Dynamic flight stability in the desert locust Schistocerca gregaria

Autonomous Expansion of Grasshopper Wings Reveals External Forces Contribute to Final Adult Wing Shape

Ecdysis, transformation from juvenile to adult form in insects, is time-consuming and leaves insects vulnerable to predation. For winged insects, the process of wing expansion during ecdysis, unfurling and expanding the wings, is a critical bottleneck in achieving sexual maturity. Internal and external forces play a role in wing expansion. Vigorous abdominal pumping during wing expansion allows insects to pressurize and inflate their wings, filling them with hemolymph. In addition, many insects adopt expansion-specific postures and, if inhibited, do not expand their wings normally, suggesting that external forces such as gravity may play a role. However, two previous studies over 40 years ago, reported that the forewings of swarming locusts can expand autonomously when removed from the emerging insect and laid flat on a saline solution. Termed "autoexpansion," we replicated previous experiments of autoexpansion on flat liquid media, documenting changes in both wing length and area over time while also focusing on the role of gravity in autoexpansion. Using the North American bird grasshopper Schistocerca americana, we tested four autoexpansion treatments of varying surface tension and hydrophobicity (gravity, deionized water, buffer, and mineral oil) while simultaneously observing and measuring intact, normal wing expansion. Finally, we constructed a simple model of a viscoelastic expanding wing subjected to gravity, to determine whether it could capture aspects of wing expansion. Our data confirmed that wing autoexpansion does occur in S. americana, but autoexpanding wings, especially hindwings, failed to increase to the same final length and area as intact wings. We found that gravity plays an important role in wing expansion, early in the expansion process. Combined with the significant mass increase we documented in intact wings, it suggests that hydraulic pumping of hemolymph into the wings plays an important role in increasing the area of expanding wings, especially in driving expansion of the large, pleated hindwings. Autoexpansion in a non-swarming orthopteran suggests that local cues driving wing autoexpansion may serve a broader purpose, reducing total expansion time and costs by shifting some processes from central to local control. Documenting wing autoexpansion in a widely studied model organism and demonstrating a mathematical model provides a tractable new system for exploring higher level questions about the mechanisms of wing expansion and the implications of autoexpansion, as well as potential bioinspiration for future technologies applicable to micro-air vehicles, space exploration, or medical and prosthetic devices.

Effect of Hindwings on the Aerodynamics and Passive Dynamic Stability of a Hovering Hawkmoth

Insects are able to fly stably in the complex environment of the various gusts that occur in nature. In addition, many insects suffer wing damage in their lives, but many species of insects are capable of flying without their hindwings. Here, we evaluated the effect of hindwings on aerodynamics using a Navier-Stokes-based numerical model, and then the passive dynamic stability was evaluated by coupling the equation of motion in three degrees of freedom with the aerodynamic forces estimated by the CFD solver under large and small perturbation conditions. In terms of aerodynamic effects, the presence of the hindwings slightly reduces the efficiency for lift generation but enhances the partial LEV circulation and increases the downwash around the wing root. In terms of thrust, increasing the wing area around the hindwing region increases the thrust, and the relationship is almost proportional at the cycle-averaged value. The passive dynamic stability was not clearly affected by the presence of the hindwings, but the stability was slightly improved depending on the perturbation direction. These results may be useful for the integrated design of wing geometry and flight control systems in the development of flapping-winged micro air vehicles.

Aspect Ratio Effects on the Aerodynamic Performance of a Biomimetic Hummingbird Wing in Flapping

Hummingbirds are flapping winged creatures with unique flight mechanisms. Their flight pattern is more similar to insects than other birds. Because their flight pattern provides a large lift force at a very small scale, hummingbirds can remain hovering while flapping. This feature is of high research value. In order to understand the high-lift mechanism of hummingbirds' wings, in this study a kinematic model is established based on hummingbirds' hovering and flapping process, and wing models imitating the wing of a hummingbird are designed with different aspect ratios. Therefore, with the help of computational fluid dynamics methods, the effect of aspect ratio changes on the aerodynamic characteristics of hummingbirds' hovering and flapping are explored in this study. Through two different quantitative analysis methods, the results of lift coefficient and drag coefficient show completely opposite trends. Therefore, lift-drag ratio is introduced to better evaluate aerodynamic characteristics under different aspect ratios, and it is found that the lift-drag ratio reaches a higher value when AR = 4. A similar conclusion is also reached following research on the power factor, which shows that the biomimetic hummingbird wing with AR = 4 has better aerodynamic characteristics. Furthermore, the study of the pressure nephogram and vortices diagram in the flapping process are examined, leading to elucidation of the effect of aspect ratio on the flow field around hummingbirds' wings and how these effects ultimately lead to changes in the aerodynamic characteristics of the birds' wings.

Role of wing inertia in maneuvering bat flights

The role of aerodynamics and wing inertia on the motion dynamics for the maneuvering flight of two bats from two species of roundleaf bats,H. armigerandH. prattiare investigated. Comparative studies among a straight flight, two ascending sweeping right turns, and a U-turn reveal that inertial forces play an essential and sometimes crucial role in the maneuvers. The translational trajectory of the bat is mostly driven by aerodynamic forces generated by the wings along the flight path, whereas inertial forces for the most part drive the intra-cycle fluctuations. However, inertial forces are found to contribute non-trivially to the ascending motion of theH. armigerduring the sweeping turn and the U-turn. The roll maneuver is found to be primarily driven by aerodynamic asymmetries during flight, whereas the yaw maneuver is primarily driven by imbalances in wing inertial moments. Inertial moments resulting from Coriolis and centrifugal forces are found to play an important role in accurate yaw prediction. The moment due to Coriolis force plays a very prominent role in predicting the correct yaw angle during the extreme 180° U-turn.

