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Frequency-Modulated Control for Insect-Scale Flapping-Wing Vehicles
Abstract
Many insects utilize both amplitude and frequency modulation of their wingstrokes to control flight, a combination with potential advantages for flapping-wing micro-aerial vehicle (FWMAV) flight control as we attempt to mimic the agility of small biological fliers. However, frequency-modulated control is uncommon in insect-scale FWMAVs, and these vehicles have not yet demonstrated graceful, mid-wingstroke frequency transitions in flight. We propose a method to allow active frequency control as a primary control variable, and describe a method to achieve smooth frequency transitions in flight. We demonstrate that frequency, in combination with other flapping parameters, may be used to generate arbitrary, time-varying forces and torques. Additionally, we explore the advantages of frequency modulation in FWMAV flight, applying a frequency-based method to control the Harvard RoboBee during hovering flight.
... Inspired by natural fliers, many robotic fliers across different sizes use elastic energy storage, i.e. mechanical or magnetic springs that operate in parallel to the actuators; their wing frequencies are often designed to function at the mechanical resonant frequency of the entire wing motor system [29][30][31][32][33]. However, robotic fliers scarcely use active frequency control [33] and while several robots use active amplitude control [32,34,35], actuator energy efficiency was the main consideration when designing the elastic energy storage. ...
... Inspired by natural fliers, many robotic fliers across different sizes use elastic energy storage, i.e. mechanical or magnetic springs that operate in parallel to the actuators; their wing frequencies are often designed to function at the mechanical resonant frequency of the entire wing motor system [29][30][31][32][33]. However, robotic fliers scarcely use active frequency control [33] and while several robots use active amplitude control [32,34,35], actuator energy efficiency was the main consideration when designing the elastic energy storage. Notably, for Robobee, there is a significant trade-off between efficiency and wingbeat frequency modulation, as the energetic benefit due to resonance quickly diminishes beyond ±5% of resonant frequency [7,29]. ...
Natural fliers with flapping wings face the dual challenges of energy efficiency and active control of wing motion for achieving diverse modes of flight. It is hypothesized that flapping-wing systems use resonance to improve muscle mechanical output energy efficiency, a principle often followed in bioinspired flapping-wing robots. However, resonance can limit the degree of active control, a trade-off rooted in the dynamics of wing motor systems and can be potentially reflected in muscle work loops. To systematically investigate how energy efficiency trades off with active control of wingbeat frequency and amplitude, here we developed a parsimonious model of the wing motor system with either synchronous or asynchronous power muscles. We then non-dimensionalized the model and performed simulations to examine model characteristics as functions of Weis-Fogh number and dimensionless flapping frequency. For synchronous power muscles, our model predicts that energy efficiency trades off with frequency control rather than amplitude control at high Weis-Fogh numbers; however, no such trade-off was found for models with asynchronous power muscles. The work loops alone are insufficient to fully capture wing motor characteristics, and therefore fail to directly reflect the trade-offs. Finally, using simulation results, we predict that natural fliers function at Weis-Fogh numbers close to 1.
... Currently, piezoelectric bimorphs are a common actuation method of insect scale FWMAVs [63][64][65] because they have a favorable power density at those length scales. Amplitude modulation has been the common control strategy for these piezo-based FWMAVs, but there is evidence that frequency modulation can improve attitude control [66]. Similar to the control strategies employed during maneuvering, insects must modulate wingbeat kinematics to compensate for reduced surface area following wing damage. ...
