When taking off from a sloping surface, flies have to reorient themselves dorsoventrally and stabilize their body by actively controlling their flapping wings. We have observed that righting is achieved solely by performing a rolling manoeuvre. How flies manage to do this has not yet been elucidated. It was observed here for the first time that hoverfly reorientation is entirely achieved within 6 wingbeats (48.8 ms) at angular roll velocities of up to 10×103 deg s−1 and that the onset of their head rotation consistently follows that of their body rotation after a time lag of 16 ms. The insects' body roll was found to be triggered by the asymmetric wing stroke amplitude, as expected. The righting process starts immediately with the first wingbeat and seems unlikely to depend on visual feedback. A dynamic model for the fly's righting reflex is presented, which accounts for the head/body movements and the time lag recorded in these experiments. This model consists of a closed-loop control of the body roll, combined with a feedforward control of the head/body angle. During the righting manoeuvre, a strong coupling seems to exist between the activation of the halteres (which measure the body's angular speed) and the gaze stabilization reflex. These findings again confirm the fundamental role played by the halteres in both body and head stabilization processes.

The righting reflex in animals has been investigated in a long series of experiments on vertebrates and invertebrates. Etienne-Jules Marey was the first author to describe in detail how cats orient themselves as they fall (Marey, 1894). Hoverflies, which are among the main flying pollinators, are able to perform impressive aerobatic feats in complex environments (Wang, 2005; Wystrach and Graham, 2012; Mou et al., 2011); in particular, hovering. Flies can land on all surfaces, including plants and walls, and they can even settle upside down on the ceiling (Liu et al., 2019). Just after take-off, they have to adopt the normal right-side up position in order to be able to fly: this action is called the righting reflex.

A classical approach to studying the righting reflex consists of dropping an animal into free fall with its legs pointing upwards. The animal will tend to rotate its body along its body axis and land on its legs. Some well-known experiments have been performed along these lines on mammalian taxa (Magnus, 1924) such as cats (Kane and Scher, 1969) and rats (Pellis et al., 1991), and more recently on wingless insect species such as stick insects (Zeng et al., 2017), ants (Yanoviak et al., 2010) and aphids (Ribak et al., 2013; Meresman et al., 2014). However, to our knowledge, no free-fall righting experiments of this kind have ever been performed on flies with their legs pointing upwards.

Previous studies in wingless animals have shown that righting reflexes can involve two different mechanisms: either an inertial or an aerodynamic control system. During inertial righting processes, the falling animal orients segments of its body so as to create an instantaneous moment of inertia, which triggers a rotation of the body (Marsden and Ostrowski, 1998) by moving the torso (as in cats and rodents), the legs (as in other mammals, reptiles and amphibians) or the tail (as in lizards and kangaroo rats); whereas aerodynamic control occurs in wingless insects such as aphids, ants and stick insect larvae (see Jusufi et al., 2011). When these animals perform appendicular movements (i.e. with their legs), bilaterally asymmetric forces induce a rotation of the body around its longitudinal axis (Jusufi et al., 2011; Ribak et al., 2013; Zeng et al., 2017).

Fruit flies are able to produce torque from aerodynamic forces by generating asymmetric wing motion (Ristroph et al., 2010; Sane, 2003; Beatus et al., 2015; Ristroph et al., 2013). The present study focused on how the hoverfly controls its head and body-roll orientation, focusing in particular on the aerodynamic processes resulting in righting torque. Beatus et al. (2015) have established that fruit flies can control their body-roll angle by establishing a stroke-amplitude asymmetry. Fruit flies can also generate active roll damping (60×103 deg s−1; see Beatus et al., 2015) to stabilize their roll movements even when exposed to extreme speed perturbations within the duration of a single wingbeat, namely within 5 ms. As fruit flies and blowflies are endowed with an efficient gaze stabilization reflex, which can be used to compensate for thorax rotations and thus to stabilize the visual world across the retina (Hardcastle and Krapp, 2016; Taylor and Krapp, 2007; Hengstenberg et al., 1986; Egelhaaf, 2002), head/body movements can be expected to occur during the righting process.

Based on previous studies on aerial righting reflexes (Zeng et al., 2017), we developed a new experimental setup with which winged insects can be released from an upside-down position (see Fig. 1 and details in Materials and Methods). The present paper first describes the asymmetric wing movements triggering the body righting process, before addressing the kinematics of the hoverfly's righting reflex, focusing on the head, body and head/body angles. Results related to additional experiments (loaded halteres with glue, lighting from below, head–thorax glued) are presented and discussed. A dynamic model for the righting reflex involving both feedback and feedforward control systems is then described. This model is consistent with a previously published control-block diagram of the fly's performance involving a proportional control of the roll movements based on the roll speed measured by the halteres (Beatus et al., 2015). The halteres, which are two ancestral hindwings beating in anti-phase with the wings, are ‘gyroscopic’ sense organs which quickly measure the fly's rotational speed in space (Pringle and Gray, 1948; Nalbach, 1993; Hengstenberg, 1998; Dickinson and Muijres, 2016). We also describe an additional feedforward mechanism possibly controlling the neck motor system, which accounts for the time lag observed between the insect's head and body during the righting process. As suggested in previous studies and confirmed by an elegant recent model for haltere dynamics (Mohren et al., 2019), the halteres act as body angular rate sensors which are sensitive to both Coriolis and centrifugal forces. In the present model, the halteres are involved in two nested feedback loops controlling the roll rate and the roll angle and in the feedforward system, controlling the head orientation with respect to the thorax.