Accommodating unobservability to control flight attitude with optic flow

Attitude control is an essential flight capability. Whereas flying robots commonly rely on accelerometers¹ for estimating attitude, flying insects lack an unambiguous sense of gravity^2,3. Despite the established role of several sense organs in attitude stabilization^3-5, the dependence of flying insects on an internal gravity direction estimate remains unclear. Here we show how attitude can be extracted from optic flow when combined with a motion model that relates attitude to acceleration direction. Although there are conditions such as hover in which the attitude is unobservable, we prove that the ensuing control system is still stable, continuously moving into and out of these conditions. Flying robot experiments confirm that accommodating unobservability in this manner leads to stable, but slightly oscillatory, attitude control. Moreover, experiments with a bio-inspired flapping-wing robot show that residual, high-frequency attitude oscillations from flapping motion improve observability. The presented approach holds a promise for robotics, with accelerometer-less autopilots paving the road for insect-scale autonomous flying robots⁶. Finally, it forms a hypothesis on insect attitude estimation and control, with the potential to provide further insight into known biological phenomena^5,7,8 and to generate new predictions such as reduced head and body attitude variance at higher flight speeds⁹.

Longitudinal Trim and Dynamic Stability Analysis of a Seagull-Based Model

Understanding the mechanisms of trim and flight stability in birds is critical to guide the design of bionic micro air vehicles. The complex movements (plunging, sweeping, twisting) and morphing of wings always keeps the flapping flight of birds in dynamic equilibrium, which makes it difficult to determine the critical factors of trim and stability. Hence, a model has been developed that takes real complex movement and the calculation of unsteady aerodynamics into consideration. Two trim methods, including wash-out and forward-sweep, have been used to achieve equilibrium in the longitudinal direction. It is interesting to find that these two methods are both important to realize a larger take-off weight, lower power consumption, and stronger longitudinal stability. This implies that the seagull probably uses both of them to obtain the requirement of equilibrium and stability, which further inspires the design of seagull-inspired micro air vehicles.

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).

Multi-modal locomotor costs favor smaller males in a sexually dimorphic leaf-mimicking insect

Background

In most arthropods, adult females are larger than males, and male competition is a race to quickly locate and mate with scattered females (scramble competition polygyny). Variation in body size among males may confer advantages that depend on context. Smaller males may be favored due to more efficient locomotion leading to higher mobility during mate searching. Alternatively, larger males may benefit from increased speed and higher survivorship. While the relationship between male body size and mobility has been investigated in several systems, how different aspects of male body morphology specifically affect their locomotor performance in different contexts is often unclear.

Results

Using a combination of empirical measures of flight performance and modelling of body aerodynamics, we show that large body size impairs flight performance in male leaf insects (Phyllium philippinicum), a species where relatively small and skinny males fly through the canopy in search of large sedentary females. Smaller males were more agile in the air and ascended more rapidly during flight. Our models further predicted that variation in body shape would affect body lift and drag but suggested that flight costs may not explain the evolution of strong sexual dimorphism in body shape in this species. Finally, empirical measurements of substrate adhesion and subsequent modelling of landing impact forces suggested that smaller males had a lower risk of detaching from the substrates on which they walk and land.

Conclusions

By showing that male body size impairs their flight and substrate adhesion performance, we provide support to the hypothesis that smaller scrambling males benefit from an increased locomotor performance and shed light on the evolution of sexual dimorphism in scramble competition mating systems.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12862-022-01993-z.

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.

Effect and correction of control delay in longitudinal dynamics of insect hovering flight

Sensor-to-actuator delay is inevitable in any complex control system, be it one for a free-flying insect or a mimicking insectlike robotic flyer. In this work, we analyze the effects of control delay (latency) on the hovering performance of a model insect flyer, as exemplified by the hummingbird hawkmoth Re∼3000, and determine how control coefficients or gains may be modified to ameliorate the adverse effects of latency. The analyses are based on a simplified or reduced dynamic model of the hovering flyer. The longitudinal dynamics of the hovering flyer comprises the coupled forward (backward) and vertical translations and pitch rotation of the flyer, with kinematical wing actions being governed by proportional-differential (PD) closed-loop control. Keeping to the same PD control coefficients as a stable reference zero-delay case, the flight system becomes overly responsive at a small control delay, eventually diverging when delay approaches around one wing cycle. Stable hovering may be regained for control delay of up to several wingbeats by suitably reducing or softening the PD control coefficients. The results of the analyses are validated by a series of time-based simulations using the simplified dynamic model and a high-fidelity three-dimensional computational fluid dynamics with fluid structure-body interaction model of the hovering flyer. The simulations also show that noncyclic asymptotic oscillations about the mean equilibrium hovering state are enhanced with larger control delay. The analyses and simulations have helped us to gain a better understanding of the effects of control latency in insect free flight, which may be relevant for the design of mimetic insect flyers.

