was reinserted. In statistical analyses, we used the total number of aperture transits (hereafter ‘transit number’), including those not recorded on high-speed video, as a factor to model changes in performance throughout experiments. The rate of missed transits or ‘sampling intensity’ decreased slightly as transit number increased; the predicted probability of filming a transit varied between 0.4 for the first transit and 0.67 for the last transit (analysis of deviance between a logistic model including only bird ID and one including bird ID and transit number, d.f.=4, χ²=26.05, P<0.001). In simulations based on these data, uneven sampling over the range of transit number neither biased best-fit model coefficients nor inflated the type I error rate above 0.05. The absolute time from the beginning of the first day of experiments for each bird was also investigated as an indicator of experience, but we found that using the cumulative number of aperture transits resulted in better-fitting models. Instances of wing or body contact with the edge of the aperture were identified and recorded manually for all transits.

Transits were filmed laterally and from below using two high-speed cameras focused on the center of the aperture (HiSpec 1, 1280×1024 pixel resolution, Fastec Imaging Corporation). Optical axes were aligned orthogonal to gravity using a spirit level, and camera mounts remained fixed throughout experiments. Cameras were positioned about 88 cm from the center of the aperture. Trials were recorded at 500 frames s⁻¹ with 0.2 ms exposure per frame. Cameras were synchronized with phase lock, set to use a circular buffer, and manually triggered with an external TTL signal.

The trajectory of the bill tip was tracked automatically for all trials using a set of close-up template images. The position of the bill tip was reconstructed from the side and bottom camera views using a calibration checkerboard and built-in functions in MATLAB's Computer Vision System Toolbox (version 2016a, The MathWorks Inc.). A minimum-jerk trajectory (a quintic spline represented by a 5th degree polynomial for coordinates versus time) was then fitted to the bill tip trajectory using least squares. Average velocity of the bill tip during transit was calculated as =(x_exit−x_entry)/(transit duration), where x_entry and x_exit were obtained by evaluating the bill tip trajectory fit at the beginning and end of transit, respectively. The y-coordinate at these times was used to calculate the change in height of the bill tip during transit, δy=y_exit−y_entry. Average acceleration of the bill tip during transit was calculated as =(v_exit−v_entry)/(transit duration), where v_entry and v_exit were obtained by first analytically differentiating the spline fit to obtain a velocity function and then evaluating the velocity function at the beginning and end of transit, respectively.

To quantify transit behavior, wing angle was calculated from wing tip position and the estimated shoulder location, which was assumed to be fixed relative to the bill tip. Wing tip and bill tip positions (hereafter ‘keypoints’) were automatically extracted from video data using neural network keypoint detectors and custom code written in Mathematica (version 10.1, 2015, Wolfram Inc.). All trials were inspected visually for tracking errors, which occurred in 15 out of 640 trials. These errors were fixed by hand-specifying keypoint locations in several frames surrounding the error. Although it was not possible to blind investigators to treatments during experiments, the analysis software used to track bird kinematics was blinded to both aperture size and transit number. We also noted for each trial any evidence of physical contact of the wings with the aperture edges.

When performing the swept technique, birds did not roll their bodies or turn their heads, but when performing the sideways technique, both body roll and head turning led to deviations of true shoulder locations from the fixed estimates. Body roll causes the projection of the shoulders onto the horizontal plane to become more in line with the central axis of the body, leading to slightly more extreme wing angle estimates than in actuality. Head turning usually occurs simultaneously with body roll, and causes the bill tip position to shift away from the leading wing, resulting in an underestimate of the leading wing angle and overestimate of trailing wing angle. In a sample of hand-annotated, mid-aperture frames from two swept and five sideways trials, the only measurement that showed error >5 deg was the trailing wing angle when birds used the sideways technique. When combined, deviations from fixed shoulder estimates from body roll and head turning cancel out for the leading wing angle (<1 deg error), but add together for the trailing wing angle. On average, true trailing angle was 21 deg less extreme than estimated trailing wing angle. This error only occurs for the sideways technique because birds did not roll their bodies or turn their heads when performing the swept technique. The technique parameter used in subsequent analyses, leading wing angle, is therefore expected to be fairly accurate (details are available from Dryad: https://doi.org/10.5061/dryad.41ns1rnmd).