Biological material

Episyrphus balteatus (De Geer 1776) pupae were purchased from Katz Biotech AG, Baruth, Germany. They were fed with pollen and honey ad libitum. To facilitate the manipulation, a drop of iron glue (composed of 45% beeswax, 45% rosin and 10% iron dust) was placed on the thorax. Small cylindrical magnets (Supermagnete, Gottmadingen, Germany; diameter 2 mm, length 1 mm, mass 23 mg) magnetized with the iron glue were used to make manipulation of the insects with ceramic clamps easier and gentler. Flies were released upside-down from a suction-based custom-built device. Its surface consisted of a downward-facing Fluon-coated plastic angled ridge, which minimized the occurrence of leg adhesion to the substrate. Suction was applied via a capillary glass tube (diameter ∼1 mm) introduced into a small hole in the middle of the plastic ridge. The device was attached to the top of the box, the horizontal position of which was monitored with a spirit level. The capillary tube was connected to a vacuum source, and the air pressure was valve controlled. In each trial, the insect to be tested was placed on a Fluon-coated carrier surface with its mesosternum (i.e. the mid-thoracic ventral surface located near the centre of mass) connected via suction to the opening of the capillary tube. Magnets were detached after transferring the insects to the device, before they were released. We always checked before each experiment whether the hoverflies equipped with the iron glue could fly in the breeding cages, in order to ensure that their flight ability was not affected by the glue. A total number of 13 falls involving 4 males and 6 females were recorded.

Experimental set-up and protocols

Aerial righting performances were recorded with a high-speed video camera (Phantom Miro M11O) at a rate of 1600 frames s−1 (1280×800 pixels). The macro lens used (Nikon Micro-Nikkor AF-S DX Micro 40 mm f/2.8 G) gave a good compromise between the size of the fly, the resolution and the visual field (the fly-to-camera distance was about 20 cm). The hoverfly was placed upside-down with a custom-built device inspired by Zeng et al. (2017), and released by turning off the vacuum source. The experimental arena was covered with a white diffuser (PMMA WH02, 3 mm thick) and illuminated from above by a halogen light (Kaiser Studiolight H; 5.6×10−13 W m−2). An optic fibre ring light (Schott, KL 1500) connected to a halogen light source via an optic fibre (Xenophot HLX, OSRAM) was placed around the camera lens to enhance the quality and the brightness of the video. The camera was triggered automatically as soon as the insect entered its field of view (Fig. 1A).

Fig. 1.

Illustration of the aerial righting reflex andthe tracking process. (A) The experimental set-up used to analyse the hoverfly (Episyrphus balteatus) aerial righting reflex. The observation cage consisted of a 40×40×40 cm transparent PVC box covered with a white optical diffuser, illuminated from above or below by a halogen light, and from the side by an optic fibre ring light placed around the camera lens. The hoverfly was held upside-down on the ceiling of this box by means of a small capillary tube connected to a vacuum pump. When the vacuum source was turned off, the fly was released and started falling. The fall was recorded with a high-speed video camera equipped with a macro lens operating at a rate of 1600 frames s−1 in the full sensor resolution mode (1280×800 pixels). (B) A typical aerial righting reflex sequence (from trial 1). Here, we can see a series of body and head rotations making the fly reorient itself dorsoventrally from the upside-down position to the right-side up position, corresponding to roll angles of 180 and 0 deg, respectively. Green points indicate the top and bottom positions of the head tracked. The time frame (in ms) is indicated in the case of each fly's orientation performance. (C) Head and body angle relative to the absolute frame: head (θHR), thorax (θTR). Head/body angle (θHB) is defined in the fly's frame. Angles are defined relative to the vertical. The angle θHB was calculated using the following equation: θHBHR−θTR. (D) Tracking procedure. To estimate the hoverflies' body orientation, three pairs of points were tracked: the junction between two pairs of forelegs and hindlegs (hindlegs in orange and forelegs in red) and the junction between the wings and the body (in blue). The orientation of the head was measured based on the top and bottom dots (the green dots marked on the head).

Fig. 1.

Illustration of the aerial righting reflex andthe tracking process. (A) The experimental set-up used to analyse the hoverfly (Episyrphus balteatus) aerial righting reflex. The observation cage consisted of a 40×40×40 cm transparent PVC box covered with a white optical diffuser, illuminated from above or below by a halogen light, and from the side by an optic fibre ring light placed around the camera lens. The hoverfly was held upside-down on the ceiling of this box by means of a small capillary tube connected to a vacuum pump. When the vacuum source was turned off, the fly was released and started falling. The fall was recorded with a high-speed video camera equipped with a macro lens operating at a rate of 1600 frames s−1 in the full sensor resolution mode (1280×800 pixels). (B) A typical aerial righting reflex sequence (from trial 1). Here, we can see a series of body and head rotations making the fly reorient itself dorsoventrally from the upside-down position to the right-side up position, corresponding to roll angles of 180 and 0 deg, respectively. Green points indicate the top and bottom positions of the head tracked. The time frame (in ms) is indicated in the case of each fly's orientation performance. (C) Head and body angle relative to the absolute frame: head (θHR), thorax (θTR). Head/body angle (θHB) is defined in the fly's frame. Angles are defined relative to the vertical. The angle θHB was calculated using the following equation: θHBHR−θTR. (D) Tracking procedure. To estimate the hoverflies' body orientation, three pairs of points were tracked: the junction between two pairs of forelegs and hindlegs (hindlegs in orange and forelegs in red) and the junction between the wings and the body (in blue). The orientation of the head was measured based on the top and bottom dots (the green dots marked on the head).

Image processing and analysis

As shown in Fig. 1D, the wing positions were recorded from two pairs of natural markers (at the wing junction points and wing tips). In the head, body and head/body study, the positions of the hoverfly's body were indicated by three pairs of markers placed at the two pairs of legs (front legs and hindlegs) and the wing junction points, and a single pair of markers placed at the top and bottom of the head was used to indicate the position of the head. All the trackers moving over a uniform background were recorded using the Tracker Video Analysis and Modeling Tool (©2018 Douglas Brown; see Fig. 1B,D). The stroke amplitude of the left (φL) and right wings (φR) relative to the body's orientation were defined as the angle between the wing angle (wing junction and wing tip) and the body roll angle (at the junction between the two wings). The stroke plane angle could not be measured because of the orientation of the camera, but we were only interested here in the relative difference between the left and right wingbeat amplitudes. The head and body roll orientation relative to the vertical were estimated in this way during aerial righting (Fig. 1C). To check the body roll orientation values (where θTR denotes thorax roll), we calculated the mean position of the two pairs of legs and the orientation of the wing junction angle. The leg and wing vectors are orthogonal to the dorsoventral body orientation. To determine the head orientation (where θHR denotes head roll), the two head tracking points (top and bottom) were used (Fig. 1B,D). In the normal right-side up position (legs pointing downwards), the head and body were taken to have a 0 deg inclination, while in the upside-down starting position (legs pointing upwards), the head and body were taken to have a 180 deg inclination (Fig. 1A,B).

