ABSTRACT

In the presence of wind or background image motion, flies are able to maintain a constant retinal slip velocity by regulating flight speed to the extent permitted by their locomotor capacity. Here we investigated the retinal slip compensation of tethered blue bottle flies (Calliphora vomitoria) flying semi-freely along an annular corridor in a magnetically levitated flight mill enclosed by two motorized cylindrical walls. We perturbed the flies' retinal slip by spinning the cylindrical walls, generating bilaterally averaged retinal slip perturbations from −0.3 to 0.3 m s−1 (or −116.4 to 116.4 deg s−1). When the perturbation was less than ∼0.1 m s−1 (38.4 deg s−1), the flies successfully compensated the perturbations and maintained a retinal slip velocity by adjusting their airspeed up to 20%. However, with greater retinal slip perturbation, the flies' compensation became saturated as their airspeed plateaued, indicating that they were unable to further maintain a constant retinal slip velocity. The compensation gain, i.e. the ratio of airspeed compensation and retinal slip perturbation, depended on the spatial frequency of the grating patterns, being the largest at 12 m−1 (0.04 deg−1).

INTRODUCTION

Flying insects rely heavily on retinal image motion to control their flight (Borst et al., 2010; Srinivasan and Zhang, 2004). They often regulate flight speed by maintaining a constant retinal slip velocity (or optic flow) (David, 1982; Serres et al., 2008; Srinivasan et al., 1996, 2000), which can be extracted over a broad range of image spatiotemporal frequencies (Fry et al., 2009). This differs from the classical optomotor turning response to rotating grating patterns (Borst et al., 2010; Hausen and Egelhaaf, 1989), which is sensitive to image temporal frequency that depends on the image spatial frequency at a given retinal slip velocity (Borst and Egelhaaf, 1989).

Visual control of forward flight in insects is commonly studied using flight tunnels in free-flight (David, 1982; Fuller et al., 2014; Serres et al., 2008; Srinivasan et al., 1996) or tethered-flight settings (David, 1978; Lawson and Srinivasan, 2017). Recent efforts by the authors also demonstrated the potential of using flight mills to study forward flight in semi-free settings with controlled flight conditions (Hsu et al., 2019). While evidence has shown that free-flying insects in flight tunnels are able to maintain a constant retinal slip velocity in the presence of wind or background image motion (David, 1982; Srinivasan et al., 1996), it is unknown whether the same speed-regulation behavior also remains in tethered flies flying semi-freely in a flight mill.

Flying insects change their flight speed mainly through body-pitch dominated vectoring as well as magnitude modulation of cycle-averaged wing aerodynamic forces; however with relatively small changes in the force direction relative to the body, a mechanism commonly described as the ‘helicopter model’ (David, 1978; Muijres et al., 2014). On the other hand, it has been also observed that insects can change their flight speeds in the absence of any pitch maneuvers. For example, fruit flies can use a swimming-like paddling wing motion for thrust and speed modulation (Ristroph et al., 2011) and drone flies can produce significant airspeed changes, with negligible body pitch variations around 0 deg, at least for a short period of time (3–10 s) (Meng and Sun, 2016). As these relatively scarce observations suggest that insects are at least capable of relying only on the changes in wing motion to fly at different speeds and therefore do not have to conform to the helicopter model, it is unclear if they still modulate flight speed to maintain a constant retinal slip velocity with a constrained pitch, and to what extent can the changes of wing motion modulate speed before the locomotor limit is reached.

In this study, we used a motorized magnetically levitated (MAGLEV) flight mill, modified from those used in Hsu et al. (2019), to study the steady-state speed regulation and retinal slip compensation in blue bottle flies (Calliphora vomitoria). The MAGLEV flight mill enables the flies to drive voluntarily a rotating shaft with frictionless pivot joint and fly continuously in an annular corridor enclosed by two cylindrical walls, thereby simulating one degree-of-freedom forward flight; then, the cylindrical walls with grating patterns were motorized to provide controlled visual perturbations to the flies' retinal slip. With this setup, we aimed to address two main questions: (1) do flies attempt to compensate the perturbations applied to their retinal slip when flying in the flight mill, thereby maintaining a constant retinal slip, similar to those observed in free flight? and (2) to what extent can flies regulate flight speed using only the wing kinematic changes without varying body pitch? In the experiments, the flies were constrained at a fixed body pitch (0 deg while flying in the annular corridor, and the two cylindrical walls generated the retinal slip perturbations via their co-rotations at the same angular velocity. We quantified the flies' responses in terms of the changes in their airspeeds and retinal slip velocities, as functions of retinal slip perturbations.