Wing angle trajectories (solid lines in Fig. 2C,F) were separated into wing angle offset (dashed lines in Fig. 2C,F) and amplitude components using local polynomial regression fitting (loess) smoothing in R (http://www.R-project.org/). Trajectories consisted of an approximately 40 Hz amplitude-modulated signal, corresponding to wing flaps, on top of a smoothly varying offset angle that changed at a lower rate (less than ∼5 Hz). The loess smoothing parameter was set based on a linear regression with trial length, which was estimated empirically by visualizing a set of example trajectories (Badger et al., 2023). The smoothed trajectories captured changes in wing sweep angle occurring over time scales much slower than a typical 25 ms wingbeat period, and tracked the angle about which the wings flapped over time. Wing stroke amplitude about the offset angle was estimated by subtracting the offset angle from the original wing angle and passing the signal through an envelope function using the ‘spectral’ package in R (https://CRAN.R-project.org/package=spectral).

Wing kinematics were highly variable over the course of hundreds of transits, so we characterized variation in wing angle offset trajectories by projecting them onto a lower dimensional manifold via principal component analysis (e.g. Riskin et al., 2008). Wing angle offset trajectories were first aligned to a common time scale using bill tip entry and tail exit from the aperture, and were then resampled to a common length (200 points). We interleaved leading and trailing wing offset angles to obtain a single vector for each transit and performed a principal component analysis using R (http://www.R-project.org/). We obtained coefficients for each resampled trajectory and visualized the modes of trajectory variation. We also assessed the proportion of variance explained by the principal components and measured the mean error of reconstructed trajectories. Although transit technique showed some evidence of being drawn from a multimodal distribution, variation in technique variables occurred over a continuous range and was therefore treated as a continuous variable in subsequent analyses (Fig. 3).

We investigated the effects of aperture negotiation on birds' mid-aperture behavior and flight trajectories using general linear models in R (http://www.R-project.org/). We parameterized transit technique (i.e. behavior within the aperture) using the mean leading and trailing wing angles, which were highly correlated with the first and second principal component of the wing kinematics analyses described above, and using the mean leading and trailing wing stroke amplitudes. We quantified aperture negotiation performance using the following four ‘performance variables’: horizontal velocity, vertical acceleration, vertical velocity and height lost during transit. To assess the effect of aperture dimensions, and transit number (hereafter ‘experimental variables’) on transit technique and performance variables, we fitted linear mixed models using the ‘nlme’ package in R (https://CRAN.R-project.org/package=nlme; http://www.R-project.org/).

In the aforementioned models, aperture width, aperture height and transit number (scaled to range from −0.5 to 0.5) were included as continuous predictors. An independent analysis was performed for each bird because the sample size (n=4) was less than that recommended for random factors (Bolker, 2015). Flight direction was included as a categorical predictor in all models to account for potential directional asymmetries between the two halves of the flight arena. Parameters for interactions among aperture width, aperture height and transit number were also included. We predicted that an increase in either height or width would have a larger effect on performance when the other dimension was smaller (a negative interaction slope) or, equivalently, that there would be an effect of total aperture area (the area of an ellipse is π×width×height). We also predicted that if birds utilized novel negotiation techniques for small apertures, performance might improve only for those apertures (i.e. there would be a negative interaction coefficient for either the width×transit number or height×transit number interactions). In contrast, flight performance might improve with transit number only for large apertures because of a hard constraint imposed by small apertures (i.e. a positive interaction coefficient for the width×transit number or height×transit number interactions). To model possible correlations among trials within a particular aperture presentation sequence due to shared but unmeasured variables (such as air pressure), a unique set identifier was included as a random factor.