The head/body angle θHB was obtained as the difference between the absolute head roll angle and the absolute thorax roll angle: θHBHR−θTR. Cluster analyses of normalized wingbeat amplitude differences (see Fig. 2C) were performed with R (www.R-project.org) while the other analyses were performed with MATLAB (R2018a, MathWorks, Natick, MA, USA). The evolution with time of all the angles measured and the roll angle velocities were calculated by applying a Savitzky–Golay filter (order 2, window: 35). As the body always rights before the complete reorientation of the head (see Fig. 3), it was assumed here that the righting reflex started with the first wingbeat and ended when θHB was equal to zero (i.e. when the head was realigned with the body). We therefore focused on the hoverfly's body kinematics during this brief part of the fall.

Fig. 2.

Wing kinematics on the rollaxis. (A) Stroke amplitude (positional angle) φ for the two wings (φ­R, right wing; φ­L, left wing) over time during one clockwise rotation (trial 7). The period of a wingbeat between the upstroke (φUp) and downstroke (φDown) is indicated. Body roll angle θTR is also shown. (B) Peak-to-peak stroke amplitude (φmax) recorded in one trial (trial 7) for the left and right wings. Upstrokes (upward arrowheads) and downstrokes (downward arrowheads) are differentiated. Lines correspond to the mean value of the upstroke and downstroke amplitudes in the case of each wingbeat. (C) θTR versus normalized difference in wingbeat amplitude [=φ­R−φ­L)/180] during six trials (trials 3, 5, 6, 7, 10 and 12). Two clusters were found to exist, giving a bss/tss (between sum of squares/total sum of squares) of 85.1%.

Fig. 2.

Wing kinematics on the rollaxis. (A) Stroke amplitude (positional angle) φ for the two wings (φ­R, right wing; φ­L, left wing) over time during one clockwise rotation (trial 7). The period of a wingbeat between the upstroke (φUp) and downstroke (φDown) is indicated. Body roll angle θTR is also shown. (B) Peak-to-peak stroke amplitude (φmax) recorded in one trial (trial 7) for the left and right wings. Upstrokes (upward arrowheads) and downstrokes (downward arrowheads) are differentiated. Lines correspond to the mean value of the upstroke and downstroke amplitudes in the case of each wingbeat. (C) θTR versus normalized difference in wingbeat amplitude [=φ­R−φ­L)/180] during six trials (trials 3, 5, 6, 7, 10 and 12). Two clusters were found to exist, giving a bss/tss (between sum of squares/total sum of squares) of 85.1%.

Fig. 3.

Plots of head, body and head/body angleHR, θTR and θHB) over time. Right-side up and upside-down positions correspond to roll angles of 0 and 180 deg, respectively. Thick lines are means and shaded areas are s.d. The s.d. for θTR and θHB was due to differences between the three body tracking methods used (see Materials and Methods: hindleg, foreleg and wing junctions). The solid vertical line indicates the time of the first wingbeat and the dotted horizontal lines indicate the angles 180, 0 and −90 deg. The time lag between θTR and θHR is indicated by the double arrow in trial 1.

Fig. 3.

Plots of head, body and head/body angleHR, θTR and θHB) over time. Right-side up and upside-down positions correspond to roll angles of 0 and 180 deg, respectively. Thick lines are means and shaded areas are s.d. The s.d. for θTR and θHB was due to differences between the three body tracking methods used (see Materials and Methods: hindleg, foreleg and wing junctions). The solid vertical line indicates the time of the first wingbeat and the dotted horizontal lines indicate the angles 180, 0 and −90 deg. The time lag between θTR and θHR is indicated by the double arrow in trial 1.

Additional experiments confirming the validity of the model

In order to test the dynamic model for the righting reflex, we performed some additional experiments. In previous experiments (Nalbach, 1993; Nalbach and Hengstenberg, 1994), it has been shown that flies with the halteres removed are unable to stay aloft in flight or start their wingbeats. To confirm the role of the halteres, we loaded the halteres with a small drop of glue. We deposited a 0.2 mg drop of glue (50% beeswax, 50% rosin; equivalent to 1% of the mass of E. balteatus) onto the tip of each haltere under visual control using an eyepiece-less stereo microscope (Mantis Elite by Vision Engineering) with a magnification of 15. We also tested the hoverfly's response to a strong change in the lighting conditions by illuminating hoverflies from below with a white halogen light (Kaiser Studiolight H, irradiance of 1.76×10−11 W m−2). Finally, we tested whether the righting reflex was driven by head rotation by gluing the head to the thorax, as detailed above for the halteres but with a 0.6 mg drop of glue. Body and head rotations were recorded using a high-speed video camera (Phantom VEO E310) at a rate of 3600 frames s−1 (resolution: 1280×800 pixels). A total of 11 falls (from 1 male and 2 females) were recorded in the loaded halteres condition, 13 falls (from 3 males and 1 female) in the altered lighting conditions (illumination from below) and 6 falls (from 2 females) in the head–thorax glued condition. Mean additional mass estimates were obtained by loading a piece of paper with 10 drops of glue and calculating the extra mass as the total mass divided by 10.

In the loaded halteres condition, the falling flies could be viewed from the side. Projected distance calculations were therefore performed in order to estimate the head and body angles (see Fig. S1; Viollet and Zeil, 2013).

Statistical comparisons were performed with R (www.R-project.org) on the experimental variables between the normal condition and the two additional conditions – illumination from below and loaded halters – with a post hoc Kruskal–Dunn test and on one variable – time to onset of the righting reflex – between six samples of six trials of the normal condition and the head–thorax glued condition with a Wilcoxon test.