MATERIALS AND METHODS

Motorized magnetically levitated (MAGLEV) flight mill apparatus

A motorized MAGLEV flight mill (Fig. 1A), modified from that developed by Hsu and co-workers (Hsu et al., 2019), was used in this study. The flight mill shaft (carbon fiber, ∅︀2×302 mm, 38 g, 1.3×104 g mm2 around pivot axis; 2.6×102 g mm2 around the pitch axis), with three permanent magnets (∅︀2.38×9.5 mm, 1.27 g for each permanent magnet) placed at its center, was levitated by two vertically aligned electromagnets (XRN-XP-80-38, XRN corp., China). A proportional-integral-derivative (PID) controller generated pulse width modulation (PWM) signals to the electromagnets (NPN using the feedback of the permanent magnets' vertical position measured by a linear Hall effect sensor. The flies, tethered to one end of the shaft, flew in an annular corridor of the flight mill enclosed by an inner (diameter 0.254 m) and an outer (diameter 0.349 m) cylindrical wall, which were centered via a vertical metal post and were driven by stepper motors via timing gears and pulleys. Both cylindrical walls displayed vertical grating patterns with one of the three spatial frequencies (SF, the number of the grating cycles per meter): 24 m−1, 12 m−1 and ∼0 m−1 (white background with no pattern) (or 0.08, 0.04 and ∼0 deg−1 in angular units, linear units were calculated based on the angular units using the radius of the fly's circular path at the center of the annular corridor, which was 0.151 m) (Michelson contrast C=(ImaxImin)/(Imax+Imin), where Imax and Imin are the maximum and minimum luminance of the pattern, respectively). Note that only linear units were used in the rest of the paper. The spatial frequencies on the outer and inner cylindrical walls were kept identical, which ensured identical temporal frequency applied to both eyes of the flies, thereby to minimize the turning responses of flies (Borst et al., 2010).

Fig. 1.

Experimental apparatus and methods. (A) The design of the MAGLEV flight mill system: (a) timing gears, pulleys and stepper motors, (b) permanent magnets and mill rotating shaft, (c) Hall effect sensor, (d) electromagnets, (e) laser-and-photodiode pairs, (f) outer and (g) inner cylindrical walls with squared wave grating patterns. Magnified cutaway view: blue bottle fly tethered at 0 deg body pitch with an angle pin. (B) Grating patterns with three spatial frequencies (SF=∼0, 12 and 24 m−1) used in the experiments. (C) Retinal-slip perturbations (Uc) are given syn-directionally (green dotted arrow) or anti-directionally (red dotted arrow). With no perturbation the fly flies with an airspeed Ua0 (same as ground speed Ug0) generating an opposite retinal slip velocity Ur0. Syn-directional (anti-directional) perturbation Uc decreases (increases) the retinal slip velocity Ur, which is compensated by the fly via increasing (decreasing) its airspeed (Ua).

Fig. 1.

Experimental apparatus and methods. (A) The design of the MAGLEV flight mill system: (a) timing gears, pulleys and stepper motors, (b) permanent magnets and mill rotating shaft, (c) Hall effect sensor, (d) electromagnets, (e) laser-and-photodiode pairs, (f) outer and (g) inner cylindrical walls with squared wave grating patterns. Magnified cutaway view: blue bottle fly tethered at 0 deg body pitch with an angle pin. (B) Grating patterns with three spatial frequencies (SF=∼0, 12 and 24 m−1) used in the experiments. (C) Retinal-slip perturbations (Uc) are given syn-directionally (green dotted arrow) or anti-directionally (red dotted arrow). With no perturbation the fly flies with an airspeed Ua0 (same as ground speed Ug0) generating an opposite retinal slip velocity Ur0. Syn-directional (anti-directional) perturbation Uc decreases (increases) the retinal slip velocity Ur, which is compensated by the fly via increasing (decreasing) its airspeed (Ua).

The cylindrical walls were co-rotated either syn-directionally or anti-directionally relative to the flight direction of the flies, therefore decreases or increases the fly's retinal slip velocity, respectively. Here we consider the bilaterally averaged linear velocity of the grating patterns on inner and outer cylindrical walls (Uc) as the effective retinal slip perturbation applied to the flies. Uc can be calculated as the product of the angular velocity of the cylindrical walls and the radius of the fly's circular path at the center of the annular corridor.