To test the hypothesis that transit technique would be correlated with aperture negotiation performance after controlling for aperture dimensions and transit number, we first statistically controlled for experimental conditions to rule out spurious relationships. For example, an observed correlation between raw technique and performance measurements could arise from a model in which experimental treatment affects both technique and performance but technique does not directly affect performance, versus a model in which experimental treatment affects technique and technique also affects performance (Badger et al., 2019). Specifically, we first modeled technique and performance variables as linear functions of presentation set, aperture dimensions, flight direction and transit number as described above, and obtained residuals rT and rP for technique and performance variables, respectively. We then assessed correlations between these residuals to determine whether the technique influenced performance. We determined the significance of correlations between residuals of the performance models (rP) and the residuals of the technique model (rT) using a Pearson's product-moment correlation test. All P-values were adjusted to control for false discovery rate (Benjamini and Yekutieli, 2001).

Normality of residuals was checked qualitatively for all models, and homogeneity of variance was tested for all variables in all models (Pinheiro and Bates, 2000). As expected, variance in wing asymmetry (as parameterized by leading wing angle) was slightly lower for the smallest aperture than for the others because birds almost exclusively used the swept technique to transit the smallest aperture. We incorporated unequal variance across apertures into the models (to account for this mild heteroscedasticity) using the ‘weights’ argument of the ‘gls’ function in ‘nlme’ (https://CRAN.R-project.org/package=nlme; http://www.R-project.org/), but doing so changed neither the direction nor the magnitude of parameter estimates.

To investigate differences among birds, we refitted the above models on the full dataset and included bird ID as a fixed effect with four levels. We then performed simultaneous tests for general linear hypotheses post hoc tests using the ‘emmeans’ (https://CRAN.R-project.org/package=emmeans) package. In these models, we included parameters for bird ID interactions with transit number, transit number by height, and transit number by width to allow for the effect of transit number, transit number×height, and transit number×width to vary independently among birds.

We also conducted analyses with aperture shape parameterized as a categorical variable (rather than using values for aperture width and height) followed by post hoc comparisons among apertures, but doing so did not change either the significance or the interpretation of the main results. In addition, we evaluated the effect of transit number on transit technique and performance variables using generalized additive models, but the observed relationships did not appear to be non-linear and the estimated associations between residual performance variables were unchanged. Also, residual leading wing angle did not differ in either magnitude or significance between the additive and linear models. We therefore chose to use linear mixed models because they allowed estimation of a slope parameter for transit number.

Two well-defined strategies were used to negotiate narrow apertures (Movie 1), one of which was a distinctive sideways maneuver characterized by asymmetric wing motions (Fig. 2A–C; Movie 1). Here, birds shifted the mean position of the leading wing forward and that of the trailing wing backward, but continued to flap throughout transit. Thus, the leading wing, body and then trailing wing sequentially entered and exited the aperture. A second transit strategy involved bilaterally symmetric positioning of the wings, whereby birds paused flapping and held both wings approximately 90 deg backwards from the transverse axis (Fig. 2D–F; Movie 1). For this case, birds varied the extent to which the wings were posteriorly positioned, but did so symmetrically about the sagittal plane.

To more finely characterize transit strategy, we collected trajectories of the left and right wing angles for each trial using video sequences from the bottom view camera (Fig. 2B,E), and projected wing angle offset trajectories during transit onto a lower dimensional manifold (via principal component analysis; see Materials and Methods). The first principal component (PC1) was highly correlated with mean leading wing angle averaged over each transit (r=0.99, P<0.001 for all birds; Fig. S1), and was also correlated with the leading wing stroke amplitude (r=0.63, 0.54, 0.74 and 0.60 for the four birds, respectively, P<0.001 for all birds) and trailing wing stroke amplitude (r=0.77, 0.71, 0.76 and 0.71 for the four birds, respectively, P<0.001 for all birds). The second principal component (PC2) was highly correlated with mean trailing wing angle as averaged over each transit (r=0.99, P<0.001 for all birds), and was only slightly correlated with leading wing stroke amplitude (r=0.11, 0.48, 0.55 and 0.26, P=0.21, <0.001, <0.001 and =0.002 for the four birds, respectively). Because of these strong correlations, we hereafter use ‘mean leading wing angle’ and ‘mean trailing wing angle’ to refer to PC1 and PC2, respectively. The third principal component (PC3) influenced the timing of the peak shift in wing angle offset relative to aperture entry and exit, but PC3 was not analyzed further. Wing angle trajectories reconstructed using PC1, PC1 and PC2, and PC1 to PC3 explained 48%, 87% and 95% of the variation, respectively, in trajectory data for wing angle offset. Mean error between reconstructed and wing angle offset trajectories was 14, 8.5 and 5.9 deg, respectively. Although many trials qualitatively exhibited asymmetric and swept postures, the distributions of mean leading and trailing wing angles indicate that birds used maneuvers along a spectrum between the asymmetric and swept extremes (Fig. 3). To further investigate why transit technique varied so greatly, and why hummingbirds used one technique over another, we measured several flight performance metrics derived from each transit.

