Flexural rigidity of hawkmoth antennae depends on the bending direction

To probe its environment, the flying insect controllably flexes, twists, and maneuvers its antennae by coupling mechanical deformations with the sensory output. We question how the materials properties of insect antennae could influence their performance. A comparative study was conducted on four hawkmoth species: Manduca sexta, Ceratomia catalpae, Manduca quinquemaculata, and Xylophanes tersa. The morphology of the antennae of three hawkmoths that hover while feeding and one putatively non-nectar-feeding hawkmoth (Ceratomia catalpa) do not fundamentally differ, and all the antennae are comb-like (i.e., pectinate), markedly in males but weakly in females. Applying different weights to the free end of extracted cantilevered antennae, we discovered anisotropy in flexural rigidity when the antenna is forced to bend dorsally versus ventrally. The flexural rigidity of male antennae was less than that of females. Compared with the hawkmoths that hover while feeding, Ceratomia catalpae has almost two orders of magnitude lower flexural rigidity. Tensile tests showed that the stiffness of male and female antennae is almost the same. Therefore, the differences in flexural rigidity are explained by the distinct shapes of the antennal pectination. Like bristles in a comb, the pectinations provide extra rigidity to the antenna. We discuss the biological implications of these discoveries in relation to the flight habits of hawkmoths. Flexural anisotropy of antennae is expected in other groups of insects, but the targeted outcome may differ. Our work offers promising new applications of shaped fibers as mechanical sensors. STATEMENT OF SIGNIFICANCE: Insect antennae are blood-filled, segmented fibers with muscles in the two basal segments. The long terminal segment is muscle-free but can be flexed. Our comparative analysis of mechanical properties of hawkmoth antennae revealed a new feature: antenna resistance to bending depends on the bending direction. Our discovery replaces the conventional textbook scenario considering hawkmoth antennae as rigid rods. We showed that the pectinate antennae of hawkmoths behave as a comb in which the bristles resist bending when they come together. This anisotropy of flexural resistance offers a new mode of environmental sensing that has never been explored. The principles we found apply to other insects with non-axisymmetric antennae. Our work offers new applications for shaped fibers that could be designed to sense the flows.

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

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

Thrust enhancement and degradation mechanisms due to self-induced vibrations in bio-inspired flying robots

Bio-inspired flying robots (BIFRs) which fly by flapping their wings experience continuously oscillating aerodynamic forces. These oscillations in the driving force cause vibrations in the motion of the body around the mean trajectory. In other words, a hovering BIFR does not remain fixed in space; instead, it undergoes oscillatory motion in almost all directions around the stationary point. These oscillations affect the aerodynamic performance of the flier. Assessing the effect of these oscillations, particularly on thrust generation in two-winged and four-winged BIFRs, is the main objective of this work. To achieve such a goal, two experimental setups were considered to measure the average thrust for the two BIFRs. The average thrust is measured over the flapping cycle of the BIFRs. In the first experimental setup, the BIFR is installed at the end of a pendulum rod, in place of the pendulum mass. While flapping, the model creates a thrust force that raises the model along the circular trajectory of the pendulum mass to a certain angular position, which is an equilibrium point and is also stable. Measuring the weight of the BIFR and the equilibrium angle it obtains, it is straightforward to estimate the average thrust, by moment balance about the pendulum hinge. This pendulum setup allows the BIFR model to freely oscillate back and forth along the circular trajectory about the equilibrium position. As such, the estimated average thrust includes the effects of these self-induced vibrations. In contrast, we use another setup with a load cell to measure thrust where the model is completely fixed. The thrust measurement revealed that the load cell or the fixed test leads to a higher thrust than the pendulum or the oscillatory test for the two-winged model, showing the opposite behavior for the four-winged model. That is, self-induced vibrations have different effects on the two BIFR models. We felt that this observation is worth further investigation. It is important to mention that aerodynamic mechanisms for thrust generation in the two and four-winged models are different. A two-winged BIFR generates thrust through traditional flapping mechanisms whereas a four-winged model enjoys a clapping effect, which results from wing-wing interaction. In the present work, we use a motion capture system, aerodynamic modeling, and flow visualization to study the underlying physics of the observed different behaviors of the two flapping models. The study revealed that the interaction of the vortices with the flapping wing robots may play a role in the observed aerodynamic behavior of the two BIFRs.