After being released upside-down, E. balteatus hoverflies are able to right themselves starting from the first wingbeat by generating a 180 deg roll rotation via an asymmetric stroke amplitude between the right and left wings, defined by the positional angles φ­R and φ­L, respectively, as shown in Fig. 2A. Two phases can be observed during the righting process: the first phase where, in the case of a clockwise rotation, φ­L is larger than φ­R, followed by the second phase, where φ­R becomes larger than φ­L (see Fig. 2A,B). The stroke amplitudes of the two wings recorded during trial 7 are shown in Fig. 2A. Fig. 2B shows the occurrence of a smooth transition between the peak-to-peak stroke amplitudes of the left and right wings versus each wingbeat period. It can therefore be concluded that the body rotation results from the difference in stroke amplitude. At the first wingbeat, active torque roll is triggered by the difference between the right and left wing stroke amplitudes, but after five wingbeats, the sign of the difference is reversed, resulting in an active counter-torque roll, stabilizing the fly's attitude on the roll axis. As shown in Fig. 2C, where the thorax angle (θTR) is plotted versus the normalized wingbeat amplitude difference, the presence of two clusters is clear. The reversal of the sign of the normalized wingbeat amplitude difference observed during the righting manoeuvre suggests that the torque roll movement is suddenly reversed during the righting process, in line with the occurrence of an aggressive manoeuvre.

Righting was therefore studied here from the first wingbeat to the end of the righting process (see Figs 3 and 4), defined as the moment when θHB (head/body angle) became equal to 0 deg. As can be seen from Fig. 3, the amplitude and duration of the righting process were fairly variable. It was observed in some cases that hoverflies kept on rotating after reaching 0 deg (i.e. −90 deg in trial 1; see Fig. 3), while in other cases, they stopped righting before reaching an angle of 0 deg (i.e. 25 deg in trial 12; see Fig. 3). Despite the disparities observed among the responses, the time elapsing before the first wingbeat (median value 23.75 ms), the time taken by the hoverflies to reorient themselves (median value 48.8 ms), the number of wingbeats (median value 6 wingbeats) and the distance travelled during the righting process (median value 39.6 mm) did not vary conspicuously (Fig. 5).

Fig. 4.

Dynamic analysis of the righting performance. Illustration of the various phases in the righting process (top) and the roll angular speed of the thorax (Ω­TR), head (ΩHR) and head/body (ΩHB) versus time in one trial (trial 2; bottom). The lines correspond to the mean value obtained with the three tracking methods used (hindleg, foreleg and wing junctions) and the shaded areas to the s.d. The solid vertical line corresponds to the first wingbeat and the dotted vertical line marks the border between the two righting phases. Maximum time lag corresponds to the time lag between the body and head peak angular speeds.

Fig. 4.

Dynamic analysis of the righting performance. Illustration of the various phases in the righting process (top) and the roll angular speed of the thorax (Ω­TR), head (ΩHR) and head/body (ΩHB) versus time in one trial (trial 2; bottom). The lines correspond to the mean value obtained with the three tracking methods used (hindleg, foreleg and wing junctions) and the shaded areas to the s.d. The solid vertical line corresponds to the first wingbeat and the dotted vertical line marks the border between the two righting phases. Maximum time lag corresponds to the time lag between the body and head peak angular speeds.

As observed in Fig. 3, a time lag occurred systematically between θTR (thorax roll angle) and θHR (head roll angle): the body initiated the righting response before the head. The maximum value of this time lag was determined by subtracting the time at the minimum value of the head roll angular speed (ΩHR) from the time at the minimum value of the body roll angular speed (ΩTR) (see Fig. 4). As shown in Figs 3 and 5E, the maximum time lag ranged from 9 ms to 28 ms.

Fig. 5.

Aerial righting reflex variables recorded in each of the 13 trials. (A) Time to the first wingbeat. (B) Falling height. (C) Duration of the aerial righting reflex. (D) Number of wingbeats. (E) Maximum time lag between θTR and θHR. (F) Maximum value of θHB. Median value is indicated by the horizontal dotted line.

Fig. 5.

Aerial righting reflex variables recorded in each of the 13 trials. (A) Time to the first wingbeat. (B) Falling height. (C) Duration of the aerial righting reflex. (D) Number of wingbeats. (E) Maximum time lag between θTR and θHR. (F) Maximum value of θHB. Median value is indicated by the horizontal dotted line.

To account for the time lag observed between θTR and θHR, it seemed worth analysing the dynamics of θHB. The time lag between θTR and θHR resulted from changes in θHB (Fig. 3). θTR rotated first, while θHR remained constant, resulting in an increase in θHB from a null value to a maximum value, and θHR then started to rotate and to catch up with θTR, resulting in a decrease in θHB from the maximum value down to null. Disparities were also observed between the 13 trials in the maximum value of θHB, which ranged from less than 50 deg (in trials 4 and 13) to more than 100 deg (in trials 7 and 11; see Fig. 3 and Fig. 5F).

Fast 180 deg roll rotations performed by hoverflies during the righting process resulted from angular speeds ΩHR and ΩTR as fast as −10×103 deg s−1 (see trial 2 in Fig. 4). Thanks to the low inertia (Iroll of 9.76e−12 kg m−2) and the fast dynamics (48.8 ms; see Fig. 5), a hoverfly can produce fast body angular speeds when required to achieve a complete righting process. The time elapsing between ΩTR and ΩHR is also clearly visible in Fig. 4: ΩTR started to increase before ΩHR. Two phases can be observed, depending on the value of ΩHB. The hoverfly's righting states and phases are shown in Fig. 4, where it can be seen that the head rotated first anti-clockwise to compensate for the rotation of the thorax, and then clockwise in order to become realigned with the body.

Previous studies have shown that θHB is stabilized and compensates for the changes in θTR (Hengstenberg, 1993; Hardcastle and Krapp, 2016; Sandeman and Markl, 1980). The best way of compensating quickly for these changes is surely to measure them directly and to use this measurement to compensate for them. We adopted the hypothesis that the time elapsing between θTR and θHR might result from the gaze stabilization reflex.

For the three additional experiments shown in Fig. 6 and Figs S2–S4 (illumination from below, loaded halteres and head–thorax glued), hoverflies were always able to right themselves. When illuminated from below, hoverflies righted themselves in a similar short period of time (median value 61.11 ms) with a shorter time lag (median value 8.1 ms, significant difference) and a smaller θHB (median value 44.19 deg, significant difference) than for the illumination from above condition. When halteres were loaded with glue, flies righted themselves faster (median value 29.72 ms, significant difference) with a smaller time lag (median value 6.1 ms, extremely significant difference) and a similar θHB (median value 58.21 deg). When the head and thorax were glued together, no significant differences were found in terms of duration of the righting reflex (median value 44.72 ms).