We found that transit strategy significantly influenced the overall flight trajectory (Fig. 4). With the asymmetric technique, hummingbirds flew more slowly and did not accelerate downward as quickly (as indicated by vertical acceleration of the bill tip) as with the swept technique. Greater bilateral wing asymmetry (as measured by the leading wing angle) was inversely correlated with flight velocity (r=−0.48, −0.25, −0.44 and −0.38, P=0.03 for bird 2 and P<0.001 for the others; Fig. 4C), but yielded an increased vertical acceleration (r=0.76, 0.55, 0.70 and 0.56, P<0.001 for all birds; Fig. 4B), after controlling for aperture dimensions, transit number, flight direction and aperture presentation set (see Materials and Methods). Mean leading and trailing wing stroke amplitudes showed similarly high correlations with vertical acceleration.

All four hummingbirds used both swept and asymmetric transit strategies to negotiate each of the tested apertures except for the smallest (6×6 cm), for which they used almost exclusively the swept technique (Fig. 5). The leading wing was swept significantly farther forward (i.e. a more asymmetric technique) for wider apertures (effect size β=7.7, 7.7, 6.2 and 3.2 deg cm⁻¹, P<0.001 for all birds) and somewhat farther forward for taller apertures (β=3.7, 4.9, 3.4 and 3.9 deg cm⁻¹, P=0.083, 0.004, 0.43 and 0.007 for birds 1–4, respectively; Fig. 5), but only bird 4 showed a significant interaction effect between aperture width and height on the leading wing angle (β=−0.7, 0.7, 0.0 and −1.4 deg cm⁻², P>0.9 for birds 1–3, P=0.039 for bird 4). Because all birds successfully negotiated the smallest aperture using the swept technique, the minimum aperture diameter that hummingbirds could negotiate was not identified. Physical impact of wings with the aperture edges was observed in 7.7% of transits (see data in Dryad: https://doi.org/10.5061/dryad.41ns1rnmd). After controlling for experimental variables, the absolute value of the mean leading wing angle was the only tested technique variable for which we detected a consistent association with the likelihood of wing contact (likelihood ratio tests, χ²₁=22.0, 24.1, 5.1 and 3.8, P<0.001 for birds 1 and 2, and P=0.20 and 0.37 for birds 3 and 4, respectively). For each degree the mean leading wing angle moved away from zero, birds were 12%, 10%, 7% and 6% less likely to contact the aperture (logistic regressions; see data in Dryad: https://doi.org/10.5061/dryad.41ns1rnmd). When the mean leading wing angle was low in magnitude, wings were typically held outward from the body, potentially enabling more frequent contact with the edges of the aperture.