Flying insects have a robust flight system that allows them to fly even when their forewings are damaged. The insect must adjust wingbeat kinematics to aerodynamically compensate for the loss of wing area. However, the mechanisms that allow insects with asynchronous flight muscle to adapt to wing damage are not well understood. Here, we investigated the phase and amplitude relationships between thorax deformation and flapping angle in tethered flying bumblebees subject to wing clipping and weighting. We used synchronized laser vibrometry and high-speed videography to measure thorax deformation and flapping angle, respectively. We found that changes in wing inertia did not affect thorax deformation amplitude but did influence wingbeat frequency. Increasing wing inertia increased flapping amplitude and caused a phase lag between thorax deformation and flapping angle, whereas decreasing wing inertia did not affect flapping amplitude and caused the flapping angle to lead thorax deformation. Our findings indicate that bumblebees adapt to wing damage by adjusting their wingbeat frequency rather than altering their wing stroke amplitude. Additionally, our results suggest that bumblebees operate near a wing-hinge-dominated resonant frequency, and that moments generated by steering muscles within the wing hinge influence the phase between thorax deformation and wing stroke nontrivially. These insights can inform the design of resilient, insect-inspired flapping-wing micro air vehicles.
... However, there are other tradeoffs inherent in operating at resonance that become important for wingbeat control and stability that have not been fully considered in insect flight [19]. For example, when actuated at the resonant frequency of maximum wingstroke amplitude, any control change to the wingbeat frequency will result in a decrease in the wing amplitude and thus would require more energy input per wingstroke to achieve lift [8,20]. Thus, while resonance can aid in energetic efficiency it can also limit the flapper's ability to quickly change wingstroke kinematics. ...
Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases with N) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1<N<10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.
... 13 For these reasons, the most suitable use of piezoelectric actuators is in applications that actually require >10-Hz frequencies, such as actuating wings for flying microrobots, where their frequency response is simply unmatched, regardless of their performance in other metrics, such as energy density, force output, and efficiency. 19 Piezoelectric actuators were also used to enable miniature water striders walking on the water interface at frequencies of ~40 Hz. 20 In their article in this issue, Kim et al. describe a variety of lightweight water striders that employ piezoelectric actuators to walk on water, whereby these actuators have the suitable size scale, power density, and frequency response. 21 ...
To power miniature mobile robots, the body structure must integrate actuators, sensing, wiring, an energy source, power converters, and computing. The system-level performance relies on the interplay among these complementary elements and the fabrication technologies that enable them. While new materials, fabrication, and bioinspired designs are enabling advancements toward insect-scale untethered and autonomous robots, challenges remain in achieving high power efficiency fast actuation and heterogeneous integration. This article overviews the state of the art, opportunities, and challenges covered in this issue of MRS Bulletin.
... Moreover, there is a burgeoning interest in creating flapping wing platforms that take inspiration from a wide array of flying creatures. This includes exploring the flight mechanisms of bats, which can fly without tail structures [34][35][36], as well as drawing insights from flying insects for the development of miniaturized flapping wing aerial vehicles (FWAVs) capable of operating at higher flapping frequencies [37][38][39][40][41][42][43][44][45][46][47][48]. Additionally, researchers are even exploring the possibilities of designing FWAVs inspired by the flight characteristics of dinosaurs [49]. ...
Flapping Wing Air Vehicles (FWAVs) have proven to be attractive alternatives to fixed wing and rotary air vehicles at low speeds because of their bio-inspired ability to hover and maneuver. However, in the past, they have not been able to reach their full potential due to limitations in wing control and payload capacity, which also has limited endurance. Many previous FWAVs used a single actuator that couples and synchronizes motions of the wings to flap both wings, resulting in only variable rate flapping control at a constant amplitude. Independent wing control is achieved using two servo actuators that enable wing motions for FWAVs by programming positions and velocities to achieve desired wing shapes and associated aerodynamic forces. However, having two actuators integrated into the flying platform significantly increases its weight and makes it more challenging to achieve flight than a single actuator. This article presents a retrospective overview of five different designs from the “Robo Raven” family based on our previously published work. The first FWAVs utilize two servo motors to achieve independent wing control. The basic platform is capable of successfully performing dives, flips, and button hook turns, which demonstrates the potential maneuverability afforded by the independently actuated and controlled wings. Subsequent designs in the Robo Raven family were able to use multifunctional wings to harvest solar energy to overcome limitations on endurance, use on-board decision-making capabilities to perform maneuvers autonomously, and use mixed-mode propulsion to increase payload capacity by exploiting the benefits of fixed and flapping wing flight. This article elucidates how each successive version of the Robo Raven platform built upon the findings from previous generations. The Robo Raven family collectively addresses requirements related to control autonomy, energy autonomy, and maneuverability. We conclude this article by identifying new opportunities for research in avian-scale flapping wing aerial vehicles.