Fig. 6.

Confirming the validity of the model. (A–C) Comparison of the duration of the righting reflex (A), maximum time lag (B) and maximum θHB (C) for illumination from below and loaded halteres condition versus normal condition. (D) Duration of the righting reflex under head–thorax glued condition. Box plots show the median, and upper and lower quartiles, and whiskers indicate the interquartile range. ***P<0.001, *P<0.05.

Fig. 6.

Confirming the validity of the model. (A–C) Comparison of the duration of the righting reflex (A), maximum time lag (B) and maximum θHB (C) for illumination from below and loaded halteres condition versus normal condition. (D) Duration of the righting reflex under head–thorax glued condition. Box plots show the median, and upper and lower quartiles, and whiskers indicate the interquartile range. ***P<0.001, *P<0.05.

In line with previous studies carried out at our laboratory (Goulard et al., 2015, 2016, 2018a,b), hoverflies were dropped under free-fall conditions, upside-down with their legs touching the top of the box, in order to study aerial righting in flies for the first time. As expected, hoverflies in the upside-down position were found to trigger their wingbeats and to rotate quickly in order to regain the right-side up position within a short lapse of time (48.8 ms; see Fig. 5C). These rotational manoeuvres involved asymmetric wing strokes (active torque; see Fig. 2), resulting in fast thorax roll velocities of the order of several thousands of degrees per second (range: −2×103 deg s−1 to −12×103 deg s−1; see Fig. 4).

Proprioceptive processes used to detect the upside-down state

In our set-up, hoverflies can probably use two main types of cue when they are held upside-down: the dorsal light response (DLR) and proprioceptive cues. The DLR is a reflex that several families of insects use to determine their orientation based on the fact that the brightest part of the environment is presumably located above them (Mittelstaedt, 1950; Hengstenberg, 1993; Goulard et al., 2015, 2018a; Meyer and Bullock, 1977; Schuppe and Hengstenberg, 1993). In a previous experiment, Goulard et al. (2018a) showed that lighting from below drastically affects hoverfly stabilization during free fall, which proves that hoverflies are highly sensitive to light coming from the ground. In the present case, the halogen light projected from below would provide the hoverfly (upside-down) with a vertical reference frame oriented in the appropriate position. Therefore, if the fly's righting process depended only on the DLR, we would observe the occurrence of no righting in this condition, which was never the case. In addition, we observed only a small effect of the lighting conditions on the head movement during the righting process (see Fig. 6B,C, which shows a shorter time lag and a smaller θHB), suggesting that the DLR might be involved in the feedforward control of the head as a modulation of its gain (see FNM(s) box in Fig. 7A). Further experiments are required to better understand the contribution of the DLR to the righting reflex.

Fig. 7.

Dynamicmodel of the rightingreflex. (A) Control block diagram including two nested feedback-loops: the fast feedback-loop controls the roll angular speed measured by the halteres, and the slower loop controls the roll angle on the basis of the estimated θ̂TR provided by a neural integrator. A feedforward controller transfer function FNM(s)=k/(τ1s+1) (where s is the Laplace variable, k is a gain and τ is the time constant) receives the roll speeds measured as it inputs Ω̅TR and delivers output signals which control the orientation of the head with respect to the body θHB. The latter signal is therefore proportional to the body roll speed measured Ω̅TR, but with the opposite sign (block −1). The reference input signal Ref controls the amplitude of the body roll. The value of Ref can be set based on the leg proprioceptive cues and the dorsal light response (DLR). We differentiated between the angular speed of the thorax ΩTR and the speed measured by the halteres, which was expressed as Ω̅TR. For the sake of clarity, the haltere block was split into two identical blocks. H(s)=1/(τ2s+1); εroll and εspeed are error signals; K is gain; and Uroll is the torque roll. (B) Typical time course of the simulated control input signal Uroll corresponding to torque roll.

Fig. 7.

Dynamicmodel of the rightingreflex. (A) Control block diagram including two nested feedback-loops: the fast feedback-loop controls the roll angular speed measured by the halteres, and the slower loop controls the roll angle on the basis of the estimated θ̂TR provided by a neural integrator. A feedforward controller transfer function FNM(s)=k/(τ1s+1) (where s is the Laplace variable, k is a gain and τ is the time constant) receives the roll speeds measured as it inputs Ω̅TR and delivers output signals which control the orientation of the head with respect to the body θHB. The latter signal is therefore proportional to the body roll speed measured Ω̅TR, but with the opposite sign (block −1). The reference input signal Ref controls the amplitude of the body roll. The value of Ref can be set based on the leg proprioceptive cues and the dorsal light response (DLR). We differentiated between the angular speed of the thorax ΩTR and the speed measured by the halteres, which was expressed as Ω̅TR. For the sake of clarity, the haltere block was split into two identical blocks. H(s)=1/(τ2s+1); εroll and εspeed are error signals; K is gain; and Uroll is the torque roll. (B) Typical time course of the simulated control input signal Uroll corresponding to torque roll.

Proprioceptive cues which are sensed by the chordotonal organs in the insect's legs (Tuthill and Wilson, 2016). The proprioceptive processes involved in insects' postural reflexes are stimulated by the weight of the legs (Horn and Lang, 1978; Kress and Egelhaaf, 2012; Horn, 1982). Force and load signals act as orientation cues (walking; Büschges et al., 2008; Duysens et al., 2000). Hoverflies are therefore able to quickly estimate the righting posture required to respond to loss of contact between their legs and the substrate (via the tarsal reflex) (see Binns, 1977; Fraenkel, 1932; Pringle, 1938; Dudley, 2002). As suggested in the model presented in Fig. 7, DLR combined with leg proprioception may be used by flies to estimate the angle of the surface on which they are standing, and would therefore enable them to set the value of the input reference signal Ref before taking off from a tilted surface. The input reference signal is an input signal corresponding to the reference value that the closed-loop system tries to reach in steady state. In conclusion, DLR and proprioception are likely to conflict when the lighting originates from below, but further experiments are now required to be able to clearly define their respective contributions to the righting reflex.

