Dynamic flight stability of a hovering model insect:lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was 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. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.

Aerodynamics of flexible wing in bees' hovering flight

The aerodynamics of 2-dimensional flexible wings in bees＇ normal hovering flight is studied. Four insect flapping flight coordinate systems, including a global system, a bodyfixed system, a rigid wing-fixed system and a flexible wingfixed system, are established to represent the insects＇ position, gesture, wing movement and wing deformation, respectively. Then the transformations among four coordinate systems are studied. It is found that the elliptic coordinate system can improve the computation accuracy and reduce the calculation complexity in a 2-dimensional rigid wing. The computation model of a 2-dimensional flexible wing is established, and the changes of the force, moment, and power are investigated. According to the computation results, the large lift and drag peaks at the beginning and end of the stroke can be explained by the superposition of the rapid translational acceleration, the fast pitching-up rotation and the Magnus effect; and the small force and drag peaks can be explained by the convex flow effect and the concave flow effect. Compared with the pressure force, pressure moment and translational power, the viscous force, viscous moment and rotational power are small and can be ignored.

Control for going from hovering to small speed flight of a model insect

The longitudinal steady-state control for going from hovering to small speed flight of a model insect is studied, using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques based on the linear theories of stability and control for determining the non-zero equilibrium points. Morphological and certain kinematical data of droneflies are used for the model insect. A change in the mean stroke angle （δФ） results in a horizontal forward or backward flight; a change in the stroke amplitude （δФ） or a equal change in the down- and upstroke angles of attack （δα1） results in a vertical climb or decent; a proper combination of δФ and δФ controls （or δФ and δα1 controls） can give a flight of any （small） speed in any desired direction.

Near wake vortex dynamics of a hovering hawkmoth

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.

Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper, the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical sim- ulation. The theory is based on the averaged model （which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion, so that the flapping wings＇ degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments）; the simulation solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164 Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The results show that the averaged model is valid for the hawkmoth as well as for the dronefly. Since the wingbeat frequency of the hawkmoth is relatively low （the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large） compared with many other insects, that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Stabilization control of a hovering model insect:lateral motion

Our previous study shows that the lateral disturbance motion of a model drone fly does not have inherent stability （passive stability）,because of the existence of an unstable divergence mode.But drone flies are observed to fly stably.Constantly active control must be applied to stabilize the flight.In this study,we investigate the lateral stabilization control of the model drone fly.The method of computational fluid dynamics is used to compute the lateral control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion.Controllability analysis shows that although inherently unstable,the lateral disturbance motion is controllable.By feeding back the state variables （i.e.lateral translation velocity,yaw rate,roll rate and roll angle,which can be measured by the sensory system of the insect） to produce anti-symmetrical changes in stroke amplitude and/or in angle of attack between the left and right wings,the motion can be stabilized,explaining why the drone flies can fly stably even if the flight is passively unstable.

Lateral dynamic flight stability of hovering insects: theory vs. numerical simulation

In the present paper, the lateral dynamic flight stability properties of two hovering model insects are predicted by an approximate theory based on the averaged model, and computed by numerical simulation that solves the complete equations of motion coupled with the Naviertokes equations. Comparison between the theoretical and simulational results provides a test to the validity of the assumptions made in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency （164Hz） and the other is a model hawkmoth which has relatively low wingbeat frequency （26 Hz）. The following conclusion has been drawn. The theory based on the averaged model works well for the lateral motion of the dronefly. For the hawkmoth, relatively large quantitative differences exist between theory and simulation. This is because the lateral non-dimensional eigenvalues of the hawkmoth are not very small compared with the non-dimensional flapping frequency （the largest lateral non-dimensional eigenvalue is only about 10% smaller than the non-dimensional flapping frequency）. Nevertheless, the theory can still correctly predict variational trends of the dynamic properties of the hawkmoth＇s lateral motion.

A Study on Hovering Control of Small Aerial Robot by Sensing Existing Floor Features

Since precise self-position estimation is required for autonomous flight of aerial robots, there has been some studies on self-position estimation of indoor aerial robots. In this study, we tackle the self-position estimation problem by mounting a small downward-facing camera on the chassis of an aerial robot. We obtain robot position by sensing the features on the indoor floor.In this work, we used the vertex points(tile corners) where four tiles on a typical tiled floor connected, as an existing feature of the floor. Furthermore, a small lightweight microcontroller is mounted on the robot to perform image processing for the onboard camera. A lightweight image processing algorithm is developed. So, the real-time image processing could be performed by the microcontroller alone which leads to conduct on-board real time tile corner detection. Furthermore, same microcontroller performs control value calculation for flight commanding. The flight commands are implemented based on the detected tile corner information. The above mentioned all devices are mounted on an actual machine, and the effectiveness of the system was investigated.