We mounted two laser-and-photodiode pairs on the metal post with a 120 deg spacing (Fig. 1A), and calculated the average ground speed of the flies (Ug; i.e. the forward velocity of the fly with respect to the fixed laboratory frame) based on the time lapses of the shaft passing the two laser-and-photodiode pairs. A light source (8000 lx, 100 W LED light, MonoBright LED Bi-color 750, Genaray, Brooklyn, NY, USA) was mounted on the top of the entire device to provide consistent lighting to the annular corridor.

Animal preparation and experimental procedure

We used 4- to 8-day-old blue bottle flies [Calliphora vomitoria (Linnaeus 1758)] (N=42, 32.9±8.7 mg) for the experiments. Each fly was cold anesthetized after capture from the rearing tent, then its thorax was glued orthogonally to a metal pin. The metal pin was then attached orthogonally to the flight mill rotating shaft, therefore holding the fly at approximately 0 deg body pitch angle (Fig. 1A). After being introduced into the flight mill, the flies flew continuously in a clockwise direction at the middle of the annular corridor between the two cylindrical walls (Fig. 1A, also see Movie 1). Note that since the distance between the flies and the inner and outer walls were fixed for all experiments, the linear velocity of the grating patterns on the rotating cylindrical walls was equivalent to the image velocity or the optical flow introduced to a fly's retina, i.e. the retinal slip perturbation. The retinal slip perturbations were applied to each fly with a 0.03 m s−1 interval following two sequences with opposite directions: (1) 0→0.3→−0.3→0 m s−1, and (2) 0→−0.3→0.3→0 m s−1. The results of one-way analysis of variance (ANOVA) test showed that for each SF group, the direction of the sequences has no significant effect on flies' mean forward velocity (Table S2). After each change of the perturbation velocity, the fly's forward velocity was measured after at least 40 s of waiting period to ensure that the fly flew at near steady state with low velocity fluctuation (see section Steady-state flight condition below). Individual flies were not distinguished in the analyses.

As the two cylindrical walls spun, they induced air flow between them (i.e. Taylor–Couette flow; Taylor, 1923). This wall-induced wind speed (Uw) led to a difference between the ground speed (directly measured) and the airspeed of the flies, and therefore needs to be measured and considered in the latter analysis (see next section). We measured Uw for each perturbation velocity in absence of the fly using a hot-wire anemometer (405i, Testo, Lenzkirch, Germany), and the result showed that Uw was linearly dependent on the spinning speed (Fig. S1). See more information in the supplementary information regarding the wall-induced wind.

Data analyses and model selection

The responses of the flies under retinal slip perturbations (Uc) were measured in terms of the changes in their bilaterally averaged retinal slip velocity (ΔUr) and the changes in their airspeed (ΔUa). The bilaterally averaged retinal slip velocity of the fly (Ur) can be calculated as the difference between the measured ground speed of the fly (Ua) and the bilaterally-averaged linear velocity of the grating patterns on inner and outer walls (Uc, i.e. the retinal slip perturbation),
formula
(1)
Note that in this study, we didn't distinguish the retinal slip velocities between the two eyes of the flies, as both Ur and Uc were considered bilaterally averaged.
The fly's airspeed (Ua) was calculated based on its ground speed (Ug) and the wall-induced wind speed (Uw),
formula
(2)
Note that we used the airspeed instead of the ground speed in our analysis because the former better reflected the biomechanical efforts or the constraints of the flies in compensating the perturbation.

Assuming a fly would compensate the retinal slip perturbation, it then needed to change its airspeed (or ground speed) in the same direction of the retinal slip perturbation, thereby to reduce or eliminate the changes induced by the external perturbation on its retinal slip (or ΔUr≈ 0) (Fig. 1C,D). In addition, assuming that the changes of the airspeed Ua would saturate because of biomechanical constraints when the magnitude of the perturbation (Uc) became sufficiently large, the flies would then become unable to maintain a constant retinal slip as the airspeed reached to an upper or lower bound. As a result, the ΔUr would eventually increase (or decrease) with Uc as no further compensation would be possible.

