Yaw Control Of A Hovering Flapping-wing Aerial Vehicle .
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LRA.2021.3060726, IEEE Roboticsand Automation LettersIEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JANUARY, 20211Yaw control of a hovering flapping-wing aerialvehicle with a passive wing hingeYogesh Chukewad1 and Sawyer Fuller2Abstract—Flapping-wing insect-scale robots ( 500 mg) rely onsmall changes in drive signals supplied to actuators to generateangular torques. Previous results on vehicles with passive winghinges have demonstrated roll, pitch, and position control, butthey have not yet been able to control their yaw (heading) anglewhile hovering. To actuate yaw, the speed of the downstrokecan be changed relative to the upstroke by adding a secondharmonic signal at double the fundamental flapping frequency.Previous work has shown that pitching dynamics of a passivespring-like wing hinge reduces the aerodynamic drag available toproduce yaw torque. We introduce three innovations that increaseyaw actuation torque: 1) a new two-actuator robot fly designthat increases the moment arm, 2) wider actuators that increasethe operating frequency, and 3) a phase shift to the secondharmonic signal. We validated these results through simulationand experiment. Further, we present the first demonstration ofyaw 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 steeritself.Index Terms—Micro/Nano Robots, Aerial Systems: Mechanicsand Control, Biologically-Inspired RobotsI. I NTRODUCTIONINSECT-SCALE flying robots ( 500 mg) have the potentialfor several applications such as search and rescue, surveillance, and environmental monitoring, due to their small sizeand large deployment numbers. First feedback-controlled hovering of an insect-robot, RoboBee, was demonstrated in [1],in which all but the yaw degree of freedom were controlled.Another design, Robofly, at the similar size was introduced inthe authors’ earlier work in [2], [3], [4].Despite recent developments in sensing, power, and control,we are yet to see an insect-sized dual-actuator robot withcontrolled heading or yaw angle (see Fig. 1 for yaw axis)while hovering. As mentioned in [6], control of the yaw angleof the robot is desirable for many reasons including, 1) legsrequired to be in specific orientation for landing, 2) sensor(for example, camera and IR sensor) required to point in aparticular direction, or 3) to reduce computation complexity ofthe controller (a computationally intensive switching betweenManuscript received: August, 16, 2020; Revised December, 22, 2020;Accepted January, 28, 2021.This paper was recommended for publication by Editor Xinyu Liu uponevaluation of the Associate Editor and Reviewers’ comments. This work waspartially supported by the Air Force Office of Scientific Research under grantno. FA9550-14-1-0398. (Corresponding Author: Yogesh Chukewad)1 Yogesh Chukewad is with Unchained Labs, 6870 Koll Center Pkwy,Pleasanton, CA 94566, USA. 2 Sawyer Fuller is with the Department ofMechanical Engineering, University of Washington, Seattle, WA 98195, USAyogeshc@uw.edu, minster@uw.eduDigital Object Identifier (DOI): see top of this page.Fig. 1. (a) Robofly-Expanded, a new design of a robot fly [5]. A U.S. penny isshown for scale. Inset shows how heading (absolute yaw angle) θ is measuredbetween world and robot coordinate systems, about the positive world Zaxis. (b) Comparison of Robofly-Expanded with earlier versions of flappingwing robots: RoboBee [1] and RoboFly [2]. (c) Comparison of the momentarm (distance from the center of mass to the center of pressure) of RoboflyExpanded with that of RoboFly. (d) Comparison of the width of actuators ofRoboFly and Robofly-Expanded.global and body coordinate frames for lateral position controlcan be reduced or completely eliminated).The challenge of yaw actuation in passive-hinge vehicles isnot new. Flapping with a passive hinge represents a distinctclass of aerodynamic system with behavior that differs fromsystems in which wing motion is entirely specified [7]. Yawtorque measurements in the two-actuator Harvard Robobeeaffixed to a capacitive torque sensor suggested the ability2377-3766 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.Authorized licensed