Active and passive stabilization of body pitch in insect flight

Shoulder viscoelasticity in a raptor-inspired model alleviates instability and enhances passive gust rejection

Recent experiments with gliding raptors reveal a perplexing dichotomy: remarkably resilient gust rejection, but, at the same time, an exceptionally high degree of longitudinal instability. To resolve this incompatibility, a multiple degree of freedom model is developed with minimal requisite complexity to examine the hypothesis that the bird shoulder joint may embed essential stabilizing and preflexive mechanisms for rejecting rapid perturbations while simplifying and reducing control effort. Thus, the formulation herein is centrally premised upon distinct wing pitch and body pitch angles coupled via a Kelvin-Voigt viscoelastic shoulder joint. The model accurately exhibits empirical gust response of an unstable gliding raptor, generates biologically plausible equilibrium configurations, and the viscoelastic shoulder coupling is shown to drastically alleviate the high degree of instability predicted by conventional linear flight dynamics models. In fact, stability analysis of the model predicts a critical system timescale (the time to double amplitude of a pitch divergence mode) that is commensurate within vivomeasured latency of barn owls (Tyto alba). Active gust mitigation is studied by presupposing the owl behaves as an optimal controller. The system is under-actuated and the feedback control law is resolved in the controllable subspace using a Kalman decomposition. Importantly, control-theoretic analysis precisely identifies what discrete gust frequencies may be rapidly and passively rejected versus disturbances requiring feedback control intervention.

Wax "tails" enable planthopper nymphs to self-right midair and land on their feet

The striking appearance of wax 'tails' - posterior wax projections on planthopper nymphs - has captivated entomologists and naturalists alike. Despite their intriguing presence, the functional roles of these structures remain largely unexplored. This study leverages high-speed imaging to uncover the biomechanical implications of these wax formations in the aerial dynamics of planthopper nymphs (Ricania sp.). We quantitatively demonstrate that removing wax tails significantly increases body rotations during jumps. Specifically, nymphs without wax projections undergo continuous rotations, averaging 4.3 ± 1.9 per jump, in contrast to wax-intact nymphs, who narrowly complete a full rotation, averaging only 0.7 ± 0.2 per jump. This suggests that wax structures effectively counteract rotation through aerodynamic drag forces. These stark differences in body rotation correlate with landing success: nymphs with wax intact achieve a near perfect landing rate of 98.5%, while those without wax manage only a 35.5% success rate. Jump trajectory analysis reveals transitions from parabolic to Tartaglia shapes at higher take-off velocities for wax-intact nymphs, illustrating how wax structures assist nymphs in achieving stable, controlled descents. Our findings confirm the aerodynamic self-righting functionality of wax tails in stabilizing planthopper landings, advancing our understanding of the complex interplay between wax morphology and aerial maneuverability, with broader implications for the evolution of flight in wingless insects and bioinspired robotics.

The effects of wing inertial forces and mean stroke angle on the pitch dynamics of hovering insects

This paper discusses the wing inertial effects and the important role of the mean stroke angle on the pitch dynamics of hovering insects. The paper also presents a dynamic model appropriate for averaging and discusses the pitch stability results derived from the model. The model is used to predict the body angle of five insect species during hover, which are in good agreement with the available experimental results from different literature. The results suggest that the wing inertial forces have a considerable effect on pitch dynamics of insect flight and should not be ignored in dynamic analysis of hovering insects. The results also suggest that the body of hovering insects can not be vibrationally stabilized in a non-vertical orientation. Instead, the pitch angle of a hovering insect's body is mainly due to a balance of the moment of the insect's weight and the aerodynamic moment due to flapping kinematics with a nonzero mean stroke angle. Experiments with a flapping wing device confirm this results. To clearly explain the used model and clarify the difference between vibrational and non-vibrational stabilization, first this paper discusses the vibrational control of a three-degree-of-freedom force-input pendulum with its pivot moving in a vertical plane.

Excitation of the abdominal ganglion affects the electrophysiological activity of indirect flight muscles of the honeybee Apis mellifera

Our understanding of the nervous tissues that affect the wing flapping of insects mainly focuses on the brain, but wing flapping is a rhythmic movement related to the central pattern generator in the ventral nerve cord. To verify whether the neural activity of the abdominal ganglion of the honeybee (Apis mellifera) affects the flapping-wing flight, we profiled the response characteristics of indirect flight muscles to abdominal ganglion excitation. Strikingly, a change in the neural activity of ganglion 3 or ganglion 4 has a stronger effect on the electrophysiological activity of indirect flight muscles than that of ganglion 5. The electrophysiological activity of vertical indirect flight muscles is affected more by the change in neural activity of the abdominal ganglion than that of lateral indirect flight muscles. Moreover, the change in neural activity of the abdominal ganglion mainly causes the change in the muscular activity of indirect wing muscles, but the activity patterns change relatively little and there is little change in the complicated details. This work improves our understanding of the neuroregulatory mechanisms associated with the flapping-wing flight of honeybees.

Flies adaptively control flight to compensate for added inertia

Animal locomotion is highly adaptive, displaying a large degree of flexibility, yet how this flexibility arises from the integration of mechanics and neural control remains elusive. For instance, animals require flexible strategies to maintain performance as changes in mass or inertia impact stability. Compensatory strategies to mechanical loading are especially critical for animals that rely on flight for survival. To shed light on the capacity and flexibility of flight neuromechanics to mechanical loading, we pushed the performance of fruit flies (Drosophila) near its limit and implemented a control theoretic framework. Flies with added inertia were placed inside a virtual reality arena which permitted free rotation about the vertical (yaw) axis. Adding inertia increased the fly's response time yet had little influence on overall gaze stabilization performance. Flies maintained stability following the addition of inertia by adaptively modulating both visuomotor gain and damping. By contrast, mathematical modelling predicted a significant decrease in gaze stabilization performance. Adding inertia altered saccades, however, flies compensated for the added inertia by increasing saccade torque. Taken together, in response to added inertia flies increase reaction time but maintain flight performance through adaptive neural control. Overall, adding inertia decreases closed-loop flight robustness. Our work highlights the flexibility and capacity of motor control in flight.