Therefore, to model the flies' response ΔUr as a function of Uc, we performed nonlinear regressions and model selection on two competing explanatory models developed assuming the existence or nonexistence of retinal slip compensation, i.e. a linear function model (assuming no compensation) and a cubic function model (assuming compensation existed). The cubic function was defined as:
formula
(3)
where Ur0 was the measured mean retinal slip velocity of the flies without perturbation for each trial, β0 and β3 are the coefficients of polynomials, and c is the inflection point, β0, β3 and c were obtained from nonlinear regression.
To model the flies' response ΔUa as a function of Uc, we also performed nonlinear regressions and model selection on two explanatory models: a linear function model () (assuming no airspeed saturation) and a generalized logistic function model (Richards, 1959) (assuming airspeed saturated). The generalized logistic function is defined as:
formula
(4)
where Ua0 was the measured mean airspeed of the flies without the perturbation for each trial, and were the lower and upper asymptotic bounds, representing the minimal and maximum change in airspeed, respectively, β is the growth rate, c is where the maximum growth rate occurs and γ is the asymmetry coefficient (Richards, 1959). We also defined the compensation gain as the ratio between the changes of airspeed (ΔUa) and retinal slip perturbation (Uc), evaluated locally at Uc=0,
formula
(5)
which was simply the slope for and the first derivative of at Uc=0.

We used the Levenberg–Marquardt algorithm (https://rdrr.io/cran/minpack.lm/) for the nonlinear regression to find the best fit for each model. Finally, the models were compared using Akaike information criterion (AIC) (Akaike, 1998), which evaluated the trade-off between the goodness-of-fit and the simplicity of the model.

Steady-state flight condition

After each change of the perturbation velocity, the fly's forward velocity was measured after at least 40 s of waiting period to ensure that the fly flew at near steady state with low velocity fluctuation. The steady-state flight condition can be illustrated by the velocity traces of each experimental trial within the last 30 s before switching to the next perturbation (Fig. 2). The flies' forward speed remained approximately constant within this period, and flies did not appear to accelerate or decelerate substantially. In particular, the standard deviation of velocity within the last 5 s averaged over all the trials was ±0.0083 ms−1, which illustrates the small fluctuations in velocity.

Fig. 2.

Instantaneous groundspeed (Ug) of all trials within their last 30 s. The groundspeed is color-coded based on the retinal-image velocity perturbation, green for syn-directional perturbation and red for anti-directional perturbation. No substantial speed fluctuation was observed in the experiments. The final speed at the end of each trial was used in the analysis.

Fig. 2.

Instantaneous groundspeed (Ug) of all trials within their last 30 s. The groundspeed is color-coded based on the retinal-image velocity perturbation, green for syn-directional perturbation and red for anti-directional perturbation. No substantial speed fluctuation was observed in the experiments. The final speed at the end of each trial was used in the analysis.

Estimation of equivalent free-flight velocity

Here we aim to first estimate the thrust that the flies produce in a tethered condition when flying in the flight mill and then use it to estimate the equivalent free-flight velocity in a hypothetical free flight.

First, in tethered flight, we assume that the cycle-averaged thrust generated by the wings of a fly during steady-state flight is equal to the drag acting on the fly's body and the shaft , and second, in a hypothetical free flight, we assume that the same thrust is applied to overcome only the body drag (as the shaft is absent), and therefore can propel the fly forward at a higher equivalent free-flight speed:
formula
(6)
The above force balance equation can be converted to a torque balance equation as follows:
formula
(7)
where l is the length of the rotating shaft and is the drag torque acting on the shaft (when it spins about the pivot joint at the middle of the shaft), which can be calculated as:
formula
(8)
where ρ is the mass density of the fluid, CD,shaft is the drag coefficient of the shaft (the drag of magnets and pins are neglected), v is the fly's linear velocity, r is the shaft radius, d is the diameter of the shaft's cross section, ω is the angular velocity of the shaft (and the fly), and Ashaft is the shaft surface area. The drag force acting on the fly's body can be estimated similarly as follows:
formula
(9)
where CD,body is the drag coefficient of the fly's body at 0 deg pitch angle, and Afly is the fly's surface projection area facing the incoming airflow, estimated using the flies' average body width. The coefficients used in the estimation were: CD,shaft=1.2 (Baker et al., 2012); CD,body=0.75 (Dudley and Ellington, 1990); ρ=1.225 kg m−3; d=2×10−3 m; l=0.302 m; Afly=1.3×10−5 m2.

Using the above formulas and coefficients, we estimated the thrust a fly can generate and the equivalent free-flight velocity (i.e. the speed of the fly without the shaft drag) (see Discussion). The calculation also showed that the ratio of drag torque between the shaft-fly combined and the fly alone was 19.6, and therefore the drag on the shaft caused significant velocity drop in tethered flight.

RESULTS

A total of 42 blue bottle flies (32.9±8.7 mg) were used in the experiments, producing 2228 measurements of flight speeds for the 21 cases of retinal slip perturbation (Uc) ranging from −0.3 m s−1 to 0.3 m s−1 (see the sample size for each case in Table S1). The averaged ground speed (Ug) at Uc=0 was 0.44±0.12 m s−1 among all individuals (Fig. S2) (no significant effect of SF on Ug at the P<0.05 level [F2, 201=1.304, P=0.274]). Note that ground speed equals the airspeed (Ua) and retinal slip velocity (Ur) when Uc=0.