Hummingbirds switched from asymmetric to swept techniques with increased number of transits (Fig. 6). When trials were split into either asymmetric or swept groups using the median leading wing angle across all trials, a logistic model revealed that the fraction of trials in which birds used the asymmetric technique decreased significantly with presentation set (P=0.047 for bird 1, P<0.001 for the others; Fig. 6), resulting in an increase in the odds of the swept technique by 14%, 24%, 43% and 33% with each presentation set completed, for birds 1–4, respectively. In the regression analysis, mean leading wing angle also decreased significantly with repeated transits for birds 2–4 (β=−0.05, −0.15, −0.25 and −0.24 deg per transit for birds 1–4, respectively, P=0.5 for bird 1, P<0.001 for the others). Mean leading and trailing wing stroke amplitudes also decreased significantly with repeated transits (responses were nearly identical; mean leading amplitude: β=−0.03, −0.06, −0.05 and −0.03 deg per transit, P<0.001 for all birds). Altogether, experience through repeated transits affected transit strategy (i.e. mean leading wing angle) to roughly the same degree (60 deg) as did the combined effects of aperture width and height (61 deg).

Although all birds used similar transit strategies, with comparable switching from asymmetric to swept techniques as they gained experience, bird 1 flew 27% more slowly than the other birds (mean±s.e.m. decrease of 0.43±0.05 m s⁻¹, Tukey's post hoc test, all P<0.001), and also exhibited significantly higher vertical acceleration (increase of 1.3 m s⁻², Tukey's post hoc test, all P<0.005). Interestingly, this bird also used the asymmetric technique more often than other birds and had a 21±6 deg greater leading wing angle than other birds on average (Tukey's post hoc test, P<0.001, P=0.003 and P=0.07 for bird 1 versus birds 2–4, respectively), indicating that the relationships between flight technique, horizontal flight speed and vertical acceleration observed among trials for each individual may also occur among birds. We did not observe lateralization across birds (likelihood ratio test on generalized linear model, P=0.33). Two individual birds, however, exhibited significant handedness in leading versus trailing wing when using the asymmetric technique, although the preference was for different wings (bird 1, preference for left wing, Chi-squared test, χ²₁=17.5, P<0.001, counts: 63 left, 24 right; bird 2 preference for right wing, Chi-squared test, χ²₁=7.04, P=0.03, counts: 14 left, 32 right). Bird 1's preference for transiting with the left wing first also disappeared over time (likelihood ratio test, χ²₁=5.73, P=0.02).

Flight within dense vegetation requires animals to repeatedly negotiate openings that connect obstacle-free regions. Here, hummingbirds negotiating single apertures less than 1 wingspan in diameter demonstrated multiple strategies which have significant effects on their overall trajectory. Initially, hummingbirds used a cautious strategy characterized by continuous flapping, which enabled slower flight and less downward acceleration. Over time, however, hummingbirds gradually shifted to a faster technique during which flapping was paused.

Initial use of the asymmetric technique may indicate cautiousness in novel environments – slow flight allows greater time to observe and react to upcoming obstacles. Between the first 16 transits and the last 16 transits, transit speed increased by 28% (individual bird increases: 15%, 15%, 47% and 34%; across apertures, increases ranged from 18% to 36%) and vertical acceleration decreased by 38% (individual bird decreases: 14%, 19%, 67% and 51%; across apertures, decreases ranged from 0 to 180%). The increased speed and reduced vertical acceleration associated with the swept technique necessarily increase post-transit recovery distance, but may allow birds to better negotiate known obstacles. Specifically, the use of the non-flapping swept technique may reduce the intensity of wing impact with apertures. Although the extremes of both swept and asymmetric techniques reduced the likelihood of wing impact, a much greater wing speed during flapping will intensify wing impacts and increase damage relative to that in birds using the static-wing, swept technique. Wing contact, or even sensed proximity to aperture edges, may provide learning cues for subsequent modification to approach behavior and subsequent transit. In only one of 640 trials was a body collision with the partition surrounding the aperture observed (i.e. contact of head or torso, excluding tail feathers), following which the bird recovered in eight wing strokes (about 190 ms after the start of collision), and then proceeded through the smallest aperture only 0.9 s post-recovery.