Effect of passive wing pitching on flight control in a hovering model insect and flapping-wing micro air vehicle

Passive wing pitching is a hypothesis in insect flight, and it is used widely by most flapping-wing micro air vehicles (FWMAVs). This study analyses the flight control of hovering model fruit fly and FWMAV with passive pitching wings. The longitudinal and lateral control derivatives are obtained by numerical simulation of the fluid dynamic equations coupled with the torsional spring passive pitching system. In contrast to active pitching wings, some of the control derivatives are remarkably changed by passive pitching wings, such asZ_Φ(vertical force produced by unit stroke amplitude),Z_f(vertical force produced by unit flapping frequency), andMψ0(pitching moment produced by unit rest angle). For example, increasing flapping frequency does not lead to an evident increase in lift and may even have a reverse effect. Therefore, the flight control of FWMAV with passive pitching wings should be treated with caution. For wings pitching passively with a torsional spring at the root, the differential change of the angle of attack in the downstroke and upstroke (α_dandα_u) could be achieved by modulation of the rest angle alone; however, the equal change inα_dandα_umay require an otherwise manipulation of the elastic coefficient. Results in this study provide guidelines for the design of FWMAVs in evaluating the effects of different control inputs correctly and formulating a cost-effective control scheme.

Towards locust-inspired gliding wing prototypes for micro aerial vehicle applications

In aviation, gliding is the most economical mode of flight explicitly appreciated by natural fliers. They achieve it by high-performance wing structures evolved over millions of years in nature. Among other prehistoric beings, locust is a perfect example of such natural glider capable of endured transatlantic flights that could inspire a practical solution to achieve similar capabilities on micro aerial vehicles. An investigation in this study demonstrates the effects of haemolymph on the flexibility of several flying insect wings proving that many species exist with further simplistic yet well-designed wing structures. However, biomimicry of such aerodynamic and structural properties is hindered by the limitations of modern as well as conventional fabrication technologies in terms of availability and precision, respectively. Therefore, here we adopt finite-element analysis to investigate the manufacturing-worthiness of a three-dimensional digitally reconstructed locust wing, and propose novel combinations of economical and readily available manufacturing methods to develop the model into prototypes that are structurally similar to their counterparts in nature while maintaining the optimum gliding ratio previously obtained in the aerodynamic simulations. The former is assessed here via an experimental analysis of the flexural stiffness and maximum deformation rate as EI s = 1.34 × 10-4 Nm2, EI c = 5.67 × 10-6 Nm2 and greater than 148.2%, respectively. Ultimately, a comparative study of the mechanical properties reveals the feasibility of each prototype for gliding micro aerial vehicle applications.

Multimodal integration across spatiotemporal scales to guide invertebrate locomotion

Locomotion is a hallmark of organisms that has enabled adaptive radiation to an extraordinarily diverse class of ecological niches, and allows animals to move across vast distances. Sampling from multiple sensory modalities enables animals to acquire rich information to guide locomotion. Locomotion without sensory feedback is haphazard, therefore sensory and motor systems have evolved complex interactions to generate adaptive behavior. Notably, sensory-guided locomotion acts over broad spatial and temporal scales to permit goal-seeking behavior, whether to localize food by tracking an attractive odor plume or to search for a potential mate. How does the brain integrate multimodal stimuli over different temporal and spatial scales to effectively control behavior? In this review, we classify locomotion into three ordinally ranked hierarchical layers that act over distinct spatiotemporal scales: stabilization, motor primitives, and higher-order tasks, respectively. We discuss how these layers present unique challenges and opportunities for sensorimotor integration. We focus on recent advances in invertebrate locomotion due to their accessible neural and mechanical signals from the whole brain, limbs and sensors. Throughout, we emphasize neural-level description of computations for multimodal integration in genetic model systems, including the fruit fly, Drosophila melanogaster, and the yellow fever mosquito, Aedes aegypti. We identify that summation (e.g. gating) and weighting-which are inherent computations of spiking neurons-underlie multimodal integration across spatial and temporal scales, therefore suggesting collective strategies to guide locomotion.

A semi-empirical model of the aerodynamics of manoeuvring insect flight

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

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.

Forward flight stability in a drone-fly

Previous studies on forward flight stability in insects are for low to medium flight-speeds. In the present work, we investigated the stability problem for the full range of flight speeds (0-8.6 m/s) of a drone-fly. Our results show the following: The longitudinal derivatives due to the lateral motion are approximately 3 orders of magnitude smaller than the other longitudinal derivatives. Thus, we can decouple these two motions of the insect, as commonly done for a conventional airplane. At hovering flight, the motion of the dronefly is weakly unstable owing to two unstable natural modes of motion, a longitudinal one and a lateral one. At low (1.6 m/s) and medium (3.1 m/s) flight-speeds, the unstable modes become even weaker and the flight is approximately neutral. At high flight-speeds (4.6 m/s, 6.9 m/s and 8.6 m/s), the flight becomes more and more unstable due to an unstable longitudinal mode. At the highest flight speed, 8.6 m/s, the instability is so strong that the time constant representing the growth rate of the instability (disturbance-doubling time) is only 10.1 ms, which is close to the sensory reaction time of a fly (approximately 11 ms). This indicates that strong instability may play a role in limiting the flight speed of the insect.