When Uc was relatively small (−0.12<Uc<0.10 m s−1, Fig. 3B), the flies successfully compensated the external perturbations at SF=12 m−1 by keeping the retinal slip approximately unchanged relative to those measured in the absence of the perturbation (ΔUr≈0) (Fig. 3A). The compensations existed but were significantly weaker at the higher (SF=24 m−1) or lower (SF∼0 m−1) SF (Fig. 3A), both of which resulted in a near linear trend of ΔUr in response to Uc. When the magnitude of the perturbations became large (Uc<−0.12 or Uc>0.10 m s−1, Fig. 3B), the compensation in SF=12 m−1 group also begun to weaken as ΔUr started to change linearly in the opposite direction of perturbation Uc, indicating that the flies became unable to further maintain a constant Ur.

Fig. 3.

Response of blue bottle flies under retinal slip velocity perturbation Uc. (A) The change of flies' retinal slip velocity (ΔUr) in response to the perturbation (Uc). (B) The change of flies' airspeed (ΔUa) in response to the perturbation (Uc). Solid lines and shades represent LOESS regression mean and 95% confidence interval, respectively. Airspeed plateaued (at SF=12) when retinal slip velocity perturbation is above 0.10 m s−1 or below −0.12 m s−1 (calculated by intersecting of the asymptote lines and the tangent line at the inflection point based on the data of SF=12 m−1. Teal dotted line in B). Between these two bounds (vertical dashed lines), blue bottle flies successfully maintained fully compensated retinal slip velocity region. Horizontal green and red arrows indicate the syn-directional and the anti-directional retinal-slip perturbations, respectively. Retinal slip compensation corresponds to a syn-directional change of flies' airspeed or ground speed with respect to the perturbation, regardless of the perturbation is syn-directional or anti-directional to the flies absolute airspeed or ground speed. Note that the changes in retinal slip velocity and the airspeed are both referenced from the averaged ground speed in the absence of perturbation (Uc=0), which equals 0.44±0.12 m s−1.

Fig. 3.

Response of blue bottle flies under retinal slip velocity perturbation Uc. (A) The change of flies' retinal slip velocity (ΔUr) in response to the perturbation (Uc). (B) The change of flies' airspeed (ΔUa) in response to the perturbation (Uc). Solid lines and shades represent LOESS regression mean and 95% confidence interval, respectively. Airspeed plateaued (at SF=12) when retinal slip velocity perturbation is above 0.10 m s−1 or below −0.12 m s−1 (calculated by intersecting of the asymptote lines and the tangent line at the inflection point based on the data of SF=12 m−1. Teal dotted line in B). Between these two bounds (vertical dashed lines), blue bottle flies successfully maintained fully compensated retinal slip velocity region. Horizontal green and red arrows indicate the syn-directional and the anti-directional retinal-slip perturbations, respectively. Retinal slip compensation corresponds to a syn-directional change of flies' airspeed or ground speed with respect to the perturbation, regardless of the perturbation is syn-directional or anti-directional to the flies absolute airspeed or ground speed. Note that the changes in retinal slip velocity and the airspeed are both referenced from the averaged ground speed in the absence of perturbation (Uc=0), which equals 0.44±0.12 m s−1.

The observed compensation to maintain ΔUr≈0 was mainly the result of the changes in flies' airspeed in response to the perturbation, as flies changed their airspeed in the same direction of the perturbation. This was confirmed by monotonically increasing trends of ΔUa with Uc (Kc=dΔUa/dUc), within the fully compensated retinal slip region for all three SF cases (Fig. 3B). The compensation gain was significantly higher for SF=12 m−1 (Kc=0.868), compared with those of SF=0 m−1 (Kc=0.233) and SF=24 m−1 (Kc=0.337). The airspeed changes exhibited saturation under large perturbations, most apparently for SF=12 and 24 m−1 (Fig. 3B). For SF=24 m−1, the upper and lower bounds of ΔUa were 0.034±0.009 m s−1 and −0.089±0.010 m s−1 (means±95% CI), respectively. For SF=12 m−1, the upper and lower bounds of ΔUa were 0.095±0.010 m s−1 and −0.091±0.014 m s−1 (means±95% CI).