Research on Aerodynamic Characteristics of Hovering Rotor Based on Leading Edge Droop

In view of the reduction of hovering efficiency near high tension when a helicopter rotor hovers,a numerical simulation method of lifting rotor hovering aerodynamic characteristics based on leading edge droop is established in this paper. It is dominated by Reynolds average N-S equation in integral form. Firstly,VR-12 airfoil is taken as the research object,and the influence of leading edge droop angle on the aerodynamic characteristics of two-dimensional airfoil is studied. Secondly,the modified 7 A rotor is taken as the research object,and the effects of different leading edge droop angles at the position of blade r/R=0.75—1 on the aerodynamic characteristics in hover are explored. It is found that the leading edge droop can significantly improve the aerodynamic characteristics of two-dimensional airfoil and three-dimensional hovering rotor near high angle of attack,and can effectively inhibit the generation of stall vortex.

Stabilization control of a bumblebee in hovering and forward flight

Our previous study shows that the hovering and forward flight of a bumblebee do not have inherent stability （passive stability）. But the bumblebees are observed to fly stably. Stabilization control must have been applied. In this study, we investigate the longitudinal stabilization control of the bumblebee. The method of computational fluid dynamics is used to compute the control derivatives and the techniques of eigenvalue and eigenvector analysis and modal decomposition are used for solving the equations of motion. Controllability analysis shows that at all flight speeds considered, although inherently unstable, the flight is controllable. By feedbacking the state variables, i.e. vertical and horizontal velocities, pitching rate and pitch angle （which can be measured by the sensory system of the insect）, to produce changes in stroke angle and angle of attack of the wings, the flight can be stabilized, explaining why the bumblebees can fly stably even if they are passively unstable.

Numerical analysis of the three-dimensional aerodynamics of a hovering rufous hummingbird(Selasphorus rufus)

Hummingbirds have a unique way of hover- ing. However, only a few published papers have gone into details of the corresponding three-dimensional vortex struc- tures and transient aerodynamic forces. In order to deepen the understanding in these two realms, this article presents an integrated computational fluid dynamics study on the hovering aerodynamics of a rufous hummingbird. The original morphological and kinematic data came from a former researcher＇s experiments. We found that conical and sta- ble leading-edge vortices （LEVs） with spanwise flow inside their cores existed on the hovering hummingbird＇s wing surfaces. When the LEVs and other near-field vortices were all shed into the wake after stroke reversals, periodically shed bilateral vortex rings were formed. In addition, a strong downwash was present throughout the flapping cycle. Time histories of lift and drag were also obtained. Combining the three-dimensional flow field and time history of lift, we believe that high lift mechanisms （i.e., rotational circulation and wake capture） which take place at stroke reversals in insect flight was not evident here. For mean lift throughout a whole cycle, it is calculated to be 3.60 g （104.0 % of the weight support）. The downstroke and upstroke provide 64.2 % and 35.8 % of the weight support, respectively.

Methods of spacecraft impulsive relative hovering and trajectory safety analysis

Based on the analytical solutions of T-H equations and its state transition matrix form,the open-loop control method of spacecraft impulsive relative hovering was studied,which is promising for practical engineering use.The true anomaly intervals of the hovering impulse were optimized by the nonlinear mathematical programming.Based on the calculation of collision probability,the method of safety analysis and risk management was proposed.The numerical simulations show that the introduced relative hovering method can be used for circular and elliptical reference orbits hovering.Furthermore,the local optimal solution can be obtained by applying the true anomaly intervals optimization method.The maximum collision probability and the minimum relative distance nearly appear at the same time.And,the smaller the relative distance is,the larger the collision probability.

High-Order Discontinuous Galerkin Method for Hovering Rotor Simulations Based on a Rotating Reference Frame

An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.

Eagles Are Hovering at the Cradle of Love Songs

In the late autumn of 2007,the Southwest Branch of China Airlines sent offone A319 airbus,named B6238,to cross over Mt.Gongkya (7556 meters above sea level) and safely land at the Kangding Airport - which is acknowledged as the world's second highest airport.The success of the experimental flight ends the history of unavailabil- ity of civil airline flights in Garze Autonomous Prefecture of Sichuan Province.It also marks the closure of the final preparation phase and readiness to move to the next stage-l...

Hybrid Design and Performance Tests of a Hovering Insect-inspired Flapping-wing Micro Aerial Vehicle

Hovering ability is one of the most desired features in Flapping-Wing Micro Air Vehicles （FW-MAVs）. This paper presents a hybrid design of flapping wing and fixed wing, which combines two flapping wings and two fixed wings to take advantage of the double wing clap-and-fling effect for high thrust production, and utilizes the fixed wings as the stabilizing surfaces for inherently stable hovering flight. Force measurement shows that the effect of wing clap-and-fling significantly enhances the cycle-averaged vertical thrust up to 44.82% at 12.4 Hz. The effect of ventral wing clap-and-fling due to presence of fixed wings produces about 11% increase of thrust-to-power ratio, and the insect-inspired FW-MAV can produce enough cycle-averaged vertical thrust of 14.76 g for lift-offat 10 Hz, and 24 g at maximum frequency of 12.4 Hz. Power measurement indicates that the power consumed for aerodynamic forces and wing inertia, and power loss due to gearbox friction and mechanism inertia was about 80% and 20% of the total input power, respectively. The proposed insect-inspired FW-MAV could endure three-minute flight, and demonstrate a good flight performance in terms of vertical take-off, hovering, and control with an onboard 3.7 V-70 mAh LiPo battery and control system.