Air-to-land transitions: from wingless animals and plant seeds to shuttlecocks and bio-inspired robots

Recent observations of wingless animals, including jumping nematodes, springtails, insects, and wingless vertebrates like geckos, snakes, and salamanders, have shown that their adaptations and body morphing are essential for rapid self-righting and controlled landing. These skills can reduce the risk of physical damage during collision, minimize recoil during landing, and allow for a quick escape response to minimize predation risk. The size, mass distribution, and speed of an animal determine its self-righting method, with larger animals depending on the conservation of angular momentum and smaller animals primarily using aerodynamic forces. Many animals falling through the air, from nematodes to salamanders, adopt a skydiving posture while descending. Similarly, plant seeds such as dandelions and samaras are able to turn upright in mid-air using aerodynamic forces and produce high decelerations. These aerial capabilities allow for a wide dispersal range, low-impact collisions, and effective landing and settling. Recently, small robots that can right themselves for controlled landings have been designed based on principles of aerial maneuvering in animals. Further research into the effects of unsteady flows on self-righting and landing in small arthropods, particularly those exhibiting explosive catapulting, could reveal how morphological features, flow dynamics, and physical mechanisms contribute to effective mid-air control. More broadly, studying apterygote (wingless insects) landing could also provide insight into the origin of insect flight. These research efforts have the potential to lead to the bio-inspired design of aerial micro-vehicles, sports projectiles, parachutes, and impulsive robots that can land upright in unsteady flow conditions.

Wing Kinematics-Based Flight Control Strategy in Insect-Inspired Flight Systems: Deep Reinforcement Learning Gives Solutions and Inspires Controller Design in Flapping MAVs

Flying insects exhibit outperforming stability and control via continuous wing flapping even under severe disturbances in various conditions of wind gust and turbulence. While conventional linear proportional derivative (PD)-based controllers are widely employed in insect-inspired flight systems, they usually fail to deal with large perturbation conditions in terms of the 6-DoF nonlinear control strategy. Here we propose a novel wing kinematics-based controller, which is optimized based on deep reinforcement learning (DRL) to stabilize bumblebee hovering under large perturbations. A high-fidelity Open AI Gym environment is established through coupling a CFD data-driven aerodynamic model and a 6-DoF flight dynamic model. The control policy with an action space of 4 is optimized using the off-policy Soft Actor-Critic (SAC) algorithm with automating entropy adjustment, which is verified to be of feasibility and robustness to achieve fast stabilization of the bumblebee hovering flight under full 6-DoF large disturbances. The 6-DoF wing kinematics-based DRL control strategy may provide an efficient autonomous controller design for bioinspired flapping-wing micro air vehicles.

Neuromuscular embodiment of feedback control elements in Drosophila flight

While insects such as Drosophila are flying, aerodynamic instabilities require that they make millisecond time scale adjustments to their wing motion to stay aloft and on course. These stabilization reflexes can be modeled as a proportional-integral (PI) controller; however, it is unclear how such control might be instantiated in insects at the level of muscles and neurons. Here, we show that the b1 and b2 motor units-prominent components of the fly's steering muscle system-modulate specific elements of the PI controller: the angular displacement (integral) and angular velocity (proportional), respectively. Moreover, these effects are observed only during the stabilization of pitch. Our results provide evidence for an organizational principle in which each muscle contributes to a specific functional role in flight control, a finding that highlights the power of using top-down behavioral modeling to guide bottom-up cellular manipulation studies.

A gyroscope-free visual-inertial flight control and wind sensing system for 10-mg robots

Tiny “gnat robots,” weighing just a few milligrams, were first conjectured in the 1980s. How to stabilize one if it were to hover like a small insect has not been answered. Challenges include the requirement that sensors be both low mass and high bandwidth and that silicon-micromachined rate gyroscopes are too heavy. The smallest robot to perform controlled hovering uses a sensor suite weighing hundreds of milligrams. Here, we demonstrate that an accelerometer represents perhaps the most direct way to stabilize flight while satisfying the extreme size, speed, weight, and power constraints of a flying robot even as it scales down to just a few milligrams. As aircraft scale reduces, scaling physics dictates that the ratio of aerodynamic drag to mass increases. This results in reduced noise in an accelerometer’s airspeed measurement. We show through simulation and experiment on a 30-gram robot that a 2-milligram off-the-shelf accelerometer is able in principle to stabilize a 10-milligram robot despite high noise in the sensor itself. Inspired by wind-vision sensory fusion in the flight controller of the fruit fly Drosophila melanogaster , we then added a tiny camera and efficient, fly-inspired autocorrelation-based visual processing to allow the robot to estimate and reject wind as well as control its attitude and flight velocity using a Kalman filter. Our biology-inspired approach, validated on a small flying helicopter, has a wind gust response comparable to the fruit fly and is small and efficient enough for a 10-milligram flying vehicle (weighing less than a grain of rice).

Dynamic stability in hovering flight of insects with different sizes

Previous works on the flight dynamic stability of insects have focused on relatively large insects. Here, the longitudinal flight dynamic stability of two hovering miniature insects was computed. With the stability properties of the miniature insects from the present work and those of large insects from previous works, we studied the effects of insect size on the stability properties in the full range of insect sizes. The following results were obtained. Although the insects considered have a 30 000-fold difference in mass, their modal structure of flight stability is the same: an unstable oscillatory mode, a stable fast subsidence mode, and a stable slow subsidence mode; because of the unstable mode, the flight is unstable. An approximate analytical expression on the growth rate of the unstable mode as a function of insect mass (m) was derived. It shows that the time to double the initial values of disturbances (t_{d}) is proportional to the 0.17 power of the insect mass (m). That is, as m becomes smaller, t_{d} decreases (i.e., the instability becomes faster). This means that miniature insects need a faster nervous system to control the instability than larger insects. For example, the response time (represented by t_{d}) of a miniature insect, the gall midge (m≈0.05mg), needs to be faster by about 7 times than that of a larger insect, the hawk moth (m≈1600mg).