use limited to: University of Washington Libraries. Downloaded on February 19,2021 at 21:25:40 UTC from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LRA.2021.3060726, IEEE Roboticsand Automation Letters2IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JANUARY, 2021to produce significant yaw torque [8]. The technique reliedon its piezo actuator’s ability for high-bandwidth actuation,by flapping the wing in one direction faster than the otherdirection. Air drag varies approximately with velocity squaredin the inertia-dominated fluid mechanics of this scale (Re 3000 [9]), so that the net stroke-averaged drag force canbe varied. But in videos of its first controlled flights itcan be observed that yaw angle rotated freely [1]. Indeed,significant efforts needed to be undertaken in that work todesign a nonlinear controller that could operate regardless oforientation. For this reason it is likely that the previously measured yaw torques could be attributable to sensing error.At insect scale, the most successful previous demonstrationis hovering control of the yaw came in a design with twoextra actuators [10], for a total of four. A sophisticated linkageallowed this robot to vary the wing hinge, to actuate the angleof attack (AoA) to actuate yaw [11]. Like flies, this robot useda passive wing hinge whose neutral angle was under activecontrol [12].Successful yaw actuation on minimally-actuated (one actuator per wing) have included a Robobee steered left andright using rapid, phased pitch and roll oscillations, exploiting the nonlinearity of attitude kinematics [6]. This expendssignificant energy, was hard to control, and was not able toconsistently steer in a desired direction. In [13], a four-wingedrobot actuated yaw in free flight by extending the moment arm,but controlled flights in which yaw was controlled yaw werenot demonstrated.Yaw torque in passively-pitching wings with a spring-likerestoring moment was more closely investigated in [14]. Thatwork revealed that due to the wing hinge and to the effectof taking the time-integral of drag force on the wing, theyaw torque could reverse sign. The magnitude of this “torqueinversion” peaks at the peak lift-to-drag ratio. That workproposed additional features that established a nonlinear stresscurve for the wing hinge, negating the torque inversion.Due to this challenge, no demonstration of yaw control ona minimal (two-actuator) vehicle with spring-like hinges hasbeen made. It is not known whether wings with a physicallimit to the angle of attack are more efficient than spring-likehinges, but the latter are likely to be quieter and may avoidfatigue-based failure. Steinmeyer [15] showed that yaw canbe actuated successfully on a tethered flapper equipped withsimple linear spring hinges if the robot is driven below itsresonant frequency. At lower frequencies, the torque inversionregime can be avoided. But no controlled flight demonstrations have been reported to date. For controlled flight, crosscoupling between modes of actuation can either be neglectedor modelled, both of which have associated challenges. Inparticular, the weaker the yaw actuation authority, the strongerthe signal must be to attain consistent control over that degreeof freedom. Anecdotal evidence suggests that the complicatedmotions of flapping-wing flight have cross-coupled interactions, which are exacerbated as the actuation signal increases.But in free-flight, a yaw controller must not disrupt otheractuation modes. We conjecture that the foregoing challengeshave precluded free-flight yaw control until now.To address the problems mentioned in earlier research onFig. 