What goes up must come down: biomechanical impact analysis of falling locusts

Many insects are able to precisely control their jumping movements. Once in the air, the properties of the actual landing site, however, are almost impossible to predict. Falling insects thus have to cope with the situation at impact. In particular, for insects jumping to escape predators, a controlled landing movement appears to be a major evolutionary advantage. A quick recovery into an upright and stable body posture minimizes the time to prepare for the next escape jump. In this study, we used high-speed recordings to investigate the falling and in particular the impact behavior of Schistocerca gregaria locusts, a common model organism for studies on the biomechanics of jumping. Detailed impact analyses of free-falling locusts show that most insects typically crashed onto the substrate. Although free-falling locusts tended to spread their legs, they mostly fell onto the head and thorax first. The presence of wings did not significantly reduce impact speed; however, it did affect the orientation of the body at impact and significantly reduced the time to recover. Our results also show that alive warm locusts fell significantly faster than inactive or dead locusts. This indicates a possible tradeoff between active control versus reduced speed. Interestingly, alive insects also tended to perform a characteristic bending movement of the body at impact. This biomechanical adaptation might reduce the rebound and shorten the time to recover. The adhesive pads also play an important role in reducing the time to recover by allowing the insect to anchor itself to the substrate.

A simplified dynamic model for controlled insect hovering flight and control stability analysis

In this paper, the controlled stability of insect hovering flight is analyzed in detail based on a simplified dynamic model of the flyer and flow. The simplified dynamic model incorporates PID-based wing-kinematic controllers. The control stability of the hovering flight is evaluated based on the cycle-mean dynamic equations. The stability analyses and the simplified dynamic model allow us to derive and test the control coefficients for stable free hovering, firstly in the longitudinal mode of flight and then the lateral mode. In this manner, coefficients for wing-kinematic control for full CFD-FSI simulation could be obtained very efficiently. The coefficients thus determined are verified against full-fidelity CFD-FSI free flight simulations.

Dynamic flight stability of hovering mosquitoes

The flight of mosquitoes is unusual compared with many other insects, such as fruit-flies and honey bees: mosquitoes fly with their legs spread; they also have rather short stroke amplitude, hence use different aerodynamic mechanisms to produce lift. Could their flight-stability properties be different from those of other insects? Here, we first measured wing kinematics and morphological parameters of two hovering mosquitoes, and then use the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis to study their stability properties. We found that their natural-mode structure is the same as that of many other insects: for the longitudinal motion, one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode; for the lateral motion: an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode. The different aerodynamic mechanisms of mosquitoes do not change the major aerodynamic derivatives. The spread legs of mosquitoes have great effect on the moments of inertia and make the eigenvalue of the stable lateral mode much smaller. However, the leg-spreading has only a small quantitative effect on the unstable eigenvalues: the magnitudes of the eigenvalues in the two unstable modes, or the growth rate of the disturbances, are reduced by approximately 11%, compared to those calculated without considering the spread legs.

Lift and power in fruitflies in vertically-ascending flight

We measured the wing kinematics of fruitflies in both vertically-ascending and hovering flights and studied the aerodynamic forces and power in the two flight modes. The average ascending velocity is 0.45 m s^-1; the stroke plane angle and the stroke frequency are the same as that in hovering flight, whilst the stroke amplitude is increased by 12% and the wing angle of attack in the latter half of a down- and upstroke both increased by 10%. Flow analysis shows that during ascending, the flies experience a downward inflow which reduces the effective angle of attack considerably. This problem is overcome by the increases in the stroke amplitude and the angle of attack, which result in a larger wing drag. As a result, the power at ascending is increased by 36% over that at hovering. Two very interesting observations were made. (1) Using the same power, level-forward flight can be about four times as fast as ascending flight. (2) Power for ascending flight is the same as that for carrying a load about 27% of the insect's weight at hovering.

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.

Role of outstretched forelegs of flying beetles revealed and demonstrated by remote leg stimulation in free flight

In flight, many insects fold their forelegs tightly close to the body, which naturally decreases drag or air resistance. However, flying beetles stretch out their forelegs for some reason. Why do they adopt this posture in flight? Here, we show the role of the stretched forelegs in flight of the beetle Mecynorrhina torquata Using leg motion tracking and electromyography in flight, we found that the forelegs were voluntarily swung clockwise in yaw to induce counter-clockwise rotation of the body for turning left, and vice versa. Furthermore, we demonstrated remote control of left-right turnings in flight by swinging the forelegs via a remote electrical stimulator for the leg muscles. The results and demonstration reveal that the beetle's forelegs play a supplemental role in directional steering during flight.

Dynamic structure of locomotor behavior in walking fruit flies

The function of the brain is unlikely to be understood without an accurate description of its output, yet the nature of movement elements and their organization remains an open problem. Here, movement elements are identified from dynamics of walking in flies, using unbiased criteria. On one time scale, dynamics of walking are consistent over hundreds of milliseconds, allowing elementary features to be defined. Over longer periods, walking is well described by a stochastic process composed of these elementary features, and a generative model of this process reproduces individual behavior sequences accurately over seconds or longer. Within elementary features, velocities diverge, suggesting that dynamical stability of movement elements is a weak behavioral constraint. Rather, long-term instability can be limited by the finite memory between these elementary features. This structure suggests how complex dynamics may arise in biological systems from elements whose combination need not be tuned for dynamic stability.

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.

Effect of body aerodynamics on the dynamic flight stability of the hawkmoth Manduca sexta

This study explores the effects of the body aerodynamics on the dynamic flight stability of an insect at various different forward flight speeds. The insect model, whose morphological parameters are based on measurement data from the hawkmoth Manduca sexta, is treated as an open-loop six-degree-of-freedom dynamic system. The aerodynamic forces and moments acting on the insect are computed by an aerodynamic model that combines the unsteady panel method and the extended unsteady vortex-lattice method. The aerodynamic model is then coupled to a multi-body dynamic code to solve the system of motion equations. First, the trimmed flight conditions of insect models with and without consideration of the body aerodynamics are obtained using a trim search algorithm. Subsequently, the effects of the body aerodynamics on the dynamic flight stability are analysed through modal structures, i.e., eigenvalues and eigenvectors in this case, which are based on linearized equations of motion. The solutions from the nonlinear and linearized equations of motion due to gust disturbances are obtained, and the effects of the body aerodynamics are also investigated through these solutions. The results showed the important effect of the body aerodynamics at high-speed forward flight (in this paper at 4.0 and 5.0 m s^-1) and the movement trends of eigenvalues when the body aerodynamics is included.