Flying Into the Wind: Insects and Bio-Inspired Micro-Air-Vehicles With a Wing-Stroke Dihedral Steer Passively Into Wind-Gusts

Natural fliers utilize passive and active flight control strategies to cope with windy conditions. This capability makes them incredibly agile and resistant to wind gusts. Here, we study how insects achieve this, by combining Computational Fluid Dynamics (CFD) analyses of flying fruit flies with freely-flying robotic experiments. The CFD analysis shows that flying flies are partly passively stable in side-wind conditions due to their dorsal-ventral wing-beat asymmetry defined as wing-stroke dihedral. Our robotic experiments confirm that this mechanism also stabilizes free-moving flapping robots with similar asymmetric dihedral wing-beats. This shows that both animals and robots with asymmetric wing-beats are dynamically stable in sideways wind gusts. Based on these results, we developed an improved model for the aerodynamic yaw and roll torques caused by the coupling between lateral motion and the stroke dihedral. The yaw coupling passively steers an asymmetric flapping flyer into the direction of a sideways wind gust; in contrast, roll torques are only stabilizing at high air gust velocities, due to non-linear coupling effects. The combined CFD simulations, robot experiments, and stability modeling help explain why the majority of flying insects exhibit wing-beats with positive stroke dihedral and can be used to develop more stable and robust flapping-wing Micro-Air-Vehicles.

The function of pitching in Beetle's flight revealed by insect-wearable backpack

The study of insect flight orientation is important for investigating flapping-wing aerodynamics and designing bioinspired micro air vehicles (MAVs). Pitch orientation plays a vital role in flight control, which has been explored less than directional control. In this study, the role of pitching maneuvers in flight was revealed by mounting an insect-wearable backpack on a beetle, which transformed the live insect into a bioelectronic device. The flight status of the cyborg beetle in a large chamber was recorded wirelessly. Accordingly, the pitch angle and forward acceleration showed a strong linear relationship. The coupling of pitch angle and forward acceleration was due to a tilted net aerodynamic force and the induced air drag. Moreover, the left and right subalar muscles of the beetle, a pair of major flight muscles, were electrically stimulated in free flight on demand to pitch up the beetle's body. We demonstrated that the induced nose-up movements were effective for decelerating the beetle in air. The flight orientation findings from the flying cyborgs would inspire a new approach to the study of flapping-wing flight and control of flapping-wing MAVs.

Finite-Size Scaling at the Edge of Disorder in a Time-Delay Vicsek Model

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing delay time initially facilitates but ultimately impedes collective ordering and turns the dynamical scaling from diffusive to ballistic. It provides an alternative explanation of swarm traits previously attributed to inertia.

Dragondrop: a novel passive mechanism for aerial righting in the dragonfly

Dragonflies perform dramatic aerial manoeuvres when chasing targets but glide for periods during cruising flights. This makes dragonflies a great system to explore the role of passive stabilizing mechanisms that do not compromise manoeuvrability. We challenged dragonflies by dropping them from selected inverted attitudes and collected 6-degrees-of-freedom aerial recovery kinematics via custom motion capture techniques. From these kinematic data, we performed rigid-body inverse dynamics to reconstruct the forces and torques involved in righting behaviour. We found that inverted dragonflies typically recover themselves with the shortest rotation from the initial body inclination. Additionally, they exhibited a strong tendency to pitch-up with their head leading out of the manoeuvre, despite the lower moment of inertia in the roll axis. Surprisingly, anaesthetized dragonflies could also complete aerial righting reliably. Such passive righting disappeared in recently dead dragonflies but could be partially recovered by waxing their wings to the anaesthetised posture. Our kinematics data, inverse dynamics model and wind-tunnel experiments suggest that the dragonfly's long abdomen and wing posture generate a rotational tendency and passive attitude recovery mechanism during falling. This work demonstrates an aerodynamically stable body configuration in a flying insect and raises new questions in sensorimotor control for small flying systems.

Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles

This paper presents a thorough review on the system identification techniques applied to flapping wing micro air vehicles (FWMAVs). The main advantage of this work is to provide a solid background and domain knowledge of system identification for further investigations in the field of FWMAVs. In the system identification context, the flapping wing systems are first categorized into tailed and tailless MAVs. The most recent developments related to such systems are reported. The system identification techniques used for FWMAVs can be classified into time-response based identification, frequency-response based identification, and the computational fluid-dynamics based computation. In the system identification scenario, least mean square estimation is used for a beetle mimicking system recognition. In the end, this review work is concluded and some recommendations for the researchers working in this area are presented.

Timing precision in fly flight control: integrating mechanosensory input with muscle physiology

Animals rapidly collect and act on incoming information to navigate complex environments, making the precise timing of sensory feedback critical in the context of neural circuit function. Moreover, the timing of sensory input determines the biomechanical properties of muscles that undergo cyclic length changes, as during locomotion. Both of these issues come to a head in the case of flying insects, as these animals execute steering manoeuvres at timescales approaching the upper limits of performance for neuromechanical systems. Among insects, flies stand out as especially adept given their ability to execute manoeuvres that require sub-millisecond control of steering muscles. Although vision is critical, here I review the role of rapid, wingbeat-synchronous mechanosensory feedback from the wings and structures unique to flies, the halteres. The visual system and descending interneurons of the brain employ a spike rate coding scheme to relay commands to the wing steering system. By contrast, mechanosensory feedback operates at faster timescales and in the language of motor neurons, i.e. spike timing, allowing wing and haltere input to dynamically structure the output of the wing steering system. Although the halteres have been long known to provide essential input to the wing steering system as gyroscopic sensors, recent evidence suggests that the feedback from these vestigial hindwings is under active control. Thus, flies may accomplish manoeuvres through a conserved hindwing circuit, regulating the firing phase-and thus, the mechanical power output-of the wing steering muscles.

Intermittent control strategy can enhance stabilization robustness in bumblebee hovering

Active flight control plays a crucial role in stabilizing the body posture of insects to stay aloft under a complex natural environment. Insects can achieve a closed-loop flight control by integrating the external mechanical system and the internal working system through manipulating wing kinematics according to feedback information from multiple sensors. While studies of proportional derivative/proportional integral derivative-based algorithms are the main subject to explore the continuous flight control mechanisms associated with insect flights, it is normally observed that insects achieve an intermittent spike firing in steering muscles to manipulate wings in flight control discontinuously. Here we proposed a novel intermittent control strategy for a 3 degree of freedom (DoF) pitch-control and explored its stabilization robustness in bumblebee hovering. An integrated computational model was established and validated, which comprises an insect-inspired dynamic flight simulator and a novel discrete feedback controller as well as a simplified free-flight dynamic model. We found that the intermittent control model can achieve an angular-dominant flight control, whereas the continuous control model corresponds to an angular-velocity-dominant one. Given the biological constraints in sensorimotor neurobiology and musculoskeletal mechanics, the intermittent control strategy was examined capable of enhancing the stabilization robustness in terms of sensory latency, stroke derivation, spike interval, and damping strength. Our results indicate that the intermittent control strategy is likely a sophisticated flight control mechanism in insect flights while providing a bioinspired flight-control design for insect size flapping-wing micro air vehicles.