Optic flow enrichment via Drosophila head and retina motions to support inflight position regulation

Developing a functional description of the neural control circuits and visual feedback paths underlying insect flight behaviors is an active research area. Feedback controllers incorporating engineering models of the insect visual system outputs have described some flight behaviors, yet they do not explain how insects are able to stabilize their body position relative to nearby targets such as neighbors or forage sources, especially in challenging environments in which optic flow is poor. The insect experimental community is simultaneously recording a growing library of in-flight head and eye motions that may be linked to increased perception. This study develops a quantitative model of the optic flow experienced by a flying insect or robot during head yawing rotations (distinct from lateral peering motions in previous work) with a single other target in view. This study then applies a model of insect visuomotor feedback to show via analysis and simulation of five species that these head motions sufficiently enrich the optic flow and that the output feedback can provide relative position regulation relative to the single target (asymptotic stability). In the simplifying case of pure rotation relative to the body, theoretical analysis provides a stronger stability guarantee. The results are shown to be robust to anatomical neck angle limits and body vibrations, persist with more detailed Drosophila lateral-directional flight dynamics simulations, and generalize to recent retinal motion studies. Together, these results suggest that the optic flow enrichment provided by head or pseudopupil rotation could be used in an insect's neural processing circuit to enable position regulation.

Development of flapping wing robot and vision-based obstacle avoidance strategy

Due to the flight characteristics such as small size, low noise, and high efficiency, studies on flapping wing robots are being actively conducted. In particular, the flapping wing robot is in the spotlight in the field of search and reconnaissance. Most of the research focuses on the development of flapping wing robots rather than autonomous flight. However, because of the unique characteristics of flapping wings, it is essential to consider the development of flapping wing robots and autonomous flight simultaneously. In this article, we describe the development of the flapping wing robot and computationally efficient vision-based obstacle avoidance algorithm suitable for the lightweight robot. We developed a 27 cm and 45 g flapping wing robot named CNUX Mini that features an X-type wing and tailed configuration to attenuate oscillation caused by flapping motion. The flight experiment showed that the robot is capable of stable flight for 1.5 min and changing its direction with a small turn radius in a slow forward flight condition. For the obstacle detection algorithm, the appearance variation cue is used with the optical flow-based algorithm to cope robustly with the motion-blurred and feature-less images obtained during flight. If the obstacle is detected during straight flight, the avoidance maneuver is conducted for a certain period, depending on the state machine logic. The proposed obstacle avoidance algorithm was validated in ground tests using a testbed. The experiment shows that the CNUX Mini performs a suitable evasive maneuver with 90.2% success rate in 50 incoming obstacle situations.

Neuromuscular embodiment of feedback control elements in Drosophila flight

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

Flying State Sensing and Estimation Method of Large-Scale Bionic Flapping Wing Flying Robot

A large bionic flapping wing robot has unique advantages in flight efficiency. However, the fluctuation of fuselage centroid during flight makes it difficult for traditional state sensing and estimation methods to provide stable and accurate data. In order to provide stable and accurate positioning and attitude information for a flapping wing robot, this paper proposes a flight state sensing and estimation method integrating multiple sensors. Combined with the motion characteristics of a large flapping wing robot, the autonomous flight, including the whole process of takeoff, cruise and landing, is realized. An explicit complementary filtering algorithm is designed to fuse the data of inertial sensor and magnetometer, which solves the problem of attitude divergence. The Kalman filter algorithm is designed to estimate the spatial position and speed of a flapping wing robot by integrating inertial navigation with GPS (global positioning system) and barometer measurement data. The state sensing and estimation accuracy of the flapping wing robot are improved. Finally, the flying state sensing and estimation method is integrated with the flapping wing robot, and the flight experiments are carried out. The results verify the effectiveness of the proposed method, which can provide a guarantee for the flapping wing robot to achieve autonomous flight beyond the visual range.