2. (a) Wing angle φ(t), measured using frames from high-speed video.The wing is flapped at 190 Hz, providing 10 frames per stroke. (b) Adrawing of a wing in frontal view; its passive wing hinge can be seen. On theright is a side view (along the length of the wing) showing the passive wingpitching angle while flapping. The angle of attack, α, is measured relative tothe horizontal plane, whereas wing hinge angle, ψ, is measured relative tothe vertical plane.yaw control, we introduce and validate two key innovationsthat are designed to increase yaw authority on vehicles withspring-like passive wing hinges. First, we show that a newrobot fly design, that reorients its piezo actuators laterally(Fig. 1(b)) and moves its wings farther from the center ofmass to increase moment arm (Fig. 1(c)), is able to increase itsyaw actuation authority. Called Robofly-Expanded (Fig 1) [5],we demonstrate that through this change it is able to actuateand control its yaw angle while hovering using PD control.The robot is able to follow simple trajectories while hovering.Second, we show that by changing the phase of the higherfrequency excitation of the wings, even greater yaw torque ispossible. We validate these results using quasi-steady analytical model for the flapping wing, as well as a lumped-parametermodel of the actuator-wing system.TABLE IPARAMETERS AND THEIR VALUES USED FOR IN SIMULATIONSParameterSymbolValueDensity of airDistance from CM to CPDistance from wing base to midpointof the wing along its lengthPeak-to-peak wing amplitudeFlapping frequencyWing hinge parameterWing massStiffness of combined actuatorand transmissionVertical distance from wingcenter of pressure to hingeHinge stiffnessWing areaρrcp1.23 kg m 32.03 cmrb w9.0 mmΦβm54 190 Hz10.32 ms 1 rad 1/20.63 mgKact105 µN mrad 1zcp1.25 mmkA4.4 µN mrad 151.2 10 6 m2ω2π2377-3766 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.Authorized licensed use limited to: University of Washington Libraries. Downloaded on February 19,2021 at 21:25:40 UTC from IEEE Xplore. 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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LRA.2021.3060726, IEEE Roboticsand Automation LettersCHUKEWAD et al.: YAW CONTROL OF A HOVERING FLAPPING-WING AERIAL VEHICLE WITH A PASSIVE WING HINGE303 0.3 0 -0.30.10210-0.101Drag (mN)Wing angle,(degree)2000.510-10-1-20-2-303 0.3 0 50.60.70.80.91t/Tt/TFig. 3. Wing angle φ(t), normalized by flapping time period, for threedifferent values of the second harmonic factor µ. The wing angle φ is scaledso that the peak magnitude achieved in a given cycle is the same regardlessof µ value.II. YAW TORQUE GENERATIONA. Robot DesignAs introduced in [5], the robot has its actuators re-orientedso that their long axes are horizontal and along the body pitchaxis (Fig. 1). One of the desirable effects of moving the wingsfather apart from the center of mass (CM) of the body is alarger moment arm. The larger moment arm, coupled withdrag induced by the flapping wings, leads to larger yaw torquegeneration.The robot is also equipped with wider actuators (Fig. 1(d))which, in combination with the transmission, leads to a higherresonant flapping frequency of 200 Hz. A drawing of thewing and its passive wing hinge is shown in Fig. 2. Itswing hinges are passive spring-like flexure joints made of thinKapton that produce passive pitching while flapping. They are3 stiffer than those of Robofly [2] and Robobee [16] to matchthe 3 wider actuators. The effect of passive wing rotation isstudied in detail and related equations of motion are derivedin [17], [18]. The new design of actuators along with stifferwing hinges allows the robot to lift more payload. For betteryaw control authority, these robots are always flown with alower payload than the maximum it can lift. This allows therobot to operate at off-optimal conditions, in which it producessignificantly lower (yet larger than its own weight) lift than itcan. The effect of the off-optimal conditions is explained indetail in the following subsection.B. Torque generationThe only actuation mode that has produced measurableyaw torques consists of creating differential drag on wingsFig. 5. Simulation results of drag acting on a flapping wing changing withtime (normalized by flapping time period), for three different values of µ.Non-zero values of µ show differential-drag generation. Horizontal lines onthe main plot (also magnified in the inset) show the stroke-averaged dragvalues for corresponding values of µ.by flapping them faster in one direction than the other. Oneof the ways to generate such split-cycle modulation is byactuating with voltage signal which also includes the secondharmonic frequency [1]. When the actuators are supplied withthis voltage signal, the wing flapping angle, φ(t) is written asfollows.