Effects of timing and magnitude of wing stroke-plane tilt on the escape maneuverability of flapping wing

Hummingbirds perform a variety of agile maneuvers, and one of them is the escape maneuver, in which the birds can steer away from threats using only 3-4 wingbeats in less than 150 ms. A distinct kinematic feature that enables the escape maneuver is the rapid backward tilt of the wing stroke plane at the beginning of the maneuver. This feature results in a simultaneous nose-up pitching and backward acceleration. In this work, we investigated how the magnitude and timing of the wing stroke-plane tilt (relative to the phase of flapping cycle) affected the generation of backward thrust, lift, and pitching moment and therefore the maneuverability of escape flight. Investigations were performed using experiments on dynamically scaled robotic wings and computational fluid dynamic simulation based on a simplified harmonic wing stroke and rotation kinematics at Re = 1000 and hummingbird wing kinematics at Re ≈ 10 000. Results showed that the wing stroke-plane tilt timing exerted a strong influence on the aerodynamic force generation. Independent of the tilt magnitude, the averaged backward thrust and pitching moment were maximized when the stroke plane tilt occurred near the end of the half strokes (e.g., upstroke and downstroke). Relative to the other timings of stroke-plane tilt, the 'optimal' timings led to a maximal backward tilt of the total aerodynamic force during the wing upstroke; hence, the backward thrust and nose-up pitching moment increased. The 'optimal' timings found in this work were in good agreement with those identified in the escape maneuvers of four species of hummingbirds. Therefore, hummingbirds may use a similar strategy in the beginning of their escape maneuver.

Vibrational control: A hidden stabilization mechanism in insect flight

It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.

Wing rapid responses and aerodynamics of fruit flies during headwind gust perturbations

Insects are the main source of inspiration for flapping-wing micro air vehicles (FWMAVs). They frequently encounter wind gust perturbations in natural environments, and effectively cope with these perturbations. Here, we investigated the rapid gust response of flies to instruct the gust stability design of FWMAVs. A novel method to produce impulsive wind gusts that lasted less than 30 ms was designed to observe flies' rapid responses. Headwind gust perturbations were imposed on 14 tethered fruit flies, and the corresponding wing motions during perturbations were recorded by three high-speed cameras. The numerical simulation method was then applied to analyze aerodynamic forces and moments induced by the changes in wing kinematics. Results shows that flies mainly utilize three strategies against headwind gust perturbations, including decreasing the magnitude of stroke positional angle at ventral stroke reversal, delayed rotation and making the deviation angles in upstroke and downstroke closer (i.e. the wing tip trajectories of upstroke and downstroke tend be closer). Consequently, flies resist increments in lift and drag induced by the headwind gusts. However, flies seem to care little about changes in pitch moment in tethered conditions. These results provide useful suggestions for the stability control of FWMAVs during headwind gust perturbations.

How do hoverflies use their righting reflex?

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.

Kinematic flexibility allows bumblebees to increase energetic efficiency when carrying heavy loads

Foraging bees fly with heavy loads of nectar and pollen, incurring energetic costs that are typically assumed to depend on load size. Insects can produce more force by increasing stroke amplitude and/or flapping frequency, but the kinematic response of a given species is thought to be consistent. We examined bumblebees (Bombus impatiens) carrying both light and heavy loads and found that stroke amplitude increased in proportion to load size, but did not predict metabolic rate. Rather, metabolic rate was strongly tied to frequency, which was determined not by load size but by the bee's average loading state and loading history, with heavily loaded bees displaying smaller changes in frequency and smaller increases in metabolic rate to support additional loading. This implies that bees can increase force production through alternative mechanisms; yet, they often choose the energetically costly option of elevating frequency, suggesting associated performance benefits that merit further investigation.

Modulation of Flight Muscle Recruitment and Wing Rotation Enables Hummingbirds to Mitigate Aerial Roll Perturbations

Both biological and artificial fliers must contend with aerial perturbations that are ubiquitous in the outdoor environment. Flapping fliers are generally least stable but also most maneuverable around the roll axis, yet our knowledge of roll control in biological fliers remains limited. Hummingbirds are suitable models for linking aerodynamic perturbations to flight control strategies, as these small, powerful fliers are capable of remaining airborne even in adverse wind conditions. We challenged hummingbirds to fly within a steady, longitudinally (streamwise) oriented vortex that imposed a continuous roll perturbation, measured wing kinematics and neuromotor activation of the flight muscles with synchronized high-speed video and electromyography and used computational fluid dynamics (CFD) to estimate the aerodynamic forces generated by observed wing motions. Hummingbirds responded to the perturbation with bilateral differences in activation of the main flight muscles while maintaining symmetry in most major aspects of wing motion, including stroke amplitude, stroke plane angle, and flapping frequency. Hummingbirds did display consistent bilateral differences in subtler wing kinematic traits, including wing rotation and elevation. CFD modeling revealed that asymmetric wing rotation was critical for attenuating the effects of the perturbation. The birds also augmented flight stabilization by adjusting body and tail posture to expose greater surface area to upwash than to the undesirable downwash. Our results provide insight into the remarkable capacity of hummingbirds to maintain flight control, as well as bio-inspiration for simple yet effective control strategies that could allow robotic fliers to contend with unfamiliar and challenging real-world aerial conditions.

Flies land upside down on a ceiling using rapid visually mediated rotational maneuvers

Flies and other insects routinely land upside down on a ceiling. These inverted landing maneuvers are among the most remarkable aerobatic feats, yet the full range of these behaviors and their underlying sensorimotor processes remain largely unknown. Here, we report that successful inverted landing in flies involves a serial sequence of well-coordinated behavioral modules, consisting of an initial upward acceleration followed by rapid body rotation and leg extension, before terminating with a leg-assisted body swing pivoted around legs firmly attached to the ceiling. Statistical analyses suggest that rotational maneuvers are triggered when flies' relative retinal expansion velocity reaches a threshold. Also, flies exhibit highly variable pitch and roll rates, which are strongly correlated to and likely mediated by multiple sensory cues. When flying with higher forward or lower upward velocities, flies decrease the pitch rate but increase the degree of leg-assisted swing, thereby leveraging the transfer of body linear momentum.