A bioinspired revolving-wing drone with passive attitude stability and efficient hovering flight

Among small rotorcraft, the use of multiple compact rotors in a mechanically simple design leads to impressive agility and maneuverability but inevitably results in high energetic demand and acutely restricted endurance. Small spinning propellers used in these vehicles contrast with large lifting surfaces of winged seeds, which spontaneously gyrate into stable autorotation upon falling. The pronounced aerodynamic surfaces and delayed stalls are believed key to efficient unpowered flight. Here, the bioinspired principles are adopted to notably reduce the power consumption of small aerial vehicles by means of a samara-inspired robot. We report a dual-wing 35.1-gram aircraft capable of hovering flight via powered gyration. Equipped with two rotors, the underactuated robot with oversized revolving wings, designed to leverage unsteady aerodynamics, was optimized for boosted flight efficiency. Through the analysis of flight dynamics and stability, the vehicle was designed for passive attitude stability, eliminating the need for fast feedback to stay upright. To this end, the drone demonstrates flight with a twofold decrease in power consumption when compared with benchmark multirotor robots. Exhibiting the power loading of 8.0 grams per watt, the vehicle recorded a flight time of 14.9 minutes and up to 24.5 minutes when equipped with a larger battery. Taking advantage of the fast revolving motion to overcome the severe underactuation, we also realized position-controlled flight and illustrated examples of mapping and surveillance applications with a 21.5-gram payload.

Longitudinal Mode System Identification of an Insect-like Tailless Flapping-Wing Micro Air Vehicle Using Onboard Sensors

In this paper, model parameter identification results are presented for a longitudinal mode dynamic model of an insect-like tailless flapping-wing micro air vehicle (FWMAV) using angle and angular rate data from onboard sensors only. A gray box model approach with indirect method was utilized with adaptive Gauss–Newton, Levenberg–Marquardt, and gradient search identification methods. Regular and low-frequency reference commands were mainly used for identification since they gave higher fit percentages than irregular and high-frequency reference commands. Dynamic parameters obtained using three identification methods with two different datasets were similar to each other, indicating that the obtained dynamic model was sufficiently reliable. Most of the identified dynamic model parameters had similar values to the computationally obtained ones, except stability derivatives for pitching moment with forward velocity and pitching rate variations. Differences were mainly due to certain neglected body, nonlinear dynamics, and the shift of the center of gravity. Fit percentage of the identified dynamic model (~49%) was more than two-fold higher than that of the computationally obtained one (~22%). Frequency domain analysis showed that the identified model was much different from that of the computationally obtained one in the frequency range of 0.3 rad/s to 5 rad/s, which affected transient responses. Both dynamic models showed that the phase margin was very low, and that it should be increased by a feedback controller to have a robustly stable system. The stable dominant pole of the identified model had a higher magnitude which resulted in faster responses. The identified dynamic model exhibited much closer responses to experimental flight data in pitching motion than the computationally obtained dynamic model, demonstrating that the identified dynamic model could be used for the design of more effective pitch angle-stabilizing controllers.

Design optimization and wind tunnel investigation of a flapping system based on the flapping wing trajectories of a beetle's hindwings

To design a flapping-wing micro air vehicle (FWMAV), the hovering flight action of a beetle species (Protaetia brevitarsis) was captured, and various parameters, such as the hindwing flapping frequency, flapping amplitude, angle of attack, rotation angle, and stroke plane angle, were obtained. The wing tip trajectories of the hindwings were recorded and analyzed, and the flapping kinematics were assessed. Based on the wing tip trajectory functions, bioinspired wings and a linkage mechanism flapping system were designed. The critical parameters for the aerodynamic characteristics were investigated and optimized by means of wind tunnel tests, and the artificial flapping system with the best wing parameters was compared with the natural beetle. This work provides insight into how natural flyers execute flight by experimentally duplicating beetle hindwing kinematics and paves the way for the future development of beetle-mimicking FWMAVs.

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.

Flow visualization and force measurement of the clapping effect in bio-inspired flying robots

In this paper, we perform experimental investigations of the aerodynamic characteristics due to wing clapping in bio-inspired flying robots; i.e., micro-air-vehicles (MAVs) that fly by flapping their wings. For this purpose, four flapping MAV models with different levels of clapping (from no clapping at all to full clapping) are developed. The aerodynamic performance of each model is then tested in terms of the average thrust and power consumption at various flapping frequencies. The results show that clapping enhance both thrust and efficiency. To gain some physical insight into the underlying physics behind this clapping-thrust-enhancement, we perform a smoke flow visualization over the wings of the four models at different instants during the flapping cycle.