φ(t) Φ sin(ωt) µ sin(2ωt)2 max[sin(ωt) µ sin(2ωt)](1)Here, ω is the wing angular velocity in rad/s, Φ is the peakto-peak wing amplitude, and µ is the peak-to-peak amplitudeof the second harmonic term, relative to the fundamentalfrequency term. The term µ is referred to as the secondharmonic factor in the rest of the paper. The variation of wingangle while flapping is shown in Fig. 3 for µ 0 and for itsextreme values of 0.3 and 0.3. We carried out experimentsand observed that the total amplitude was the same for anyvalue of µ, provided other parameters were kept constant.Therefore, we used the normalizing term in Eq. 1 to match thepeak-to-peak amplitude for any value of µ in the simulation.We present a model, inspired by [14], that entails purelytranslational wing motion and a quasi-steady aerodynamicmodel to predict yaw torque behavior. The quasi-steady modelincorporates unsteady flow effects in flapping wings such asthe leading edge vortex into effective lift and drag coefficients [19], [20]. To simplify the simulation, we assume thatwing rotation about its passive hinge is a direct function ofwing flapping velocity, assuming that inertial dynamics aroundthe wing hinge are fast relative to flapping frequency.DragLiftFit function- DragFit function- Lift3Yaw torque due toboth wings (mN-mm)Coefficients4210012345678910210-1-2-0.5Fig. 4. Model for Cdrag and Clif t vs wing velocity ẋ (translational velocityof the midpoint of the wing along its length) for Robofly wing hinge. Dashedlines indicate polynomial approximation used in simulation.-0.4-0.3-0.2-0.100.10.20.30.40.5Second harmonic factor ( )Fig. 6. The variation of stroke-averaged yaw torque generated due to bothwings with varying µ, according to the quasi-steady simulation.2377-3766 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.Authorized licensed use limited to: University of Washington Libraries. Downloaded on February 19,2021 at 21:25:40 UTC from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LRA.2021.3060726, IEEE Roboticsand Automation Letters4IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED JANUARY, 2021Drag acting on the wing, Fdrag , is given by [18]12ρCdrag (α)Arb wφ̇ φ̇ (2)2where A is wing area and ρ is air density. For simplicity,the quantity rb w is the distance from the wing base to themidpoint of the wing along its length, Cdrag is the dragcoefficient, which varies as a function of angle of attack(AoA) α [17], [18], [19] given byFdrag Cdrag (α) 1.9 1.5 cos(2α)(3)Similarly, the lift force, Flif t is given by [18]12ρClif t (α)Arb wφ̇2 ,(4)2where Clif t is the lift coefficient, a function of α [17], [18],[19], which is given byFlif t Clif t (α) 1.8 sin(2α).(5)Cdrag and Clif t are functions of α. For simplicity, wemodel the system as a linearly translating wing, with positionx rb w φ. If the α-axis dynamics are assumed to beinstantaneous, then steady-state wing velocity is a functionof α [14]:s(π/2 α),sin(π/2 α)Clif t (α) cos(π/2 α)Cdrag (α)(6)q2k0.where β is the wing hinge parameter given by ρAzcpWe performed a simple system identification procedure todetermine the value of β. For this purpose, we flapped a wingwith a bias signal of 250 V, a sinusoidal signal with a peakto-peak amplitude 2V0 of 140 V to the middle layer (carbonfiber), and at 200 Hz. The wing amplitude, φ, and AoA, α,were measured by recording the flapping of the wing using ahigh-speed camera (Phantom v7.3, Vision Research, Inc.) at3900 frames per second. Frames at extreme positions of theflapping were captured to measure the peak-to-peak amplitudeΦ. Fig. 2 shows an overlay of two frames in which the wingis at the extreme positions while flapping. With the measuredamplitude, the wing angle was generated as a sinusoidalfunction of time. Wing velocity as a function of time was thencalculated by taking the time derivative of the wing angle. Thisfunction was used to estimate the wing velocity, ẋss at midstroke (φ 0). We also estimated the corresponding α valueby measuring the length of the projection of the wing chordin the overhead view. By substituting the values of ẋss and αin Eq. 6, we determined the value of β, which is specific tothe Robofly wing hinge (Table I).We then substituted the value of β in Eq. 6 and plottedthe steady state velocity