A minimal longitudinal dynamic model of a tailless flapping wing robot for control design

Recently, several insect- and hummingbird-inspired tailless flapping wing robots have been introduced. However, their flight dynamics, which are likely to be similar to that of their biological counterparts, remain yet to be fully understood. We propose a minimal dynamic model that is not only validated with experimental data, but also able to predict the consequences of various important design changes. Specifically, the model captures the flapping-cycle-averaged longitudinal dynamics, considering the main aerodynamic effects. We validated the model with flight data captured with a tailless flapping wing robot, the DelFly Nimble, for air speeds from near-hover flight up to 3.5 m s^-1. Moreover, the model succeeds in predicting the effects of changes to the center of mass location, and to the control system gains. Hence, the model is suitable even for the initial control design phase. To demonstrate this, we have used the simulation model to tune the robot's control system for higher speeds. Using the new control parameters on the real robot improved its maximal stable speed from 4 m s^-1 to 7 m s^-1.

Modeling and control of flapping wing micro aerial vehicles

Research in robots that emulate insect flight or micro aerial vehicles (MAV) has gained significant momentum in the past decade owing to the vast number of fields they could be employed in. In this paper, key modeling and control aspects of a flapping wing MAV in hover have been discussed. Models of varying complexity have been developed by previous researchers. Here, we examine the validity of key assumptions involved in some of these models in a closed-loop control setting. Every model has limitations and with proper design of feedback control these limitations can be overcome up to a certain degree. Three nonlinear models with increasing complexity have been developed. Model I includes only the rigid body dynamics while ignoring the wing dynamics while model II includes the rigid body dynamics along with the wing kinematics. Lastly, model III encompasses the complete rigid body and the rigid wing dynamics. To ensure these higher fidelity models can be rendered unnecessary with a suitably designed controller, a method is presented wherein the controller is designed for the simplest model and tested for its robustness on the more complex models. Linear quadratic regulator (LQR) is used as the main control system design methodology. A nonlinear parameter optimization algorithm is employed to design a family of LQR control systems for the MAV. Additionally, critical performance trade-offs are illuminated, and properties at both the plant output and input are examined. Lastly, we also provide specific rules of thumb for the control system design.

Hawkmoth flight in the unsteady wakes of flowers

Flying animals maneuver and hover through environments where wind gusts and flower wakes produce unsteady flow. Although both flight maneuvers and aerodynamic mechanisms have been studied independently, little is known about how these interact in an environment where flow is already unsteady. Moths forage from flowers by hovering in the flower's wake. We investigated hawkmoths tracking a 3D-printed robotic flower in a wind tunnel. We visualized the flow in the wake and around the wings and compared tracking performance with previous experiments in a still-air flight chamber. As in still air, moths flying in the flower wake exhibit near-perfect tracking at the low frequencies at which natural flowers move. However, tracking in the flower wake results in a larger overshoot between 2 and 5 Hz. System identification of flower tracking reveals that moths also display reduced-order dynamics in wind compared with still air. Smoke visualization of the flower wake shows that the dominant vortex shedding corresponds to the same frequency band as the increased overshoot. Despite these large effects on tracking dynamics in wind, the leading edge vortex (LEV) remains bound to the wing throughout the wingstroke and does not burst. The LEV also maintains the same qualitative structure seen in steady air. Persistence of a stable LEV during decreased flower tracking demonstrates the interplay between hovering and maneuvering.

The dynamics of hovering flight in hummingbirds, insects and bats with implications for aerial robotics

We analyze the effects of morphology and wing kinematics on the performance of hovering flight. We present a simplified dynamical model with body translational and rotational degrees of freedom that incorporates the flapping, long-axis wing rotation and folding of the wing. To validate our simulation, we compare our results with direct measurements from hovering insects, hummingbirds and bats. Results show that long-axis wing rotation angle (a proxy for pronation) has a significant effect on energy efficiency. For a given wing rotation amplitude, the hovering system has a power-optimal flapping frequency for each stroke-plane orientation, and that frequency closely corresponds to the wingbeat frequencies observed in a diverse range of hummingbird species. We find that larger animals (with larger total mass and wing size), such as bats, require more power to maintain a stable hovering orbit and that hovering with a constant wingspan becomes increasingly impractical with increasing body size. We show, as an exemplar, that for a system of the size of a hovering bat, e.g. Glossophaga soricina, hovering with constant wingspan is dynamically possible, but is implausible and inefficient. For these conditions, hovering with varying wingspan, retracting the wing on the upstroke, is a more realistic hovering modality.

Living in a trash can: turbulent convective flows impair Drosophila flight performance

Turbulent flows associated with thermal convection are common in areas where the ground is heated by solar radiation, fermentation or other processes. However, it is unknown how these flow instabilities affect the locomotion of small insects, like fruit flies, that inhabit deserts and urban landscapes where surface temperatures can reach extreme values. We quantified flight performance of fruit flies (Drosophila melanogaster) traversing a chamber through still air and turbulent Rayleigh-Bénard convection cells produced by a vertical temperature gradient. A total of 34% of individuals were unable to reach the end of the chamber in convection, although peak flow speeds were modest relative to typical outdoor airflow. Individuals that were successful in convection were faster fliers and had larger wing areas than those that failed. All flies displayed higher pitch angles and lower mean flight speeds in convection. Successful individuals took longer to cross the chamber in convection, due to lower flight speeds and greater path sinuosity. All individuals displayed higher flapping frequencies in convection, and successful individuals also reduced stroke amplitude. Our results suggest that thermal convection poses a significant challenge for small fliers, resulting in increased travel times and energetic costs, or in some cases precluding insects from traversing these environments entirely.