In this paper, we presented the design, integration, and experimental verification of a flapping wing apparatus. The purpose for this apparatus is to provide a framework to study the applicability of various types of sensors on flapping wings in the presence of forward speed. This work is inspired by the discoveries of mechanosensory hairs on insect wings that perform like strain-gauge sensors. To design the apparatus, we started by kinematic analysis of a crank-slider mechanism to actuate the wings. After that, we constructed the equations of motion of the entire system to find the proper gear ratio, motor properties, and other geometric dimensions. For the aerodynamic modeling, we used a quasi-steady formulation and presented a closed-form solution for the aerodynamic torque. Then, we explained the integration process and manufacturing of the main parts and presented two prototypes for the apparatus. At the end, we showed the final constructed versions of the apparatus and presented the experimental response and compared them with the simulation.
Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties—an illustration of the extraordinary robustness of these natural motors.
Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.
The superior maneuverability of insect flight is enabled by rapid and significant changes in aerodynamic forces, a result of subtle and precise change of wing kinematics. The high sensitivity of aerodynamic force to wing kinematic change demands precise and instantaneous feedback control of the wing motion trajectory, especially in the presence of various parameter uncertainties and environmental disturbances. Current work on flapping wing robots was limited to open-loop averaged wing kinematics control. Here we present instantaneous closed-loop wing trajectory tracking of a DC motor direct driven wing-thorax system under resonant flapping. A dynamic model with parameter uncertainties and disturbances was developed and validated through system identification. For wing trajectory generation, we designed a Hopf oscillator based central pattern generator with smooth convergence. Using the linearized model while treating the nonlinearity as disturbance, we designed a proportional-integral-derivative (PID) controller and a linear quadratic regulator (LQR) for instantaneous wing trajectory tracking at 24 Hz; Using the original nonlinear model, we designed a nonlinear controller to achieve robust performance at over 30 Hz. The control algorithms were implemented and compared experimentally on a 7.5 g Flapping Wing Micro Air Vehicle (MAV). The experiments showed that the PID and nonlinear controls resulted in precise trajectory tracking; while LQR controller tracked with less precision but with smaller input effort. In addition, the nonlinear control algorithm achieved better tracking of wing trajectories with varying amplitude, bias, frequency, and split-cycles while adapting to the variations on wing morphological parameters such as wing geometry and stiffness. Furthermore, the lift force measurements of the nonlinear control results were compared with those of open-loop average wing kinematics control commonly adopted in current designs.
Flapping wing micro air vehicles continue to be a growing field, with ongoing research into unsteady, low Reynolds number aerodynamics, microfabrication, and fluid-structure interaction. However, research into flapping wing control of such micro air vehicles continues to lag. Existing research uniformly consists of proposed control laws that are validated by computer simulations of quasi-steady blade-element formulas. Such simulations use numerous assumptions and cannot be trusted to fully describe the flow physics. Instead, such control laws must be validated on hardware. In earlier work, a novel control technique, biharmonic amplitude and bias modulation, was proposed and analyzed with these same quasi-steady blade-element formulas. In this work, the biharmonic amplitude and bias modulation control technique was implemented on a flapping wing prototype (4cm wing length) and tested on a six-component force/torque sensor. Experiments verified that the prototype can generate nearly uncoupled forces and moments for motion in five degrees of freedom when using the biharmonic amplitude and bias modulation control technique, and that these forces can be reasonably predicted by the blade-element formulas.