Consistent with the above observations, the model selection results (Table 1) showed that for SF=12 m−1 the AIC favored models assuming the existence of retinal slip compensation and airspeed saturation, i.e. and , while for SF=0 m−1 the AIC favored the models assuming no compensation and no airspeed saturation, i.e. , . For SF=24 m−1, AIC favored the model assuming no retinal slip compensation and the model assuming the existence of airspeed saturation .

Table 1.

Model selection results based on Akaike's information criterion (AIC)

Model selection results based on Akaike's information criterion (AIC)
Model selection results based on Akaike's information criterion (AIC)

DISCUSSION

In this work, we studied the responses of blue bottle flies subjected to retinal slip perturbation while flying in the motorized MAGLEV flight mill with a constrained pitch. Similar to those observed in free-flight conditions (David, 1982; Serres et al., 2008; Srinivasan et al., 1996, 2000), the flies appeared to compensate retinal slip perturbations by changing their airspeed (or ground speed) syn-directionally with the perturbation. The retinal slip perturbations were almost fully compensated when they were between −0.12 m s−1 and 0.10 m s−1 at SF=12 m−1, with a compensation gain at 0.868, significantly higher than those for SF=∼0 and 24 m−1. The observed dependency on image spatial frequency in the speed compensation responses was similar to those identified in the free-flight acceleration responses of fruit flies (Drosophila melanogaster) (Fry et al., 2009), which showed that the response strength was among the strongest at SF of 12 m−1, but reduced substantially at 24 m−1. It is likely that the blue bottle flies are unable to resolve spatial frequencies beyond 0.08 deg−1 because of the low resolution of their compound eyes (Land, 1997). Compared with classical optomotor turning response (Bender and Dickinson, 2006; Borst et al., 2010), we expect that the dependency on spatial frequency in retinal slip compensation or acceleration responses was relatively weak, as the retinal slip velocity can be extracted robustly over a broad range of image spatiotemporal frequencies (Fry et al., 2009), while the optomotor turning response is proportional to image temporal frequency that depends on image spatial frequency at a fixed image velocity (Borst et al., 2010).

When the magnitude of the retinal slip velocity perturbation became large, speed compensation weakened as the changes in airspeed plateaued, as flies were unable to adjust their airspeed beyond approximately ±0.1 m s−1 (or +22% and −21% compared with the average airspeed at Uc=0 under SF=12 m−1). This was possibly due to a compound of biomechanical constraints, including the constrained pitch and their force-vectoring ability via changes of wing motion (Hsu et al., 2019). Note that in fully tethered flies without speed regulation (which existed in the current flight mill experiment), changes in flies' bilateral retinal slip elicited changes in their thrust (Götz, 1968), although the inclination of the total force vector remained constant, similar to those observed in our previous work (Hsu et al., 2019). It is also worth noting that the current study was limited to the steady-state responses, while flies are likely capable of large transient modulation of wing motion during rapid aerodynamic maneuvers and flight stabilization (Ristroph et al., 2010). In free flight, it was shown that fruit flies were be able to compensate for retinal slip up to approximately 100% (compared with the speed under no stimuli) in response to changes in visual stimulus (Mronz and Lehmann, 2008). Therefore, it can be speculated that with a free body pitch, e.g. by tethering a fly to the flight mill via a micro bearing, the successful compensation region (Fig. 2B) can be further expanded to larger magnitude of the retinal slip perturbations.

In conclusion, to address the two motivating questions of this study, our results showed that: (1) similar to those observed in free flight, flies flying in MAGLEV flight mill did attempt to reduce the changes in retinal slip induced by the external visual perturbation, and the perturbation was fully compensated by the flies when the perturbation magnitude was relatively small, and (2) flies were capable of adjusting flight speed using only the wing kinematic changes during steady-state flight, however the amount of adjustment was relatively small (less than 0.1 m s−1). In addition to retinal slip compensations, fly airspeed response is also dependent on spatial frequencies, which is strongest at 12 m−1.

Previous studies have also shown that flies regulate their speed using both visual and antennal mechanosensory feedback (Fuller et al., 2014); the former measures the retinal slip and the latter measures the changes in airspeed instead of absolute airspeed (Taylor and Krapp, 2007). The visual feedback is likely to have a longer delay but plays a more dominant role in regulating the steady-state flight speed. On the other hand, antennal feedback has a shorter delay and enables more rapid transient response to airflow perturbations, thereby functioning to stabilize the visual velocity controller; however, it plays a weaker role in determining the steady-state flight speed (Fuller et al., 2014). These results are consistent with the current results as well as those in David (1982), both of which focus on the steady-state flight, and show that the flies tend to maintain a constant retinal slip despite the changes in airspeed, as long as they flew within their biomechanical limits.