as a function of α, for a possiblerange of velocities. We combined the steady-state velocity asthe function of α with Eq. 3 and Eq. 5 and determined Clif tand Cdrag as functions of the stead-state velocity. For thissimulation we didn’t consider the wing inertia and assumedẋ ẋss . This assumption is consistent with the simplifiedtranslational quasi-steady model presented in [14]. We plottedẋss βthe coefficients as the functions of ẋss in Fig. 4 along with thepolynomial fit functions generated using Curve Fitting Toolboxin MATLAB.Now, we move on to the simulation part which makes use ofthe empirical value of the wing hinge parameter. In this part,we decided to simulate for the flapping frequency of 190 Hzto slow down the dynamics in the corresponding experimentswhich are presented later. Using Eq. 4 and Clif t (ẋ), therequired peak-to-peak wing amplitude (Φ) was determinedsuch that the total lift was equal to the weight of the robot.Referring to the wing angle plotted in Fig. 3 for threedifferent values of µ, the drag was calculated using Eq. 2and Cdrag (ẋ) for one whole cycle and plotted against timein Fig. 5. For µ 0, it can be seen that the drag force issymmetric about mean stroke position. However, in case ofµ 0.3, the drag is significantly larger in one direction thatthe other. Similar but opposite pattern was observed in case ofµ 0.3, as expected. The torque due to two wings was thencalculated using τyaw 2rcp Fdrag , where rcp is the distancebetween the CM of the robot and the CP of the wing, projectedon horizontal plane. τyaw is plotted for various values of µ inFig. 6. The torque values estimated from the simulation arecomparable with those from the results presented in [14]. Itshould also be noted that the
global and body coordinate frames for lateral position control can be reduced or completely eliminated). The challenge of yaw actuation in passive-hinge vehicles is not new. Flapping with a passive hinge represents a distinct class of aerodynamic system with behavior that differs from systems in which wing motion is entirely specied [7]. Yaw
Yaw Moment Equation The yaw moment is the moment about the zbody axis and is positive if it moves the nose of the plane to the right. The big contributor to the yaw moment is the vertical tail. . This effect is sometimes called the “p” effect. The “p” effect is caused by the asymmetric loading of the propeller due to the angle of .File Size: 219KB
movement. Yaw system components of a utility-scale wind turbine are pictured in Fig. 1.1. Friction pads Yaw motor Cable bundle Slew gear Nacelle Down-tower Figure 1.1: Components around the yaw system of a MW-class turbine. Another yaw system composed of one motor and one gear-set is shown in Fig. 1.2. Dc motor Worm gear Slew gear Tower Nacelle
But hang gliders don't have any direct yaw control. Yaw Stability Hang gliders achieve directional (yaw) stability because of the swept wing design. If a glider is flying straight ahead, the air is meeting both wings at an angle (that angle being determined by the nose angle of the glider).
data acquisition device from National Instrument, NI-USB-6001 is present. This is used for reading the pitch and yaw angles of the helicopter, and for sending the control voltages to the pitch and yaw motors. There are also other components like the power supply unit and
data acquisition device from National Instrument, NI-USB-6001 is present. This is used for reading the pitch and yaw angles of the helicopter, and for sending the control voltages to the pitch and yaw motors. There are also other components like the power supply unit and
Includes statistical variation in systems performance “fleet” yaw – Can be applied to body armor and other types of barrier evaluation First study performing comparative P(I) analysis for M855, MK262, and M80 (among others) – Assessments including yaw effects and other considerations – Incap
River, Rhode Island 11:40 A. Beyer; The view from the field – what are the greatest policy needs and opportunities to get more of this work done M. Yaw (M. Yaw & S. Aston); Design and Physical Model Testing of a Bottomless Baffled Culvert N. Burnett; Burst swimming in areas of tur
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