Bees with attitude: the effects of directed gusts on flight trajectories

Flight is a complicated task at the centimetre scale particularly due to unsteady air fluctuations which are ubiquitous in outdoor flight environments. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping organisms are linked with their resultant flight trajectories and performance, yet little is understood about how isolated unsteady aerodynamic phenomena affect the interlaced dynamics of such systems. In this study, we examined freely flying bumblebees subject to a single isolated gust to emulate aerodynamic disturbances encountered in nature. Bumblebees are expert commanders of the aerial domain as they persistently forage within complex terrain elements. By tracking the three-dimensional dynamics of bees flying through gusts, we determined the sequences of motion that permit flight in three disturbance conditions: sideward, upward and downward gusts. Bees executed a series of passive impulsive maneuvers followed by active recovery maneuvers. Impulsive motion was unique in each gust direction, maintaining control by passive manipulation of the body. Bees pitched up and slowed down at the beginning of recovery in every disturbance, followed by corrective maneuvers which brought body attitudes back to their original state. Bees were displaced the most by the sideward gust, displaying large lateral translations and roll deviations. Upward gusts were easier for bees to fly through, causing only minor flight changes and minimal recovery times. Downward gusts severely impaired the control response of bees, inflicting strong adverse forces which sharply upset trajectories. Bees used a variety of control strategies when flying in each disturbance, offering new insights into insect-scale flapping flight and bio-inspired robotic systems.This article has an associated First Person interview with the first author of the paper.

Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories

This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

Design and evaluation of a deformable wing configuration for economical hovering flight of an insect-like tailless flying robot

Studies on wing kinematics indicate that flapping insect wings operate at higher angles of attack (AoAs) than conventional rotary wings. Thus, effectively flying an insect-like flapping-wing micro air vehicle (FW-MAV) requires appropriate wing design for achieving low power consumption and high force generation. Even though theoretical studies can be performed to identify appropriate geometric AoAs for a wing for achieving efficient hovering flight, designing an actual wing by implementing these angles into a real flying robot is challenging. In this work, we investigated the wing morphology of an insect-like tailless FW-MAV, which was named KUBeetle, for obtaining high vertical force/power ratio or power loading. Several deformable wing configurations with various vein structures were designed, and their characteristics of vertical force generation and power requirement were theoretically and experimentally investigated. The results of the theoretical study based on the unsteady blade element theory (UBET) were validated with reference data to prove the accuracy of power estimation. A good agreement between estimated and measured results indicated that the proposed UBET model can be used to effectively estimate the power requirement and force generation of an FW-MAV. Among the investigated wing configurations operating at flapping frequencies of 23 Hz to 29 Hz, estimated results showed that the wing with a suitable vein placed outboard exhibited an increase of approximately 23.7%  ±  0.5% in vertical force and approximately 10.2%  ±  1.0% in force/power ratio. The estimation was supported by experimental results, which showed that the suggested wing enhanced vertical force by approximately 21.8%  ±  3.6% and force/power ratio by 6.8%  ±  1.6%. In addition, wing kinematics during flapping motion was analyzed to determine the reason for the observed improvement.

Modeling visual-based pitch, lift and speed control strategies in hoverflies

To avoid crashing onto the floor, a free falling fly needs to trigger its wingbeats quickly and control the orientation of its thrust accurately and swiftly to stabilize its pitch and hence its speed. Behavioural data have suggested that the vertical optic flow produced by the fall and crossing the visual field plays a key role in this anti-crash response. Free fall behavior analyses have also suggested that flying insect may not rely on graviception to stabilize their flight. Based on these two assumptions, we have developed a model which accounts for hoverflies´ position and pitch orientation recorded in 3D with a fast stereo camera during experimental free falls. Our dynamic model shows that optic flow-based control combined with closed-loop control of the pitch suffice to stabilize the flight properly. In addition, our model sheds a new light on the visual-based feedback control of fly´s pitch, lift and thrust. Since graviceptive cues are possibly not used by flying insects, the use of a vertical reference to control the pitch is discussed, based on the results obtained on a complete dynamic model of a virtual fly falling in a textured corridor. This model would provide a useful tool for understanding more clearly how insects may or not estimate their absolute attitude.

On the basis of vision-based feedback control of optic flow occurring during insects’ flight, we developed a dynamic model that accounts for the pitch orientation and speed in plummeting flies. We compared the hoverflies’ responses with our model and showed that an optic-flow based control strategy can be used to correct the initial pitch misorientation caused by the free fall situation. To complete the model, we combined the closed-loop control of the vertical optic flow with an additional feedback control loop based on the value of the absolute pitch orientation. The need for this measurement to stabilize the pitch orientation raises the question as whether this is also the case in dipterans. After ruling out the possibility that insects may use gravity acceleration cues to control their flight, for which no experimental evidence has been found so far, we discussed the three main sensory processes possibly involved in in their ability to control their attitude. Our model provides a useful tool for studying the various sensory processes possibly involved in dipterans’ flight stabilization abilities as well as the interactions between these processes.

Biomechanics and biomimetics in insect-inspired flight systems

Insect- and bird-size drones-micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environments are now an active and well-integrated research area. MAVs normally operate at a low speed in a Reynolds number regime of 10(4)-10(5) or lower, in which most flying animals of insects, birds and bats fly, and encounter unconventional challenges in generating sufficient aerodynamic forces to stay airborne and in controlling flight autonomy to achieve complex manoeuvres. Flying insects that power and control flight by flapping wings are capable of sophisticated aerodynamic force production and precise, agile manoeuvring, through an integrated system consisting of wings to generate aerodynamic force, muscles to move the wings and a control system to modulate power output from the muscles. In this article, we give a selective review on the state of the art of biomechanics in bioinspired flight systems in terms of flapping and flexible wing aerodynamics, flight dynamics and stability, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of flapping-wing MAVs with a specific focus on insect-inspired wing design and fabrication, as well as sensing systems.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.

Limitations of rotational manoeuvrability in insects and hummingbirds: evaluating the effects of neuro-biomechanical delays and muscle mechanical power

Flying animals ranging in size from fruit flies to hummingbirds are nimble fliers with remarkable rotational manoeuvrability. The degrees of manoeuvrability among these animals, however, are noticeably diverse and do not simply follow scaling rules of flight dynamics or muscle power capacity. As all manoeuvres emerge from the complex interactions of neural, physiological and biomechanical processes of an animal's flight control system, these processes give rise to multiple limiting factors that dictate the maximal manoeuvrability attainable by an animal. Here using functional models of an animal's flight control system, we investigate the effects of three such limiting factors, including neural and biomechanical (from limited flapping frequency) delays and muscle mechanical power, for two insect species and two hummingbird species, undergoing roll, pitch and yaw rotations. The results show that for animals with similar degree of manoeuvrability, for example, fruit flies and hummingbirds, the underlying limiting factors are different, as the manoeuvrability of fruit flies is only limited by neural delays and that of hummingbirds could be limited by all three factors. In addition, the manoeuvrability also appears to be the highest about the roll axis as it requires the least muscle mechanical power and can tolerate the largest neural delays.