Controlled banked turns in coleopteran flight measured by a miniature wireless inertial measurement unit

The mechanisms and principles of insect flight have long been investigated by researchers working on micro and nano air vehicles (MAVs/NAVs). However, studies of insect flight maneuvers require high speed filming and high spatial resolution in a small experimental space, or the tethering of the insect to a fixed place. Under such artificial conditions, the insects may deviate its flying behavior from that of regular flight. In this study, we mounted a tiny wireless system, or 'backpack', on live beetles (Mecynorrhina torquata; length 62 ± 8 mm; mass 7.4 ± 1.3 g) freely flying in a large laboratory space. The backpack contains a micro inertial measurement unit (IMU) that was especially designed and manufactured for this purpose. Owing to the small mass (∼1.30 g) and dimensions (∼2.3 cm²) of the backpack and the high accuracy of the IMU, we could remotely record the beetle in free flight. The free flight data revealed a strong linear correlation between the roll angle and yaw angular velocity. The strength of the correlation was quantified by the correlation coefficients and mean values. The change in roll angle preceded the change in yaw angular velocity. Moreover, there were frequent fluctuations in the roll angular velocity, which were uncorrelated with the yaw angular velocity. Apart from the strong correlation, these findings imply that Mecynorrhina torquata actively manipulates its roll rotation without coupling to the yaw rotation.

Dynamics and stability of directional jumps in the desert locust

Locusts are known for their ability to jump large distances to avoid predation. The jump also serves to launch the adult locust into the air in order to initiate flight. Various aspects of this important behavior have been studied extensively, from muscle physiology and biomechanics, to the energy storage systems involved in powering the jump, and more. Less well understood are the mechanisms participating in control of the jump trajectory. Here we utilise video monitoring and careful analysis of experimental directional jumps by adult desert locusts, together with dynamic computer simulation, in order to understand how the locusts control the direction and elevation of the jump, the residual angular velocities resulting from the jump and the timing of flapping-flight initiation. Our study confirms and expands early findings regarding the instrumental role of the initial body position and orientation. Both real-jump video analysis and simulations based on our expanded dynamical model demonstrate that the initial body coordinates of position (relative to the hind-legs ground-contact points) are dominant in predicting the jumps’ azimuth and elevation angles. We also report a strong linear correlation between the jumps’ pitch-angular-velocity and flight initiation timing, such that head downwards rotations lead to earlier wing opening. In addition to offering important insights into the bio-mechanical principles of locust jumping and flight initiation, the findings from this study will be used in designing future prototypes of a bio-inspired miniature jumping robot that will be employed in animal behaviour studies and environmental monitoring applications.

The complex aerodynamic footprint of desert locusts revealed by large-volume tomographic particle image velocimetry

Particle image velocimetry has been the preferred experimental technique with which to study the aerodynamics of animal flight for over a decade. In that time, hardware has become more accessible and the software has progressed from the acquisition of planes through the flow field to the reconstruction of small volumetric measurements. Until now, it has not been possible to capture large volumes that incorporate the full wavelength of the aerodynamic track left behind during a complete wingbeat cycle. Here, we use a unique apparatus to acquire the first instantaneous wake volume of a flying animal's entire wingbeat. We confirm the presence of wake deformation behind desert locusts and quantify the effect of that deformation on estimates of aerodynamic force and the efficiency of lift generation. We present previously undescribed vortex wake phenomena, including entrainment around the wing-tip vortices of a set of secondary vortices borne of Kelvin–Helmholtz instability in the shear layer behind the flapping wings.

Cost of flight and the evolution of stag beetle weaponry

Male stag beetles have evolved extremely large mandibles in a wide range of extraordinary shapes. These mandibles function as weaponry in pugnacious fights for females. The robust mandibles of Cyclommatus metallifer are as long as their own body and their enlarged head houses massive, hypertrophied musculature. Owing to this disproportional weaponry, trade-offs exist with terrestrial locomotion: running is unstable and approximately 40% more costly. Therefore, flying is most probably essential to cover larger distances towards females and nesting sites. We hypothesized that weight, size and shape of the weaponry will affect flight performance. Our computational fluid dynamics simulations of steady-state models (without membrane wings) reveal that male stag beetles must deliver 26% more mechanical work to fly with their heavy weaponry. This extra work is almost entirely required to carry the additional weight of the massive armature. The size and shape of the mandibles have only negligible influence on flight performance (less than 0.1%). This indicates that the evolution of stag beetle weaponry is constrained by its excessive weight, not by the size or shape of the mandibles and head as such. This most probably paved the way for the wide diversity of extraordinary mandible morphologies that characterize the stag beetle family.

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.

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.