Body roll model and righting response

In fruit flies, roll torque results from asymmetric wing movements (Ristroph et al., 2010, 2013; Sane, 2003; Beatus et al., 2015), which leads to a difference in the lift generated by each wing. The results in the normal condition as well as in the head–thorax glued condition obtained here tend to confirm that the aerial righting performance of E. balteatus is purely aerodynamic, i.e. hoverflies produce asymmetric flapping movements in order to trigger a torque roll and right themselves (see Fig. 2). As shown in Figs 2 and 7B (sign of the simulated torque roll signal), two phases exist: the first positive and the second negative, resulting in the righting process. The active force used to start the rotation of the body (phase 1) seems to be larger than the force used to stabilize it at the end of the righting (phase 2). Fig. 2C clearly shows two clusters, suggesting that a passive torque roll (Hedrick et al., 2009) related to the friction of the wings also contributes to the stabilization of the fly, leading to this asymmetry in the wingbeat amplitude observed during a complete righting process.

It is worth noting that we have never observed any righting manoeuvres involving body pitch rotations under normal conditions. Body pitch depends on the fly's ability to shift the centre of mass forwards (or backwards) in order to trigger a nose-up (or nose-down) pitch torque movement (Ristroph et al., 2013). Controlling the wingbeat amplitude differentially is probably much more efficient and direct than using each wingbeat's duty cycle – the ratio between the durations of the upper (upstroke ϕUp) and lower (downstroke ϕDown) parts of a wingbeat (see Fig. 2A). As explained in the Introduction, vertebrates are known to move segments of their body, legs (reptiles) or tail (lizards) in certain configurations in order to control the instantaneous moment of inertia and the angular momentum. However, most hoverflies are much smaller than vertebrates and they are exposed to more viscous aerodynamic forces (see Jusufi et al., 2011). Aerodynamic interactions are therefore likely to predominate over inertial effects. We never observed the occurrence of any righting movements without any wingbeats being triggered and the head–thorax glued condition showed that righting is not coupled to any head movement. We therefore modelled the roll dynamics in terms of a purely second-order system (a double integrator) receiving torque Uroll as its inputs and delivering, via the moment of inertia Iroll, outputs specifying the appropriate thorax roll speed ΩTR and thorax roll angle θTR. No evidence showing the presence of a neural integrator serving to estimate the roll has been obtained so far, although the existence of this component is biologically plausible as the temporal drift inherent to any vibrating rate gyro such as the halteres (Acar and Shkel, 2009) is likely to be very small during the short time required to perform righting manoeuvres. Once the righting has been accomplished, hoverflies can count on vision in addition to the thorax roll speed to estimate their body roll and compensate for any drift (see the unbiased rate gyro method based on an inertial measurement unit in Wu et al., 2015).

Closed-loop roll control during the righting process

Accurate control of the body attitude (roll) during the righting process is also necessary to be able to reach the steady-state 0 deg position (right-side up) reliably. Flies may use visual motion cues (Meresman et al., 2014; Yanoviak et al., 2010) combined with inertial measurements provided by the halteres (Dickinson et al., 1999; Fraenkel and Pringle, 1938). During flight, the halteres are known to oscillate up and down in antiphase with the wings (see Nalbach, 1993) and are therefore highly receptive to the state of wing activation (see Dickerson et al., 2019; Parween and Pratap, 2015; Deora et al., 2015, 2017; Pratt et al., 2017).

However, because of the extremely short duration of the righting reflex (∼49 ms) and the relatively long processing time required by the motion-processing neurons (about ∼50 ms in the fruit fly; see Warzecha and Egelhaaf, 2000; Frye, 2009), the righting reflex can be assumed to depend only on the angular body speed measurements provided by the halteres. The halteres are known to show fast response times of only ∼5 ms (Pringle and Gray, 1948; Sandeman and Markl, 1980; Taylor and Krapp, 2007; Dickinson and Muijres, 2016; Sherman and Dickinson, 2004, 2003; Liu et al., 2016), and the righting response times recorded here were consistent with those of the halteres. A self-stabilizing reflex has been studied in fruit flies performing cruising flights (Ristroph et al., 2010, 2013; Beatus et al., 2015). Upon undergoing an external disturbance, the fly adjusts its body orientation in order to recover its initial right-side up position within 30 ms. The roll-induced perturbations applied in the later studies amounted to about 45 deg. In addition, the halteres are known to be involved in insects' detection of fast perturbations (Ristroph et al., 2010; Dickinson et al., 1999) and in fruit flies' mediated equilibrium reflexes (Liu et al., 2016; Nalbach, 1993, 1994; Nalbach and Hengstenberg, 1994; Dickinson et al., 1999; Fox and Daniel, 2008; Huston and Krapp, 2009; Frye, 2009).

Head/body movements and time lags

Hoverflies are able to rotate their head around the roll axis with respect to their body up to a median angle of 77.7 deg (see Fig. 5F). During the righting phase, we observed a median time lag of 16.3 ms (see Fig. 5E) between the head and body rotations. The body starts to rotate first, and then the head rotates in the direction imposed by the body. Four possibilities can be envisaged for modelling this time lag. (1) As suggested by the results of a previous study on wasps (Viollet and Zeil, 2013), head orientation may be controlled by a feed-forward signal, while a copy of the command signals sent to the wing motoneurons is also sent with the opposite sign to the head position (neck) servo system. If a simple time lag is inserted into the pathway controlling the head orientation, one might wonder what the effects of this time lag might be, and how biologically relevant it is. Adding a time lag would definitely alter the performance of the gaze stabilization reflex, which plays a crucial role in blowflies (for review, see Hardcastle and Krapp, 2016). (2) As suggested by previous studies on gaze stabilization (see Hardcastle and Krapp, 2016; Mittelstaedt, 1950), without any need for halteres, passive inertial stabilization may serve to compensate for body rotations. Assuming the neck to act like a simple spiral spring, the head would first stay behind and then be pulled in the direction of the rotation imposed by the body. However, the difference in mass between the body (21 mg) and head (5 mg), corresponding to a ratio of 4.2 between the head and body moments of inertia (assuming the body to be a cylinder and the head a sphere) is not consistent with the idea that a purely passive process of stabilization might occur during the righting process. In addition, Gilbert and Bauer (1998) established that in the flesh fly, head posture results from both a passive and an active control of the head based on the prosternal organs. It would certainly be of interest to investigate hoverfly head dynamics more closely in future studies. Here, we modelled the neck motor system in the form of a first-order filter [a FNM(s) transfer function] to account for the head's moment of inertia and the friction of the neck muscles. Values of FNM(s) were obtained by fitting the model's response to the 13 trials (see Fig. 4). (3) As shown in Fig. 8B (and also in the model in Fig. 7A), we assumed that θHB is negatively proportional to ΩTR (see block −1 in the model in Fig. 7A): the head is driven by the body roll speed. The head therefore changes its rotational direction when the body roll speed decreases. Fig. 8B and Fig. 9 show that the head angle is highly correlated with the peak in the roll angular speed and not correlated with any particular value of the head/body angle. The role of a switch control would be very unclear in terms of its functionality, whereas a direct control of the head based on the body's angular speed makes sense in terms of the gaze stabilization reflex.