In this study, we experimentally studied the relationship between wingbeat frequency and resonant frequency of 30 individuals of eight insect species from five orders: Odonata (Sympetrum flaveolum), Lepidoptera (Pieris rapae, Plusia gamma and Ochlodes), Hymenoptera (Xylocopa pubescens and Bombus rupestric), Hemiptera (Tibicen linnei) and Coleoptera (Allomyrina dichotoma). The wingbeat frequency of free-flying insects was measured using a high-speed camera while the natural frequency was determined using a laser displacement sensor along with a Bruel and Kjaer fast Fourier transform analyzer based on the base excitation method. The results showed that the wingbeat frequency was related to body mass (m) and forewing area (Af), following the proportionality f ∼ m1/2/Af, while the natural frequency was significantly correlated with area density (f0 ∼ mw/Af, mw is the wing mass). In addition, from the comparison of wingbeat frequency to natural frequency, the ratio between wingbeat frequency and natural frequency was found to be, in general, between 0.13 and 0.67 for the insects flapping at a lower wingbeat frequency (less than 100 Hz) and higher than 1.22 for the insects flapping at a higher wingbeat frequency (higher than 100 Hz). These results suggest that wingbeat frequency does not have a strong relation with resonance frequency: in other words, insects have not been evolved sufficiently to flap at their wings' structural resonant frequency. This contradicts the general conclusion of other reports-–that insects flap at their wings' resonant frequency to take advantage of passive deformation to save energy.
This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts, that are used to control the six translational and rotational degrees of freedom, and to achieve asymptotic tracking of four outputs, namely, three position variables for the vehicle center of mass and the direction of one vehicle body-fixed axis. A globally defined model of the quadrotor UAV rigid body dynamics is introduced as a basis for the analysis. A nonlinear tracking controller is developed on the special Euclidean group SE(3) and it is shown to have desirable closed loop properties that are almost global. Several numerical examples, including an example in which the quadrotor recovers from being initially upside down, illustrate the versatility of the controller.
Insects could minimize the high energetic costs of flight in two ways: by employing high-efficiency muscles and by using elastic elements within the thorax to recover energy expended accelerating the wings. However, because muscle efficiency and elastic storage have proven difficult variables to measure, it is not known which of these strategies is actually used. By comparison of mechanical power measurements based on gas exchange with simultaneously measured flight kinematics in Drosophila, a method was developed for determining both the mechanical efficiency and the minimum degree of elastic storage within the flight motor. Muscle efficiency values of 10 percent suggest that insects may minimize energy use in flight by employing an elastic flight motor rather than by using extraordinarily efficient muscles. Further, because of the trade-off between inertial and aerodynamic power throughout the wing stroke, an elastic storage capacity as low as 10 percent may be enough to minimize the energetic costs of flight.
Flapping-wing micro-aerial vehicles (FWMAVs) provide unique control challenges both in control authority and in the complexity of modeling flapping-wing aeromechanics. We provide a control-critical, closed-form model for FWMAV flight, particularly tailored to augment yaw torque authority of the vehicle (a common challenge for FWMAVs). The model provides invertible nonlinear closed-form expressions for thrust and moments in terms of trigonometric polynomial input voltages and the wingstroke shape, and respects asymmetries inherent to the vehicle. We apply the model to characterize the Harvard RoboBee, providing an optimization-based system identification process. Using the inverted mapping between wingstroke shape and control axes, we achieve lateral and heading control of the vehicle. Our model and asymmetric system identification, in collaboration with the chosen control scheme, allow full control authority of the position and the heading of the vehicle.
This paper studies the trajectory tracking problem of flapping-wing micro aerial vehicles (FWMAVs) in the longitudinal plane. First of all, the kinematics and dynamics of the FWMAV are established, wherein the aerodynamic force and torque generated by flapping wings and the tail wing are explicitly formulated with respect to the flapping frequency of the wings and the degree of tail wing inclination. To achieve autonomous tracking, an adaptive control scheme is proposed under the hierarchical framework. Specifically, a bounded position controller with hyperbolic tangent functions is designed to produce the desired aerodynamic force, and a pitch command is extracted from the designed position controller. Next, an adaptive attitude controller is designed to track the extracted pitch command, where a radial basis function neural network is introduced to approximate the unknown aerodynamic perturbation torque. Finally, the flapping frequency of the wings and the degree of tail wing inclination are calculated from the designed position and attitude controllers, respectively. In terms of Lyapunov's direct method, it is shown that the tracking errors are bounded and ultimately converge to a small neighborhood around the origin. Simulations are carried out to verify the effectiveness of the proposed control scheme.