Simultaneous measurement of aerodynamic forces and kinematics in flapping wings of tethered locust

Aerodynamic and inertial forces and corresponding kinematics of flapping wings of locusts, Schistocerca americana, were investigated in a low-speed wind tunnel. The experimental setup included live locusts mounted on microbalance synchronized with a high-speed video system. Simultaneous measurements of wing kinematics and forces were carried out on three locusts at 7° angle of attack and velocities of 0 m s(-1) and 4 m s(-1). Time variations of flapping and pitching angles exhibit similar patterns in fore- and hindwings and among the animals. Significant tip to root variations in pitching angle are found in both wings. The locusts have much larger flapping and pitching amplitudes in still air causing larger oscillations in inertial forces. Inertial forces are added to the lift and thrust on one part of the stroke, resulting in higher reaction forces and subtracted on the other part. Plots of the lift demonstrate similar trends with and without the wind. The global maxima and peak-to-peak amplitudes in lift are about the same in both tests. However, local minima are significantly lower in still air, resulting in much smaller stroke-averaged lift. Amplitudes of thrust force oscillations are much higher in still air; consequently, the stroke-averaged thrust is higher compared to the non-zero freestream velocity case.

Hovering and forward flight of the hawkmoth Manduca sexta: trim search and 6-DOF dynamic stability characterization

We show that the forward flight speed affects the stability characteristics of the longitudinal and lateral dynamics of a flying hawkmoth; dynamic modal structures of both the planes of motion are altered due to variations in the stability derivatives. The forward flight speed u e is changed from 0.00 to 1.00 m s(-1) with an increment of 0.25 m s(-1). (The equivalent advance ratio is 0.00 to 0.38; the advance ratio is the ratio of the forward flight speed to the average wing tip speed.) As the flight speed increases, for the longitudinal dynamics, an unstable oscillatory mode becomes more unstable. Also, we show that the up/down (w(b)) dynamics become more significant at a faster flight speed due to the prominent increase in the stability derivative Z(u) (up/down force due to the forward/backward velocity). For the lateral dynamics, the decrease in the stability derivative L(v) (roll moment due to side slip velocity) at a faster flight speed affects a slightly damped stable oscillatory mode, causing it to become more stable; however, the t(half) (the time taken to reach half the amplitude) of this slightly damped stable oscillatory mode remains relatively long (∼12T at u(e) = 1 m s(-1); T is wingbeat period) compared to the other modes of motion, meaning that this mode represents the most vulnerable dynamics among the lateral dynamics at all flight speeds. To obtain the stability derivatives, trim conditions for linearization are numerically searched to find the exact trim trajectory and wing kinematics using an algorithm that uses the gradient information of a control effectiveness matrix and fully coupled six-degrees of freedom nonlinear multibody equations of motion. With this algorithm, trim conditions that consider the coupling between the dynamics and aerodynamics can be obtained. The body and wing morphology, and the wing kinematics used in this study are based on actual measurement data from the relevant literature. The aerodynamic model of the flapping wings of a hawkmoth is based on the blade element theory, and the necessary aerodynamic coefficients, including the lift, drag and wing pitching moment, are experimentally obtained from the results of previous work by the authors.

Controlling roll perturbations in fruit flies

Owing to aerodynamic instabilities, stable flapping flight requires ever-present fast corrective actions. Here, we investigate how flies control perturbations along their body roll angle, which is unstable and their most sensitive degree of freedom. We glue a magnet to each fly and apply a short magnetic pulse that rolls it in mid-air. Fast video shows flies correct perturbations up to 100° within 30 ± 7 ms by applying a stroke-amplitude asymmetry that is well described by a linear proportional-integral controller. For more aggressive perturbations, we show evidence for nonlinear and hierarchical control mechanisms. Flies respond to roll perturbations within 5 ms, making this correction reflex one of the fastest in the animal kingdom.

In vivo recording of aerodynamic force with an aerodynamic force platform: from drones to birds

Flapping wings enable flying animals and biomimetic robots to generate elevated aerodynamic forces. Measurements that demonstrate this capability are based on experiments with tethered robots and animals, and indirect force calculations based on measured kinematics or airflow during free flight. Remarkably, there exists no method to measure these forces directly during free flight. Such in vivo recordings in freely behaving animals are essential to better understand the precise aerodynamic function of their flapping wings, in particular during the downstroke versus upstroke. Here, we demonstrate a new aerodynamic force platform (AFP) for non-intrusive aerodynamic force measurement in freely flying animals and robots. The platform encloses the animal or object that generates fluid force with a physical control surface, which mechanically integrates the net aerodynamic force that is transferred to the earth. Using a straightforward analytical solution of the Navier-Stokes equation, we verified that the method is accurate. We subsequently validated the method with a quadcopter that is suspended in the AFP and generates unsteady thrust profiles. These independent measurements confirm that the AFP is indeed accurate. We demonstrate the effectiveness of the AFP by studying aerodynamic weight support of a freely flying bird in vivo. These measurements confirm earlier findings based on kinematics and flow measurements, which suggest that the avian downstroke, not the upstroke, is primarily responsible for body weight support during take-off and landing.

Controlling free flight of a robotic fly using an onboard vision sensor inspired by insect ocelli

Scaling a flying robot down to the size of a fly or bee requires advances in manufacturing, sensing and control, and will provide insights into mechanisms used by their biological counterparts. Controlled flight at this scale has previously required external cameras to provide the feedback to regulate the continuous corrective manoeuvres necessary to keep the unstable robot from tumbling. One stabilization mechanism used by flying insects may be to sense the horizon or Sun using the ocelli, a set of three light sensors distinct from the compound eyes. Here, we present an ocelli-inspired visual sensor and use it to stabilize a fly-sized robot. We propose a feedback controller that applies torque in proportion to the angular velocity of the source of light estimated by the ocelli. We demonstrate theoretically and empirically that this is sufficient to stabilize the robot's upright orientation. This constitutes the first known use of onboard sensors at this scale. Dipteran flies use halteres to provide gyroscopic velocity feedback, but it is unknown how other insects such as honeybees stabilize flight without these sensory organs. Our results, using a vehicle of similar size and dynamics to the honeybee, suggest how the ocelli could serve this role.