The transit techniques used by hummingbirds highlight the potential benefits of shape shifting as well as of task learning when negotiating cluttered environments. For insect-scale flying robots, not only does independent bilateral control of wing stroke amplitude enhance steering by producing torque about the roll axis (Ma et al., 2013; Zhang et al., 2016) but also asymmetric shifts in amplitude or mean stroke angle may aid negotiation of cluttered environments by allowing robots to partially maintain weight support during aperture transits (Fig. 4B). Symmetric forward and backward shifts in the mean stroke angle affect pitch in flapping robots (Ma et al., 2013; Zhang et al., 2016), but because hummingbirds performing the asymmetric maneuver always shift one wing forward and one wing backward, no appreciable shift in the center of aerodynamic force occurs and no net pitching torque is generated. These insect-scale physical and mathematical models provide valuable platforms with which to investigate the power, control effort and wing stroke timing needed to execute novel maneuvers in tuned resonant systems (Fearing et al., 2000). When negotiating constrictions less than 1 body width in diameter, quadrotors (i.e. flying robots with four propellers) must transit ballistically and then recover following a period of reduced aerodynamic support during transit (Mellinger, Michael, and Kumar, 2012). Because propellers have a fixed diameter and modulate thrust through either angle of attack or rotation frequency, rotating propellers cannot produce downward thrust if the diameter of the constriction is less than that of the propeller. The ability to produce partial, but significant downward thrust by reducing wing stroke amplitude when flying through constrictions may be an important advantage of flapping wing robots over those producing thrust with propellers. Our observation that technique choice mediates a tradeoff between horizontal velocity and vertical acceleration suggests that flying robots may also benefit from multiple strategies optimized for different contexts.

Because a decrease in aperture width reduced hummingbird flight speed twice as much as did a similar decrease in aperture height (Fig. 4A), foliage geometry may also play an important role in determining movement strategies. Hummingbirds can hover, and also modulate forces and moments (force-vector) with respect to initial body orientation (Altshuler et al., 2012; Cheng et al., 2016a). Thus, the limits to clutter negotiation at the low speeds considered here (∼1–3 m s⁻¹) likely derive from environmental geometry or dynamic stability during maneuvers (Cheng et al., 2016b), rather than from trajectory dynamics or constraints on visual processing as they do for birds not capable of prolonged hovering (Lin et al., 2014). Unlike in the case of pigeons (Williams and Biewener, 2015), the difference in energetic cost between gap traversal techniques is likely to be very small compared with the energetic cost of sustained flight, which represents about 34% of a hummingbird's daily energy budget (Wolf and Hainsworth, 1971). Energetic efficiency is therefore unlikely to be a driver of technique choice in these experiments.

We demonstrate how hummingbirds' unique hovering and sideways flight abilities facilitate multiple maneuvering strategies as they negotiate apertures less than 1 wingspan in diameter. Hummingbirds adjust their transit strategy in response to changes in aperture size and shape and as they gain experience over hundreds of repeated transits. Furthermore, switching between transit strategies significantly affected the subsequent flight trajectory. Flight within cluttered environments is widespread in birds, which likely target the midpoints of gaps between obstacles (Pérez-Campanero Antolín and Taylor, 2023). Identifying, steering toward and negotiating such apertures has the potential to elicit maximum performance from the visual, control and maneuvering systems simultaneously.

Flight through clutter also mediates many relationships between the aforementioned high-level physiological processes and multiple ecologically relevant interactions with vegetation, including nesting, territory defense and pollination. In addition to feeding from flowers, hummingbirds routinely fly near and within vegetation while foraging for arthropods (Stiles, 1995). Both foraging tasks may require the ability to adaptively switch between transit strategies in the course of complex aerial maneuvers. Such experiential learning of a complex locomotor task may be particularly advantageous when flying through diverse types of vegetation and other obstacles that present unpredictable spatial challenges. Further research on how birds negotiate natural vegetation with complex geometries would be of particular interest.

We thank the biomechanics seminar participants at the University of California, Berkeley, core research facilities of the Department of Integrative Biology, University of California, Berkeley, and the Center for Interdisciplinary Bio-inspiration in Education and Research for critical discussions and resources. Portions of the data and results in this paper were previously published in the PhD thesis of M.A.B. (Badger, 2016).