A stability perspective of bioinspired unmanned aerial vehicles performing optimal dynamic soaring

The phenomenon of dynamic soaring, as exhibited by soaring birds, has long been a biological inspiration for aerospace and control engineers. If this fascinating phenomenon, which allows soaring birds to perform almost unpowered flight using wind shear, can be mimicked by unmanned aerial vehicles (UAVs), then there is substantial potential for technological and economic enhancement of UAV performance. Although there has been a considerable amount of research covering the modeling, optimization, control and simulation aspects of different UAVs performing dynamic soaring, there is little to no conclusive work analyzing the stability of such UAVs in soaring orbits. In this paper we present a comprehensive framework for determining the stability of soaring UAVs utilizing both linear (Floquet-based) and nonlinear (contraction theory-based) techniques. Floquet stability analysis was inconclusive, which led to the use of a nonlinear contraction formulation to reach a conclusive stability assessment for an actual nonlinear fixed-wing UAV performing dynamic soaring. Furthermore, parametric variation along with numerical simulations were conducted to ascertain the response of the actual nonlinear system when perturbed from the nominal motion studied in this paper. The analysis and simulations revealed that the system possesses instability as the UAV motion diverges from its nominal trajectory and follows an undesirable path. From this result we conclude, for the first time in the literature as far as we are aware, that UAVs performing dynamic soaring in an optimal way to reduce wind shear requirements are inherently unstable. The results of this work suggest that mimicking of dynamic soaring by UAVs will require careful investigation of tracking and regulatory controls that need to be implemented.

State-space aerodynamic model reveals high force control authority and predictability in flapping flight

Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.

Wing shape optimization design inspired by beetle hindwings in wind tunnel experiments

Flighted beetles have deployable hindwings, which enable them to directly reduce their body size, and thus are excellent bioinspired prototypes for microair vehicles (MAVs). The wing shape of MAVs has an important influence on their aerodynamics. In this paper, wing shapes, inspired from three beetle species' hindwings and designed in terms of the wing camber angle, geometry (including wing length, aspect ratio (AR), and taper ratio (TR)) and wing area, were selected and varied to optimize lift together with the efficiency of wing. All the wings were fabricated by a Tyvek membrane and tested in a wind tunnel. The camber angle and AR were found to have a critical role in force production. The best performance was obtained by a wing with a camber angle of 10°, wing length of 125 mm, AR of 7.06, TR of 0.40 and wing area of 4115 mm².

Aerodynamic effects on an emulated hovering passerine with different wing-folding amplitudes

Bird flight involves complicated wing kinematics, especially during hovering flight. The detailed aerodynamic effects of wings with higher degrees of freedom (DOFs) remain to be further investigated. Therefore, we designed a novel multiarticulate flapping-wing robot with five DOFs on each wing. Using this robot we aimed to investigate the more complicated wing kinematics of birds, which are usually difficult to test and analyze. In this study the robot was programmed to mimic the previously observed hovering motion of passerines, and force measurements and particle image velocimetry experiments. We experimented with two different wing-folding amplitudes: one with a larger folding amplitude, similar to that of real passerines, and one with only half the amplitude. The robot kinematics were verified utilizing direct linear transformation, which confirmed that the wing trajectories had an acceptable correlation with the desired motion. According to the lift force measurements, four phases of the wingbeat cycle were characterized and elaborated through camera images and flow visualization. We found that the reduction in folding amplitude caused a higher negative force during upstrokes and also induced a greater positive force at the initial downstroke through 'wake capture'. This could increase the vertical oscillation while hovering despite a minor increase in average force production. This phenomenon was not observed during forward flight in previous studies. Our results provide a critical understanding of the effect of wing folding which is required for designing the wing kinematics of future advanced flapping-wing micro aerial vehicles.

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

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

Good vibrations for flapping-wing flyers

Studies of insect flight reveal how flapping-induced vibrations augment flight stability of tailless flapping-wing flyers.