Pitch perfect: how fruit flies control their body pitch angle

Flapping insect flight is a complex and beautiful phenomenon that relies on fast, active control mechanisms to counter aerodynamic instability. To directly investigate how freely-flying D. melanogaster control their body pitch angle against such instability, we perturb them using impulsive mechanical torques and film their corrective maneuvers with high-speed video. Combining experimental observations and numerical simulation, we find that flies correct for pitch deflections of up to 40° in 29±8 ms by bilaterally modulating their wings' front-most stroke angle in a manner well-described by a linear proportional-integral (PI) controller. Flies initiate this corrective process only 10±2 ms after the perturbation onset, indicating that pitch stabilization involves a fast reflex response. Remarkably, flies can also correct for very large-amplitude pitch perturbations–greater than 150°–providing a regime in which to probe the limits of the linear-response framework. Together with previous studies regarding yaw and roll control, our results on pitch show that flies' stabilization of each of these body angles is consistent with PI control

Lateral dynamic flight stability of a model hoverfly in normal and inclined stroke-plane hovering

Many insects hover with their wings beating in a horizontal plane ('normal hovering'), while some insects, e.g., hoverflies and dragonflies, hover with inclined stroke-planes. Here, we investigate the lateral dynamic flight stability of a hovering model hoverfly. The aerodynamic derivatives are computed using the method of computational fluid dynamics, and the equations of motion are solved by the techniques of eigenvalue and eigenvector analysis. The following is shown: The flight of the insect is unstable at normal hovering (stroke-plane angle equals 0) and the instability becomes weaker as the stroke-plane angle increases; the flight becomes stable at a relatively large stroke-plane angle (larger than about 24°). As previously shown, the instability at normal hovering is due to a positive roll-moment/side-velocity derivative produced by the 'changing-LEV-axial-velocity' effect. When the stroke-plane angle increases, the wings bend toward the back of the body, and the 'changing-LEV-axial-velocity' effect decreases; in addition, another effect, called the 'changing-relative-velocity' effect (the 'lateral wind', which is due to the side motion of the insect, changes the relative velocity of its wings), becomes increasingly stronger. This causes the roll-moment/side-velocity derivative to first decrease and then become negative, resulting in the above change in stability as a function of the stroke-plane angle.

Predicting fruit fly's sensing rate with insect flight simulations

Without sensory feedback, flies cannot fly. Exactly how various feedback controls work in insects is a complex puzzle to solve. What do insects measure to stabilize their flight? How often and how fast must insects adjust their wings to remain stable? To gain insights into algorithms used by insects to control their dynamic instability, we develop a simulation tool to study free flight. To stabilize flight, we construct a control algorithm that modulates wing motion based on discrete measurements of the body-pitch orientation. Our simulations give theoretical bounds on both the sensing rate and the delay time between sensing and actuation. Interpreting our findings together with experimental results on fruit flies' reaction time and sensory motor reflexes, we conjecture that fruit flies sense their kinematic states every wing beat to stabilize their flight. We further propose a candidate for such a control involving the fly's haltere and first basalar motor neuron. Although we focus on fruit flies as a case study, the framework for our simulation and discrete control algorithms is applicable to studies of both natural and man-made fliers.

A theoretical analysis of pitch stability during gliding in flying snakes

Flying snakes use their entire body as a continuously morphing 'wing' to produce lift and shallow their glide trajectory. Their dominant behavior during gliding is aerial undulation, in which lateral waves are sent posteriorly down the body. This highly dynamic behavior, which is unique among animal gliders, should have substantial effects on the flight dynamics and stability of the snakes, resulting from the continuous redistribution of mass and aerodynamic forces. In this study, we develop two-dimensional theoretical models to assess the stability characteristics of snakes in the pitch direction. Previously measured force coefficients are used to simulate aerodynamic forces acting on the models, and undulation is simulated by varying mass. Model 1 is a simple three-airfoil representation of the snake's body that possesses a passively stable equilibrium solution, whose basin of stability contains initial conditions observed in experimental gliding trajectories. Model 2 is more sophisticated, with more degrees of freedom allowing for postural changes to better represent the snake's real kinematics; in addition, a restoring moment is added to simulate potential active control. The application of static and dynamic stability criteria show that Model 2 is passively unstable, but can be stabilized with a restoring moment. Overall, these models suggest that undulation does not contribute to stability in pitch, and that flying snakes require a closed-loop control system formed around a passively stable dynamical framework.

Strategies for the stabilization of longitudinal forward flapping flight revealed using a dynamically-scaled robotic fly

The ability to regulate forward speed is an essential requirement for flying animals. Here, we use a dynamically-scaled robot to study how flapping insects adjust their wing kinematics to regulate and stabilize forward flight. The results suggest that the steady-state lift and thrust requirements at different speeds may be accomplished with quite subtle changes in hovering kinematics, and that these adjustments act primarily by altering the pitch moment. This finding is consistent with prior hypotheses regarding the relationship between body pitch and flight speed in fruit flies. Adjusting the mean stroke position of the wings is a likely mechanism for trimming the pitch moment at all speeds, whereas changes in the mean angle of attack may be required at higher speeds. To ensure stability, the flapping system requires additional pitch damping that increases in magnitude with flight speed. A compensatory reflex driven by fast feedback of pitch rate from the halteres could provide such damping, and would automatically exhibit gain scheduling with flight speed if pitch torque was regulated via changes in stroke deviation. Such a control scheme would provide an elegant solution for stabilization across a wide range of forward flight speeds.