Fig. 8.

Response of the righting reflex model. (A) Response of θTR, θHR and θHB versus time to a reference input signal Ref=180 deg. The model accounts for the time lag observed (arrow; see Figs 3,4 and Fig. 5E) between head and body. (B) Main angular speed Ω and head/body orientation θHB plotted versus time in order to explain the time lag observed during the roll manoeuvre. Because of the feedforward control system (see Fig. 7), the θHB can be seen to have faithfully followed the changes in the body angular speed measured Ω̅TR, taking the opposite sign (−1 block in the model). θHB is driven by the body roll speed. The head therefore compensates for the body rotation (in the first phase) and then rotates in the same direction as the body (in the second phase) when the sign of the head speed becomes negative at the instant indicated by the vertical dashed lines. Model parameters: Ref=180 deg, K=1.22e−9, Iroll=9.76e−12 kg m−2, H(s)=1/(0.0035s+1), FNM(s)=0.012/(0.004s+1). Model parameters were defined by fitting the model to the data recorded in the 13 trials previously performed (see Fig. 3). (C,D) Comparison between θTR (C) and θHR (D) data obtained with the model and in the 13 trials. Model parameters were the same as previously stated, with K variation (9.760×10−10, 1.098×10−09, 1.220×10−09), FNM(s) variation (8.5×10−3, 10×10−3, 13×10−3) and Uroll variation (3.5×10−3, 4×10−3, 5×10−3). Thick lines are means and shaded areas are s.d. due to K, FNM(s) and Uroll variation.

Fig. 8.

Response of the righting reflex model. (A) Response of θTR, θHR and θHB versus time to a reference input signal Ref=180 deg. The model accounts for the time lag observed (arrow; see Figs 3,4 and Fig. 5E) between head and body. (B) Main angular speed Ω and head/body orientation θHB plotted versus time in order to explain the time lag observed during the roll manoeuvre. Because of the feedforward control system (see Fig. 7), the θHB can be seen to have faithfully followed the changes in the body angular speed measured Ω̅TR, taking the opposite sign (−1 block in the model). θHB is driven by the body roll speed. The head therefore compensates for the body rotation (in the first phase) and then rotates in the same direction as the body (in the second phase) when the sign of the head speed becomes negative at the instant indicated by the vertical dashed lines. Model parameters: Ref=180 deg, K=1.22e−9, Iroll=9.76e−12 kg m−2, H(s)=1/(0.0035s+1), FNM(s)=0.012/(0.004s+1). Model parameters were defined by fitting the model to the data recorded in the 13 trials previously performed (see Fig. 3). (C,D) Comparison between θTR (C) and θHR (D) data obtained with the model and in the 13 trials. Model parameters were the same as previously stated, with K variation (9.760×10−10, 1.098×10−09, 1.220×10−09), FNM(s) variation (8.5×10−3, 10×10−3, 13×10−3) and Uroll variation (3.5×10−3, 4×10−3, 5×10−3). Thick lines are means and shaded areas are s.d. due to K, FNM(s) and Uroll variation.

Fig. 9.

Cross-correlation and gain. (A) Normalized ΩTR and θHB for one trial (trial 12). Cross-correlation of normalized ΩTR and θHB was calculated within the temporal window (grey shaded area) starting when increasing ΩTR was higher than 0.5 and ending when θHB was lower than 0.5. The same threshold of 0.5 was applied for each trial. (B,C) Results of the cross-correlation between the normalized ΩTR and θHB for trial 12 (B; vertical dashed line indicates the maximum value of the cross-correlation) and for the 13 trials (C) where gain=maximum θHB/maximum ΩTR in each trial. Gain (k) of FNM(s) (see Fig. 8). (D) Results of the cross-correlations in the 13 trials, suggesting the existence of a strong correlation between ΩTR and θHB.

Fig. 9.

Cross-correlation and gain. (A) Normalized ΩTR and θHB for one trial (trial 12). Cross-correlation of normalized ΩTR and θHB was calculated within the temporal window (grey shaded area) starting when increasing ΩTR was higher than 0.5 and ending when θHB was lower than 0.5. The same threshold of 0.5 was applied for each trial. (B,C) Results of the cross-correlation between the normalized ΩTR and θHB for trial 12 (B; vertical dashed line indicates the maximum value of the cross-correlation) and for the 13 trials (C) where gain=maximum θHB/maximum ΩTR in each trial. Gain (k) of FNM(s) (see Fig. 8). (D) Results of the cross-correlations in the 13 trials, suggesting the existence of a strong correlation between ΩTR and θHB.