Flapping-wing insect-scale robots (
500 mg) rely on small changes in drive signals supplied to actuators to generate angular torques. Previous results on vehicles with passive wing hinges have demonstrated roll, pitch, and position control, but they have not yet been able to control their yaw (heading) angle while hovering. To actuate yaw, the speed of the downstroke can be changed relative to the upstroke by adding a second harmonic signal at double the fundamental flapping frequency. Previous work has shown that pitching dynamics of a passive spring-like wing hinge reduces the aerodynamic drag available to produce yaw torque. We introduce three innovations that increase yaw actuation torque: 1) a new two-actuator robot fly design that increases the moment arm, 2) wider actuators that increase the operating frequency, and 3) a phase shift to the second harmonic signal. We validated these results through simulation and experiment. Further, we present the first demonstration of yaw angle control on a passive-hinge vehicle in a controlled flight. Our new robot fly design, UW Robofly-Expanded, weighs 160 mg (two toothpicks) and requires only two piezo actuators to steer itself.
Insects, the largest group of animals on the earth, owe their prosperity to their ability of flight and small body sizes. The ability of flight provided means for rapid translocation. The small body size allowed access to unutilized niches. By acquiring both features, however, insects faced a new problem: They were forced to beat their wings at enormous frequencies. Insects have overcome this problem by inventing asynchronous flight muscle, a highly specialized form of striated muscle capable of oscillating at >1,000 Hz. This article reviews the structure, mechanism, and molecular evolution of this unique invention of nature.
It is challenging to analyze the aerial locomotion of bats because of the complicated and intricate relationship between their morphology and flight capabilities. Developing a biologically inspired bat robot would yield insight into how bats control their body attitude and position through the complex interaction of nonlinear forces (e.g., aerodynamic) and their intricate musculoskeletal mechanism. The current work introduces a biologically inspired soft robot called Bat Bot (B2). The overall system is a flapping machine with 5 Degrees of Actuation (DoA). This work reports on some of the preliminary untethered flights of B2. B2 has a nontrivial morphology and it has been designed after examining several biological bats. Key DoAs, which contribute significantly to bat flight, are picked and incorporated in B2's flight mechanism design. These DoAs are: 1) forelimb flapping motion, 2) forelimb mediolateral motion (folding and unfolding) and 3) hindlimb dorsoventral motion (upward and downward movement).
Inspired by the agility of flying insects and the recent development on an insect-scale aerial vehicle, we propose a single-loop adaptive flight control suite designed with an emphasis on the ability to track dynamic trajectories as a step towards the goal of performing acrobatic maneuvers as observed in real insects. Instead of the conventional approach of having cascaded control loops, the proposed controller directly regulates the commanded torques to stabilize the attitude and lateral position in a single loop. The method is verified by performing trajectory following flights with the insectlike robot. The results show that the position errors during trajectory following flights are comparable to those observed from steady hovering flights.
IT has been recently proposed by Greenewalt1 that the observed wing-beat frequency of insects and birds is equivalent to the characteristic frequency of the flight system as a mechanical oscillator. Evidence for this has come primarily from work on those higher orders of insects in which direct neural control of frequency is absent ('asynchronous' type of Roeder2). From this point of view the inverse variation of wing-beat frequency with air density reported in some species by Chadwick and Williams3 and Sotavalta4 appears anomalous. Evidence is given here which shows that such an anomaly may be due to a factor hitherto not considered in investigations of the flight of small insects: a variation of effective wing inertia with air density due to a functionally significant additional mass corresponding to a volume of air 'attached' to the wings.