Dynamic Flight Stability of a Model Hoverfly in Inclined-Stroke-Plane Hovering

Most hovering insects flap their wings in a horizontal plane, called ＇normal hovering＇. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane. In the present paper, the longitudinal dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering was studied. Computational fluid dynamics was used to compute the aerodynamic derivatives and the eigenvalue and eigenvector analysis was used to solve the equations of motion. The primary findings are as follows. （1） For inclined-stroke-plane hovering, the same three natural modes of motion as those for normal hovering were identified： one unstable oscillatory mode, one stable fast subsidence mode, and one stable slow subsidence mode. The unstable oscillatory mode and the fast subsidence mode mainly have horizontal translation and pitch rotation, and the slow subsidence mode mainly has vertical translation. （2） Because of the existence of the unstable oscillatory mode, inclined-stroke-plane hov- ering flight is not stable. （3） Although there are large differences in stroke plane and body orientations between the in- clined-stroke-plane hovering and normal hovering, the relative position between the mean center of pressure and center of mass for these two cases is not very different, resulting in similar stability derivatives, hence similar dynamic stability properties for these two types of hovering.

Influence of Center of Gravity Location on Flight Dynamic Stability in a Hovering Tailless FW-MAV:Longitudinal Motion

The influence of Center of Gravity(CG)location on longitudinal dynamic stability of hovering KUBeetle,a tailless Flapping-Wing Micro Air Vehicle(FW-MAV),is reported in this paper.The rigid-body approximation was assumed,allowing application of the standard equations of motion used for fixed-wing aircraft.For each considered location of CG,stability derivatives were obtained using the computational fluid dynamics method via the commercial software of ANSYS Fluent.The dynamic stability was studied using technique of eigenvalue analysis.There exists a narrow stable region for CG between 23%-24%of mean chord above the wing pivot point,where the longitudinal hovering of KUBeetle is passively stable.When CG is located below the stable region,the analysis identifies two subsidence modes and one unstable oscillatory mode,which makes the hovering of KUBeetle unstable.However,it can be stabilized using pitching rate feedback.When CG is located above the stable region,the system yields one stable oscillatory mode,one subsidence mode,and one divergence mode.Because of the divergence mode,the system remains unstable even with the angular rate feedback.These results share similar characteristics to another FW-MAV and insects.This study may provide a reference for FW-MAV developers.

Lateral Flight Stability of Two Hovering Model Insects

The longitudinal disturbance motion of different insects at hovering flight has the same modal structure. Here, we consider the case of lateral motion. The lateral dynamic flight stability of two model insects, hoverfly and honeybee, at hovering flight is studied. The method of computational fluid dynamics is applied to compute the stability derivatives. The techniques of eigenvalue and eigenvector analysis are used to solve the equations of motion. Results show that the lateral disturbance motion of the hoverfly has three natural modes of motion： an unstable divergence mode, a stable oscillatory mode and a stable subsidence mode, and the flight is unstable; while the honeybee has a different modal structure （a stable slow subsidence mode, a stable fast subsidence mode, and a nearly neutrally stable oscillatory mode） and the flight is nearly neutrally stable. The change in modal structure between the two insects is due to their roll-moment/side-velocity derivative having different sign, and the sign difference is because that the hoverfly has a relatively small, but the honeybee has a relatively large, distance between the wing roots and the center of mass. Thus, unlike the case of longitudinal motion, for lateral motion, some insects have different modal structures and stability properties from others.

NUMERICAL ANALYSIS OF THE GROUND EFFECT ON INSECT HOVERING

The ground effect on insect hovering is investigated using an immersed boundary-lattice Boltzmann method to solve the two-dimensional incompressible Navier-Stokes equations. A virtual model of an elliptic foil with oscillating translation and rotation near a ground is used. The objective of this study is to deal with the ground effect on the unsteady forces and vortical structures and to get the physical insights in the relevant mechanisms. Two typical insect hovering modes, i.e., normal and dragonfly hovering mode, are examined. Systematic computations have been carried out for some parameters, and the ground effect on the unsteady forces and vortical structures is analyzed.

A Neural-network-based Approach to Study the Energy-optimal Hovering Wing Kinematics of a Bionic Hawkmoth Model

This paper presents the application of an artificial neural network to develop an approach to determine and study the energy-optimal wing kinematics of a hovering bionic hawkmoth model.A three-layered artificial neural network is used for the rapid prediction of the unsteady aerodynamic force acting on the wings and the required power.When this artificial network is integrated into genetic and simplex algorithms,the running time of the optimization process is reduced considerably.The validity of this new approach is confirmed in a comparison with a conventional method using an aerodynamic model based on an extended unsteady vortex-lattice method for a sinu soidal wing kinematics problem.When studying the obtained results,it is found that actual hawkmoths do not hover under an energy-optimal condition.Instead,by tilting the stroke plane and lowering the wing positions,they can compromise and expend some energy to enhance their maneuverability and the stability of their flight.