Dynamic flight stability of a hovering model dragonfly

The longitudinal dynamic flight stability of a model dragonfly at hovering flight is studied, using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. Three natural modes of motion are identified for the hovering flight: one unstable oscillatory mode, one stable fast subsidence mode and one stable slow subsidence mode. The flight is dynamically unstable owing to the unstable oscillatory mode. The instability is caused by a pitch-moment derivative with respect to horizontal velocity. The damping force and moment derivatives (with respect to horizontal and vertical velocities and pitch-rotational velocity, respectively) weaken the instability considerably. The aerodynamic interaction between the forewing and the hindwing does not have significant effect on the stability properties. The dragonfly has similar stability derivatives, hence stability properties, to that of a one-wing-pair insect at normal hovering, but there are differences in how the derivatives are produced because of the highly inclined stroke plane of the dragonfly.

A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmoth Manduca sexta

This paper investigates the six degrees of freedom (6-DOF) flight dynamics and stability of the hawkmoth Manduca sexta using a multibody dynamics approach that encompasses the effects of the time varying inertia tensor of all the body segments including two wings. The quasi-steady translational and unsteady rotational aerodynamics of the flapping wings are modeled with the blade element theory with aerodynamic coefficients derived from relevant experimental studies. The aerodynamics is given instantaneously at each integration time step without wingbeat-cycle-averaging. With the multibody dynamic model and the aerodynamic model for the hawkmoth, a direct time integration of the fully coupled 6-DOF nonlinear multibody dynamics equations of motion is performed. First, the passive damping magnitude of each single DOF is quantitatively examined with the measure of the time taken to half the initial velocity (thalf). The results show that the sideslip translation is less damped approximately three times than the other two translational DOFs, and the pitch rotation is less damped approximately five times than the other two rotational DOFs; each DOF has the value of (unit in wingbeat strokes): thalf,forward/backward = 7.10, thalf,sideslip = 17.95, thalf,ascending = 7.13, thalf,descending = 5.77, thalf,roll = 0.68, thalf,pitch = 2.39, and thalf,yaw = 0.25. Second, the natural modes of motion, with the hovering flight as a reference equilibrium condition, are examined by analyzing fully coupled 6-DOF dynamic responses induced by multiple sets of force and moment disturbance combinations. The given disturbance combinations are set to excite the dynamic modes identified in relevant eigenmode analysis studies. The 6-DOF dynamic responses obtained from this study are compared with eigenmode analysis results in the relevant studies. The longitudinal modes of motion showed dynamic modal characteristics similar to the eigenmode analysis results from the relevant literature. However, the lateral modes of motion revealed more complex behavior, which is mainly due to the coupling effect in the lateral flight states and also between the lateral and longitudinal planes of motion. The main sources of the flight instability of the hovering hawkmoth are examined as either the longitudinal instability grown from the coupled forward/backward velocity and the pitch rate, or the lateral instability grown from the coupled sideslip velocity and the roll rate.

Vision-based flight control in the hawkmoth Hyles lineata

Vision is a key sensory modality for flying insects, playing an important role in guidance, navigation and control. Here, we use a virtual-reality flight simulator to measure the optomotor responses of the hawkmoth Hyles lineata, and use a published linear-time invariant model of the flight dynamics to interpret the function of the measured responses in flight stabilization and control. We recorded the forces and moments produced during oscillation of the visual field in roll, pitch and yaw, varying the temporal frequency, amplitude or spatial frequency of the stimulus. The moths' responses were strongly dependent upon contrast frequency, as expected if the optomotor system uses correlation-type motion detectors to sense self-motion. The flight dynamics model predicts that roll angle feedback is needed to stabilize the lateral dynamics, and that a combination of pitch angle and pitch rate feedback is most effective in stabilizing the longitudinal dynamics. The moths' responses to roll and pitch stimuli coincided qualitatively with these functional predictions. The moths produced coupled roll and yaw moments in response to yaw stimuli, which could help to reduce the energetic cost of correcting heading. Our results emphasize the close relationship between physics and physiology in the stabilization of insect flight.

Nonlinear flight dynamics and stability of hovering model insects

Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier-Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect.

Wireless stimulation of antennal muscles in freely flying hawkmoths leads to flight path changes

Insect antennae are sensory organs involved in a variety of behaviors, sensing many different stimulus modalities. As mechanosensors, they are crucial for flight control in the hawkmoth Manduca sexta. One of their roles is to mediate compensatory reflexes of the abdomen in response to rotations of the body in the pitch axis. Abdominal motions, in turn, are a component of the steering mechanism for flying insects. Using a radio controlled, programmable, miniature stimulator, we show that ultra-low-current electrical stimulation of antennal muscles in freely-flying hawkmoths leads to repeatable, transient changes in the animals' pitch angle, as well as less predictable changes in flight speed and flight altitude. We postulate that by deflecting the antennae we indirectly stimulate mechanoreceptors at the base, which drive compensatory reflexes leading to changes in pitch attitude.