An aerodynamic model, for a minimally actuated flapping wing micro air vehicle (FWMAV), is derived from blade element theory. The vehicle considered in this work is similar to the Harvard RoboFly, except that it is equipped with independently actuated wings. A blade element-based approach is used to compute both instantaneous and cycle-averaged forces and moments for a specific type of wingbeat motion that enables nearly decoupled, multi-degree-of-freedom control of the aircraft. The wing positions are controlled using oscillators whose frequencies change once per wingbeat cycle. A technique is introduced, called Split-Cycle Constant-Period Frequency Modulation with Wing Bias, that provides a high level of control input decoupling for vehicles without active angle of attack control. This technique allows the frequencies of the upstroke and down-stroke of each wing to differ such that non-zero cycle-averaged drag can be generated. Additionally, a wing bias term has been added to the wingbeat waveform and is utilized to provide pitching moment control. With this technique, it is possible to achieve five degree-of-freedom control using only two physical actuators. The present paper is concerned with the derivation of the instantaneous and cycle-averaged forces and moments for the Split-Cycle Constant-Period Frequency Modulation with Wing Bias technique. Implementation of the wing bias is discussed and modifications to the wingbeat forcing function, which are necessary to maintain a continuous wing position, are made.
Mosquito flight produces a tone as a side effect of wing movement; this tone is also a communication signal that is frequency-modulated during courtship. Recordings of tones produced by tethered flying male and female Aedes aegypti were undertaken using pairs of pressure-gradient microphones above and below, ahead and behind, and to the left and right over a range of distances. Fundamental frequencies were close to those previously reported, although amplitudes were lower. The male fundamental frequency was higher than that of the female and males modulated it over a wider range. Analysis of harmonics shows that the first six partials were nearly always within 1 Hz of integer multiples of the fundamental, even when the fundamental was being modulated. Along the front-back axis, amplitude attenuated as a function of distance raised to the power 2.3. Front and back recordings were out of phase, as were above and below, while left and right were in phase. Recordings from ahead and behind showed quadratic phase coupling, while others did not. Finally, two methods are presented for separating simultaneous flight tones in a single recording and enhancing their frequency resolution. Implications for mosquito behavior are discussed.
The split actuator microrobotic bee is the first flight-capable, insect-scale flapping-wing micro air vehicle that uses “split-cycle” constant-period frequency modulation to control body forces and torques. Building this vehicle is an intricate challenge, but by leveraging a maturing fabrication technology for microscale devices, we have developed a solution to tackle the design and fabrication difficulties. We show that the design is able to independently modulate the motions of both wings and produce roll, pitch, and yaw torques, as well as a peak lift force of 1.3 mN, in a 70mg package.
Unlike other flying insects, the wing motion of swallowtail butterflies is basically limited to flapping because their fore wings partly overlap their hind wings, structurally restricting the feathering needed for active control of aerodynamic force. Hence, it can be hypothesized that the flight of swallowtail butterflies is realized with simple flapping, requiring little feedback control of the feathering angle. To verify this hypothesis, we fabricated an artificial butterfly mimicking the wing motion and wing shape of a swallowtail butterfly and analyzed its flights using images taken with a high-speed video camera. The results demonstrated that stable forward flight could be realized without active feathering or feedback control of the wing motion. During the flights, the artificial butterfly's body moved up and down passively in synchronization with the flapping, and the artificial butterfly followed an undulating flight trajectory like an actual swallowtail butterfly. Without feedback control of the wing motion, the body movement is directly affected by change of aerodynamic force due to the wing deformation; the degree of deformation was determined by the wing venation. Unlike a veinless wing, a mimic wing with veins generated a much higher lift coefficient during the flapping flight than in a steady flow due to the large body motion.