In addition, our results showed that the flies did not attempt to maintain a constant value of its temporal frequency (i.e. frequency of the grating patterns passing a fly's retina). This was because the flies flew at similar ground speed when the spatial frequency of the patterns was changed, therefore they flew at significantly different temporal frequency in our experiments. However, our results did indicate that the gain of their retinal-slip compensation response depended on the spatial frequency (Fig. 3B).

Note that here we examined the changes in the flies' airspeed and retinal-slip velocity relative to those without perturbation, as this study focused primarily on the responses of the flies rather than their absolute thrust production and flight speed. The averaged ground speed (Ug) without perturbation was 0.44±0.12 m s−1 among all individuals flying in the flight mill, which was lower than the maximal speed (2.7 m s−1) reported in free-flying blowflies (Hoff, 1919) or the average flight speed (1.2–2.3 m s−1) reported in blowflies (Bomphrey et al., 2009). This was because the flies in the flight mill had to overcome additional drag from the rotating shaft, which was significantly higher than the aerodynamic drag from a fly's body alone. Here, we estimated the drag acting on the rotating shaft and a fly's body separately and then, by assuming the flies produce the same thrust in free flight as in the tethered flight in the flight mill, we calculated the flight velocity in a hypothetical free flight to be 1.9 m s−1 (equivalent to 0.44 m s−1 flying in the flight mill). Details of the calculation can be found in the Materials and Methods. Finally, note that the thrust capacity and the flight speed of the flies are widely known to depend on the gender of the flies, which were not distinguished in the current study.

Acknowledgements

We thank Elizabeth Seber and Ciera McFarland for assistance with the experiments.

Footnotes

Author contributions

Conceptualization: S.H., B.C.; Methodology: S.H., B.C.; Software: S.H.; Validation: S.H.; Formal analysis: S.H.; Investigation: S.H., B.C.; Resources: S.H., B.C.; Data curation: S.H.; Writing - original draft: S.H., B.C.; Writing - review & editing: S.H., B.C.; Visualization: S.H., B.C.; Supervision: B.C.; Project administration: B.C.; Funding acquisition: B.C.

Funding

This research was supported by the National Science Foundation (CMMI 1554429 to B.C.).