Design and stable flight of a 21 g insect-like tailless flapping wing micro air vehicle with angular rates feedback control

An insect-like tailless flapping wing micro air vehicle (FW-MAV) without feedback control eventually becomes unstable after takeoff. Flying an insect-like tailless FW-MAV is more challenging than flying a bird-like tailed FW-MAV, due to the difference in control principles. This work introduces the design and controlled flight of an insect-like tailless FW-MAV, named KUBeetle. A combination of four-bar linkage and pulley-string mechanisms was used to develop a lightweight flapping mechanism that could achieve a high flapping amplitude of approximately 190°. Clap-and-flings at dorsal and ventral stroke reversals were implemented to enhance vertical force. In the absence of a control surface at the tail, adjustment of the location of the trailing edges at the wing roots to modulate the rotational angle of the wings was used to generate control moments for the attitude control. Measurements by a 6-axis load cell showed that the control mechanism produced reasonable pitch, roll and yaw moments according to the corresponding control inputs. The control mechanism was integrated with three sub-micro servos to realize the pitch, roll and yaw controls. A simple PD feedback controller was implemented for flight stability with an onboard microcontroller and a gyroscope that sensed the pitch, roll and yaw rates. Several flight tests demonstrated that the tailless KUBeetle could successfully perform a vertical climb, then hover and loiter within a 0.3 m ground radius with small variations in pitch and roll body angles.

Generation of the pitch moment during the controlled flight after takeoff of fruitflies

In the present paper, the controlled flight of fruitflies after voluntary takeoff is studied. Wing and body kinematics of the insects after takeoff are measured using high-speed video techniques, and the aerodynamic force and moment are calculated by the computational fluid dynamics method based on the measured data. How the control moments are generated is analyzed by correlating the computed moments with the wing kinematics. A fruit-fly has a large pitch-up angular velocity owing to the takeoff jump and the fly controls its body attitude by producing pitching moments. It is found that the pitching moment is produced by changes in both the aerodynamic force and the moment arm. The change in the aerodynamic force is mainly due to the change in angle of attack. The change in the moment arm is mainly due to the change in the mean stroke angle and deviation angle, and the deviation angle plays a more important role than the mean stroke angle in changing the moment arm (note that change in deviation angle implies variation in the position of the aerodynamic stroke plane with respect to the anatomical stroke plane). This is unlike the case of fruitflies correcting pitch perturbations in steady free flight, where they produce pitching moment mainly by changes in mean stroke angle.

Dynamics and flight control of a flapping-wing robotic insect in the presence of wind gusts

With the goal of operating a biologically inspired robot autonomously outside of laboratory conditions, in this paper, we simulated wind disturbances in a laboratory setting and investigated the effects of gusts on the flight dynamics of a millimetre-scale flapping-wing robot. Simplified models describing the disturbance effects on the robot's dynamics are proposed, together with two disturbance rejection schemes capable of estimating and compensating for the disturbances. The proposed methods are experimentally verified. The results show that these strategies reduced the root-mean-square position errors by more than 50% when the robot was subject to 80 cm s^-1 horizontal wind. The analysis of flight data suggests that modulation of wing kinematics to stabilize the flight in the presence of wind gusts may indirectly contribute an additional stabilizing effect, reducing the time-averaged aerodynamic drag experienced by the robot. A benchtop experiment was performed to provide further support for this observed phenomenon.

Foraging in an unsteady world: bumblebee flight performance in field-realistic turbulence

Natural environments are characterized by variable wind that can pose significant challenges for flying animals and robots. However, our understanding of the flow conditions that animals experience outdoors and how these impact flight performance remains limited. Here, we combine laboratory and field experiments to characterize wind conditions encountered by foraging bumblebees in outdoor environments and test the effects of these conditions on flight. We used radio-frequency tags to track foraging activity of uniquely identified bumblebee (Bombus impatiens) workers, while simultaneously recording local wind flows. Despite being subjected to a wide range of speeds and turbulence intensities, we find that bees do not avoid foraging in windy conditions. We then examined the impacts of turbulence on bumblebee flight in a wind tunnel. Rolling instabilities increased in turbulence, but only at higher wind speeds. Bees displayed higher mean wingbeat frequency and stroke amplitude in these conditions, as well as increased asymmetry in stroke amplitude-suggesting that bees employ an array of active responses to enable flight in turbulence, which may increase the energetic cost of flight. Our results provide the first direct evidence that moderate, environmentally relevant turbulence affects insect flight performance, and suggest that flying insects use diverse mechanisms to cope with these instabilities.

High metabolic demand in neural tissues: Information and control theory perspectives on the synergism between rate and stability

Evolutionary process has been selected for inherently unstable systems in higher animals that can react swiftly to changing patterns of threat or opportunity, for example blood pressure, the immune response, and gene expression. However, these require continual strict regulation: uncontrolled blood pressure is fatal, immune cells can attack 'self' tissues, and improper gene expression triggers developmental disorders. Consciousness in particular demands high rates of metabolic free energy to both operate and regulate the fundamental biological machinery: both the 'stream of consciousness' and the 'riverbanks' that confine it to useful realms are constructed and reconstructed moment-by-moment in response to highly dynamic internal and environmental circumstances. We develop powerful necessary conditions models for such phenomena based on the Data Rate Theorem linking control and information theories in the context of inherent instability. The synergism between conscious action and its regulation underlies the ten-fold higher rate of metabolic energy consumption in human neural tissues and implies a close, culturally modulated relation between sleep disorders and certain psychopathologies.

The aerodynamics and control of free flight manoeuvres in Drosophila

A firm understanding of how fruit flies hover has emerged over the past two decades, and recent work has focused on the aerodynamic, biomechanical and neurobiological mechanisms that enable them to manoeuvre and resist perturbations. In this review, we describe how flies manipulate wing movement to control their body motion during active manoeuvres, and how these actions are regulated by sensory feedback. We also discuss how the application of control theory is providing new insight into the logic and structure of the circuitry that underlies flight stability.This article is part of the themed issue 'Moving in a moving medium: new perspectives on flight'.