This paper presents a reduced-order model of longitudinal hovering flight dynamics for dipteran insects. The quasi-steady wing aerodynamics model is extended by including perturbation states from equilibrium and paired with rigid body equations of motion to create a nonlinear simulation of a Drosophila-like insect. Frequency-based system identification tools are used to identify the transfer functions from biologically inspired control inputs to rigid body states. Stability derivatives and a state space linear system describing the dynamics are also identified. The vehicle control requirements are quantified with respect to traditional human pilot handling qualities specification. The heave dynamics are found to be decoupled from the pitch/fore/aft dynamics. The haltere-on system revealed a stabilized system with a slow (heave) and fast subsidence mode, and a stable oscillatory mode. The haltere-off (bare airframe) system revealed a slow (heave) and fast subsidence mode and an unstable oscillatory mode, a modal structure in agreement with CFD studies. The analysis indicates that passive aerodynamic mechanisms contribute to stability, which may help explain how insects are able to achieve stable locomotion on a very small computational budget.
SYNOPSIS. The cost of locomotion is rarely constant, but rather varies as an animal changes speed and direction. Ultimately, the locomotory muscles of an animal must compensate for these changing requirements by varying the amount of mechanical power that they produce. In this paper, we consider the mechanisms by which the mechanical power generated by the asynchronous flight muscles of the fruit fly, Drosophila melanogaster , is regulated to match the changing requirements during flight control behaviors. Our data come from individual flies flown in a flight arena under conditions in which stroke kinematics, total metabolic cost, and flight force are simultaneously measured. In order to increase force production, flies must increase wing beat frequency and wing stroke amplitude. Theory predicts that these kinematics changes should result in a roughly cubic increase in the mechanical power requirements for flight. However, the mechanical energy generated by muscle should increase only linearly with stroke amplitude and frequency. This discrepancy implies that flight muscles must either recruit myofibrils or increase activation in order to generate sufficient mechanical power to sustain elevated force production. By comparing respirometrically measured total metabolic power with kinematically estimated mechanical power, we have calculated that the stress in the flight muscles of Drosophila must increase by 50% to accommodate a doubling of flight force. Electrophysiological evidence suggests that this change in stress may be accomplished by an increased neural drive to the asynchronous muscles, which in turn may act to recruit additional cross bridges through an increase in cytosolic calcium.
Electrical activity from the indirect, myogenic muscles of calliphorid flies was recorded during flight. The animals were suspended from an aerodynamic balance in the laminar air-stream from a wind-tunnel. Muscle action potentials, recorded with 25 μ wire, were 5−7 msec, in duration, up to 10 mV. in amplitude and positive in sign. Frequencies were mostly under 20/sec. Frequencies in all the indirect muscles were similar, but these varied together with changes in aerodynamic power. Frequencies in the indirect muscles of the two sides varied by no more than ±10% during extreme turns to right or left (only left or only right wing beating). Electrical records from the non-myogenic direct muscles were made during tethered flight. The potentials were 2−4 msec, in duration, up to 2 mV. positive and had frequencies up to 180/sec. A nearly linear positive correlation exists between impulse frequency in the musculus latus (pleurostemal muscle), the inward movement of the pleural wall, and the wingbeat frequency, suggesting that this muscle is the basic frequency determiner. Strong turning behaviour is associated with opposed frequency changes in the pairs of antagonistic adductor and abductor muscles of the wings on the two sides of the body. The musculus dorsoventralis IV (tergo-trochanteral) is activated by a short impulse burst at the beginning of flight. It apparently acts as an oscillation starter. Flight initiation normally requires 30−60 msec. Usually activity begins in the musculus latus, which stiffens the thorax. Then simultaneously the myogenic muscles are activated and the ‘starter’ muscle causes a jump and the beginning of oscillation of the thorax. Then the wings are drawn gradually forward and full wingbeat amplitude develops within the first six wingbeats. Flight begins with maximal lift and wingbeat frequency and a nearly synchronous burst discharge in all the indirect muscles. Power production and the transmission and distribution of power are under separate control. The myogenic indirect motor varies only in total power output, this being influenced by its own state of excitation and by a muscle-controlling wingbeat frequency. Steering is accomplished by non-myogenic direct muscles which are capable of differentially engaging the two wings with the motor.