References

Akaike
,
H.
(
1998
).
Information theory and an extension of the maximum likelihood principle
. In
Selected Papers of Hirotugu Akaike
(
ed. E. Parzen, K. Tanabe G. Kitagawa
), pp.
199
-
213
.
New York, NY
:
Springer
.
Baker
,
W. E.
,
Cox
,
P.
,
Kulesz
,
J.
,
Strehlow
,
R.
and
Westine
,
P.
(
2012
).
Explosion Hazards and Evaluation
:
Elsevier
.
Bender
,
J. A.
and
Dickinson
,
M. H.
(
2006
).
A comparison of visual and haltere-mediated feedback in the control of body saccades in Drosophila melanogaster
.
J. Exp. Biol.
209
,
4597
-
4606
.
Bomphrey
,
R. J.
,
Walker
,
S. M.
and
Taylor
,
G. K.
(
2009
).
The typical flight performance of blowflies: measuring the normal performance envelope of Calliphora vicina using a novel corner-cube arena
.
PLoS ONE
4
,
e7852
.
Borst
,
A.
and
Egelhaaf
,
M.
(
1989
).
Principles of visual motion detection
.
Trends Neurosci.
12
,
297
-
306
.
Borst
,
A.
,
Haag
,
J.
and
Reiff
,
D. F.
(
2010
).
Fly motion vision
.
Annu. Rev. Neurosci.
33
,
49
-
70
.
David
,
C. T.
(
1978
).
The relationship between body angle and flight speed in free-flying Drosophila
.
Physiol. Entomol.
3
,
191
-
195
.
David
,
C. T.
(
1982
).
Compensation for height in the control of groundspeed by Drosophila in a new, “barber's pole” wind tunnel
.
J. Comp. Physiol. A
147
,
485
-
493
.
Dudley
,
T. R.
and
Ellington
,
C. P.
(
1990
).
Mechanics of forward flight in bumblebees: II. Quasi-steady lift and power requirements
. J. Exp. Biol.
148
,
53
-
88
.
Fry
,
S. N.
,
Rohrseitz
,
N.
,
Straw
,
A. D.
and
Dickinson
,
M. H.
(
2009
).
Visual control of flight speed in Drosophila melanogaster
.
J. Exp. Biol.
212
,
1120
-
1130
.
Fuller
,
S. B.
,
Straw
,
A. D.
,
Peek
,
M. Y.
,
Murray
,
R. M.
and
Dickinson
,
M. H.
(
2014
).
Flying Drosophila stabilize their vision-based velocity controller by sensing wind with their antennae
.
Proc. Natl. Acad. Sci. USA
111
,
E1182
—-
E1191
.
Götz
,
K. G.
(
1968
).
Flight control in Drosophila by visual perception of motion
.
Kybernetik
4
,
199
-
208
.
Hausen
,
K.
and
Egelhaaf
,
M.
(
1989
).
Neural mechanisms of visual course control in insects
. In
Facets of Vision
(
D. G. Stavenga and R. C. Hardie
), pp.
391
-
424
.
Springer
.
Hoff
,
W.
(
1919
).
Der flug der insekten und der vögel
.
Naturwissenschaften
7
,
159
-
162
.
Hsu
,
S.-J.
,
Thakur
,
N.
and
Cheng
,
B.
(
2019
).
Speed control and force-vectoring of bluebottle flies in a magnetically levitated flight mill
.
J. Exp. Biol.
222
,
jeb187211
.
Land
,
M. F.
(
1997
).
the resolution of insect compound eyes
.
Isr. J. Plant Sci.
45
,
79
-
91
.
Lawson
,
K. K. K.
and
Srinivasan
,
M. V.
(
2017
).
Flight control of fruit flies: dynamic response to optic flow and headwind
.
J. Exp. Biol.
220
,
2005
-
2016
.
Meng
,
X. G.
and
Sun
,
M.
(
2016
).
Wing and body kinematics of forward flight in drone-flies
.
Bioinspir. Biomim.
11
,
056002
.
Mronz
,
M.
and
Lehmann
,
F.-O.
(
2008
).
The free-flight response of Drosophila to motion of the visual environment
.
J. Exp. Biol.
211
,
2026
-
2045
.
Muijres
,
F. T.
,
Elzinga
,
M. J.
,
Melis
,
J. M.
and
Dickinson
,
M. H.
(
2014
).
Flies evade looming targets by executing rapid visually directed banked turns
.
Science
344
,
172
-
177
.
Richards
,
F. J.
(
1959
).
A flexible growth function for empirical use
.
J. Exp. Bot.
10
,
290
-
301
.
Ristroph
,
L.
,
Bergou
,
A. J.
,
Ristroph
,
G.
,
Coumes
,
K.
,
Berman
,
G. J.
,
Guckenheimer
,
J.
,
Wang
,
Z. J.
and
Cohen
,
I.
(
2010
).
Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles
.
Proc. Natl. Acad. Sci. USA
107
,
4820
-
4824
.
Ristroph
,
L.
,
Bergou
,
A. J.
,
Guckenheimer
,
J.
,
Wang
,
Z. J.
and
Cohen
,
I.
(
2011
).
Paddling mode of forward flight in insects
.
Phys. Rev. Lett.
106
,
178103
.
Serres
,
J. R.
,
Masson
,
G. P.
,
Ruffier
,
F.
and
Franceschini
,
N.
(
2008
).
A bee in the corridor: centering and wall-following
.
Naturwissenschaften
95
,
1181
-
1187
.
Srinivasan
,
M. V.
and
Zhang
,
S.
(
2004
).
Visual motor computations in insects
.
Annu. Rev. Neurosci.
27
,
679
-
696
.
Srinivasan
,
M. V.
,
Zhang
,
S.
,
Lehrer
,
M.
and
Collett
,
T. S.
(
1996
).
Honeybee navigation en route to the goal: visual flight control and odometry
.
J. Exp. Biol.
199
,
237
-
244
.
Srinivasan
,
M. V.
,
Zhang
,
S. W.
,
Chahl
,
J. S.
,
Barth
,
E.
and
Venkatesh
,
S.
(
2000
).
How honeybees make grazing landings on flat surfaces
.
Biol. Cybern.
83
,
171
-
183
.
Taylor
,
G. I.
(
1923
).
VIII. Stability of a viscous liquid contained between two rotating cylinders
.
Philos. Trans. R. Soc. Lond. Ser. Contain. Pap. Math. Phys. Character
223
,
289
-
343
.
Taylor
,
G. K.
and
Krapp
,
H. G.
(
2007
).
Sensory systems and flight stability: what do insects measure and why?
Adv. Insect Physiol.
34
,
231
-
316
.

Competing interests

The authors declare no competing or financial interests.

Supplementary information