Perching with a robotic insect using adaptive tracking control and iterative learning control

Inspired by the aerial prowess of flying insects, we demonstrate that their robotic counterpart, an insect-scale flapping-wing robot, can mimic an aggressive maneuver seen in natural fliers— landing on a vertical wall. Such acrobatic movement differs from simple lateral maneuvers or hover, and therefore requires additional considerations in the control strategy. In this paper, we propose a single-loop adaptive tracking flight control suite designed with an emphasis on the ability to track dynamic trajectories, and an iterative learning control algorithm to account for unmodeled dynamics and systematic errors for improved landing accuracy. Magnets were chosen to enable attachment to the vertical surface due to their simplicity. The proposed controller was verified in a series of hovering and aggressive translational flights. Furthermore, we show that by learning from previous failed attempts, the biologically-inspired robot could successfully perch on a magnetic wall after eight learning iterations.

Whiteflies stabilize their take-off with closed wings

The transition from ground to air in flying animals is often assisted by the legs pushing against the ground as the wings start to flap. Here, we show that when tiny whiteflies (Bemisia tabaci, body length ca. 1 mm) perform take-off jumps with closed wings, the abrupt push against the ground sends the insect into the air rotating forward in the sagittal (pitch) plane. However, in the air, B. tabaci can recover from this rotation remarkably fast (less than 11 ms), even before spreading its wings and flapping. The timing of body rotation in air, a simplified biomechanical model and take-off in insects with removed wings all suggest that the wings, resting backwards alongside the body, stabilize motion through air to prevent somersaulting. The increased aerodynamic force at the posterior tip of the body results in a pitching moment that stops body rotation. Wing deployment increases the pitching moment further, returning the body to a suitable angle for flight. This inherent stabilizing mechanism is made possible by the wing shape and size, in which half of the wing area is located behind the posterior tip of the abdomen.

Aerodynamics, sensing and control of insect-scale flapping-wing flight

There are nearly a million known species of flying insects and 13 000 species of flying warm-blooded vertebrates, including mammals, birds and bats. While in flight, their wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions. As the size of a flyer is reduced, the wing-to-body mass ratio tends to decrease as well. Furthermore, these flyers use integrated system consisting of wings to generate aerodynamic forces, muscles to move the wings, and sensing and control systems to guide and manoeuvre. In this article, recent advances in insect-scale flapping-wing aerodynamics, flexible wing structures, unsteady flight environment, sensing, stability and control are reviewed with perspective offered. In particular, the special features of the low Reynolds number flyers associated with small sizes, thin and light structures, slow flight with comparable wind gust speeds, bioinspired fabrication of wing structures, neuron-based sensing and adaptive control are highlighted.

Flight mechanics and control of escape manoeuvres in hummingbirds II. Aerodynamic force production, flight control and performance limitations

The superior manoeuvrability of hummingbirds emerges from complex interactions of specialized neural and physiological processes with the unique flight dynamics of flapping wings. Escape manoeuvring is an ecologically relevant, natural behaviour of hummingbirds, from which we can gain understanding into the functional limits of vertebrate locomotor capacity. Here, we extend our kinematic analysis of escape manoeuvres from a companion paper to assess two potential limiting factors of manoeuvring performance of hummingbirds 1) muscle mechanical power output and 2) delays in the neural sensing and control system. We focused on the magnificent hummingbird, (Eugenes fulgens, 7.8g) and black-chinned hummingbird (Archilochus alexandri, 3.1 g), which represent large and small species, respectively. We first estimated the aerodynamic forces, moments and the mechanical power of escape manoeuvres using measured wing kinematics. Comparing active-manoeuvring and passive-damping aerodynamic moments, we found that pitch dynamics were lightly damped and dominated by effect of inertia while roll dynamics were highly damped. To achieve observed closed-loop performance, pitch manoeuvres required faster sensorimotor transduction, as hummingbirds can only tolerate half the delay allowed in roll manoeuvres. Accordingly, our results suggested that pitch control may require a more sophisticated control strategy, such as those based on prediction. For the magnificent hummingbird, we estimated escape manoeuvres required muscle mass-specific power 4.5 times that during hovering. Therefore, in addition to the limitation imposed by sensorimotor delays, muscle power could also limit the performance of escape manoeuvres.

Flight mechanics and control of escape manoeuvres in hummingbirds I. Flight kinematics

Hummingbirds are nature‘s masters of aerobatic manoeuvres. Previous research shows hummingbirds and insects converged evolutionarily upon similar aerodynamic mechanisms and kinematics in hovering. Herein, we use three-dimensional kinematic data to begin to test for similar convergence of kinematics used for escape flight and to explore the effects of body size upon manoeuvring. We studied four hummingbird species in North America including two large species (magnificent hummingbird, Eugenes fulgens, 7.8 g and blue-throated hummingbird, Lampornis clemenciae, 8.0 g) and two smaller species (broad-billed hummingbird, Cynanthus latirostris, 3.4 g and black-chinned hummingbirds Archilochus alexandri, 3.1 g). Starting from a steady hover, hummingbirds consistently manoeuvred away from perceived threats using a drastic escape response that featured body pitch and roll rotations coupled with a large linear acceleration. Hummingbirds changed their flapping frequency and wing trajectory in all three degrees-of-freedom on stroke-by-stroke basis, likely causing rapid and significant alteration of the magnitude and direction of aerodynamic forces. Thus it appears that the flight control of hummingbirds does not obey the “helicopter model” that is valid for similar escape manoeuvres in fruit flies. Except for broad-billed hummingbirds, the hummingbirds had faster reaction times than those reported for visual feedback control in insects. The two larger hummingbird species performed pitch rotations and global-yaw turns with considerably larger magnitude than the smaller species, but roll rates and cumulative roll angles were similar among the four species.

Recent developments in the study of insect flight

Here we review recent contributions to the study of insect flight, in particular those brought about by advances in experimental techniques. We focus particularly on the following areas: wing flexibility and deformation, the physiology and biophysics of asynchronous insect flight muscle, the aerodynamics of flight, and stability and maneuverability. This recent research reveals the importance of wing flexibility to insect flight, provides a detailed model of how asynchronous flight muscle functions and how it may have evolved, synthesizes many recent studies of insect flight aerodynamics into a broad-reaching summary of unsteady flight aerodynamics, and highlights new insights into the sources of flight stability in insects. The focus on experimental techniques and recently developed apparatus shows how these advancements have occurred and point the way towards future experiments.