(4) As suggested by the authors of previous studies on fast haltere-induced compensatory head movements (Hengstenberg, 1993; Hardcastle and Krapp, 2016; Sandeman and Markl, 1980), the time lag observed here between the head and body responses may result from the gaze stabilization reflex being activated at the very beginning of the wingbeats. As described in our model (see Fig. 7A), the feedforward control of the head depends on the body's angular speed transmitted by the halteres. As in the simulated response (see Fig. 8A,B), the orientation of the head with respect to the body θHB is proportional to the body's angular speed ΩTR. The head therefore adopts the opposite response to that of the body. In the first phase, the head compensates for the body rotation while the body speed is increasing, and in the second phase, the head rotates as dictated by the body roll. As indicated by the dashed line in Fig. 8B, the direction of the head rotation is reversed when the body's angular speed starts to decrease. On the basis of the present model, the existence of a feedforward head control based on the thorax's angular speed suggests that the angular position of the head with respect to the body θHB must be strongly correlated with the thorax's angular speed ΩTR. We therefore analysed the cross-correlation between these two normalized signals (see Fig. 9A). The cross-correlation function applied to the 13 trials showed the existence of a median time lag of 7.5 ms (see Fig. 9D), with a standard deviation as small as 2.5 ms, which suggests the existence of a strong correlation between thorax speed and head orientation, as expected. In addition, the simulated time lag observed between the head and body upon combining a physically plausible closed-loop control of the body roll with a feedforward control of the head orientation accounts accurately for the time lag observed in hoverflies (see Fig. 8). It is worth noting that the two phases in the simulated head/body movement would require a seamless feedforward control of the head orientation based on the body's angular speed transmitted by the halteres.

Haltere-based feedback and feedforward control systems

As shown by the 3D animation presented in Movie 1, the present dynamic model can make a fly rotate by 180 deg and reach a stable steady-state orientation of 0 deg within a period of 50 ms, which is similar to that recorded in hoverflies' responses (see Fig. 5C). As shown in Fig. 8, this dynamic model shows very similar time patterns to hoverflies' average responses, as well as similar roll head/body angles and body angular speeds, which can be as fast as 10×103 deg s−1. Like blowflies, which perform fast body roll rotations of up to 2×103 deg s−1 (Schilstra and Hateren, 1999) with a maximum amplitude of ±90 deg (Hengstenberg, 1988), and Bembix wasps, which can perform extremely pronounced body roll movements with an amplitude of up to 180 deg at 2–4×103 deg s−1 (Zeil et al., 2008), E. balteatus hoverflies are another example of outstandingly fast fliers. During the high-speed rotations recorded during the righting process, the role of vision in the flight stabilization process will presumably be very small, while that of the halteres, which, with a very small latency, concomitantly deliver a feedback-loop signal stabilizing the body's roll (fruitfly: Beatus et al., 2015) and a fast feedforward signal (lasting about 3–5 ms in blowflies: Sandeman and Markl, 1980; Hengstenberg, 1993), may serve to adjust the head orientation. However, one might wonder why it is necessary for the fly to activate its gaze stabilization reflex during the righting manoeuvre. The model presented here suggests that compensatory head movements may occur as soon as the body starts to rotate at the onset of the wingbeats, which means that the halteres are also activated (Nalbach, 1993). To check whether the time lag observed between the head and body resulted from head roll control by the halteres, we loaded the haltere with a drop of glue (see Materials and Methods). The additional mass significantly shortened the time lag (median value: 6.1 ms) versus that under normal conditions or with lighting from below. We also observed a significant effect of this extra mass on the rotational dynamics, as the insects took a shorter time to rotate, which is in line with the occurrence of an increase in the maximum body angular speed, which could be as fast as 25.84×103 deg s−1 in comparison with 9.502×103 deg s−1 under normal conditions. However, a conspicuous behavioural difference was also observed not only in roll but also in pitch manoeuvres. By adding a mass at the tip of each haltere, we increased the mass moment of inertia and thus decreased the haltere's natural frequency in both the actuation and sensing directions (see Parween and Pratap, 2015). This also increased the sensitivity (gain) of the halteres to the Coriolis force (see Wu et al., 2002; Northrop, 2000). In addition, as shown by Parween et al. (2014), periodic temporal strain variations due to the Coriolis force occur at the same frequency in both pitch and roll movements (while also showing the same harmonics) but differ in terms of their amplitude. By increasing the mass, we probably increased the coupling existing between the pitch and roll perceived, degrading the fly's ability to stabilize its pitch and roll movements efficiently. Greater body rotational speeds may also have been caused by a change in the haltere gain. Lastly, in their study on mosquitoes, Dickerson et al. (2015) showed that a change of just a few nanograms in the mass of the halteres can lead to unstable flight performance. Adding a few milligrams to the hoverfly's halteres decreases the value of the haltere's lateral resonant frequency ω (in rad s−1) defined as (see Wu et al., 2002):
(1)
where kl is the lateral stiffness and m is the mass of the haltere. In consequence, increasing m certainly drastically affects the closed-loop control of the fly's body dynamics, resulting in the considerable instability we observed during the righting process.

As discussed by Taylor and Krapp (2007) and recently by Hardcastle and Krapp (2016), gaze stabilization is crucial to steady flight because it reduces motion blur. It would therefore not be surprising if the gaze stabilization reflex was activated at a very early stage during the righting manoeuvres once the wingbeats have been triggered and the halteres are therefore vibrating as well. It is worth noting that gaze stabilization is not detrimental to the fly's ability to start rotating within a very short time. A righting response lasting for about 50 ms might suffice to enable the gaze stabilization reflex to be fully operational during the subsequent cruise flight.

We are most grateful to Julien Diperi for his contribution to building the experimental set-up and to Marc Boyron for developing the electronics: all the research presented in this paper was based on their work. We also want to thank Jessica Blanc for correcting and improving the English in the manuscript.

Author contributions

Conceptualization: A.V., S.V.; Methodology: A.V., L.P., J.V., S.V.; Software: A.V.; Validation: A.V.; Formal analysis: A.V., S.V.; Investigation: A.V.; Resources: A.V.; Data curation: A.V.; Writing - original draft: A.V., S.V.; Writing - review & editing: A.V., L.P., J.V., S.V.; Visualization: A.V.; Supervision: J.V., S.V.; Funding acquisition: J.V., S.V.

Funding

We acknowledge support from the Centre National de la Recherche Scientifique (CNRS), Aix-Marseille Université and the Agence Nationale de la Recherche (ANR) (in the framework of the OrigaBot project ANR-18-CE33-0008-01).

Data availability

Data from the study have been deposited in Figshare: doi:10.6084/m9.figshare.12520448.

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Competing interests

The authors declare no competing or financial interests.

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