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AIAA 2003-5345Mechanization and Control Conceptsfor Biologically Inspired Micro AerialVehicles

David L. RaneyNASA Langley Research CenterHampton, VA 23681-2199

Eric C. SlominskiVirginia Polytechnic InstituteBlacksburg, VA 24061

AIAA Guidance, Navigation & Control Conference11-14 August 2003

Austin, Texas

For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.

AIAA 2003-5345

1American Institute of Aeronautics and Astronautics

Mechanization and Control Concepts for Biologically InspiredMicro Aerial Vehicles

David L. RaneyNASA Langley Research Center

Hampton, VA 23681-2199

Eric C. Slominski†

Virginia Polytechnic InstituteBlacksburg, VA 24061

Research scientist, Dynamics and Control Branch, Member AIAA.

† Graduate Student, Mechanical and Aerospace Engineering Department, Member AIAA

Copyright © 2003 by the American Institute of Aeronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code.The Government has royalty-free license to exercise all rights under the copyright claimed herein for government purposes. All otherrights reserved by the copyright owner.

ABSTRACT

It is possible that MAV designs of the future willexploit flapping flight in order to perform missions thatrequire extreme agility, such as rapid flight beneath aforest canopy or within the confines of a building. Manyof nature’s most agile flyers generate flapping motionsthrough resonant excitation of an aeroelastically tailoredstructure: muscle tissue is used to excite a vibratorymode of their flexible wing structure that creates propul-sion and lift. A number of MAV concepts have beenproposed that would operate in a similar fashion. Thispaper describes an ongoing research activity in whichmechanization and control concepts with application toresonant flapping MAVs are being explored. Structuralapproaches, mechanical design, sensing and wingbeatcontrol concepts inspired by hummingbirds, bats andinsects are examined. Experimental results from atestbed capable of generating vibratory wingbeat patternsthat approximately match those exhibited by humming-birds in hover, cruise, and reverse flight are presented.

INTRODUCTION

With numerous civil and military applications,micro-aerial vehicles (MAVs) represent an emergingsector of the aerospace market, and may one day becomequite commonplace. The Defense Advanced ResearchProjects Agency (DARPA) has generally defined theMAV as a class of aircraft with a maximum dimensionof 6 inches that is capable of operating at flight speeds ofapproximately 25 mph or less, with a mission duration of20 to 30 minutes.1 A concerted effort supported byDARPA has resulted in advancements in miniaturizeddigital electronics, low Reynolds number aerodynamics,multidisciplinary design methods and other enablingsystems technologies for MAVs. Such advances haveturned the concept of a tiny autonomous flight vehiclefor use as a rapidly deployable eye-in-the-sky fromfiction into demonstrated fact.2 Continual reductions inthe size, weight and power consumption of video andother sensing devices are improving the feasibility of

MAVs for use as inexpensive and expendable platformsin surveillance and data collection missions where largervehicles are not practical.

A number of successful fixed-wing MAV designshave been generated by several university, commercial,and government-funded endeavors. Examples shown inFigure 1 include Aerovironment’s Black Widow, theTrochoid developed by Steve Morris of MLB, and aflexible-wing design by the University of Florida.3-5 Theunique wing structure of the UF design incorporates ahighly flexible battened membrane concept inspired bysail technology. The structure consists of a carbon-epoxycomposite frame that is covered with a thin layer oflatex, and is somewhat reminiscent of a bat wing.6

Waszak has investigated the aeroelastic deformation ofthis wing structure in a series of wind tunnel tests, and adynamic simulation model of the UF MAV design hasbeen created for use in flight control law development. 7,8

Numerous civil and military applications for MAVshave been proposed, and far more have yet to beimagined. However, the potential applications of currentfixed-wing designs are necessarily limited due tomaneuver constraints. The successful fixed-wing designsmentioned above rely on relatively conventional scaled-down aerodynamics and flight control approaches, andthey do not possess the flight agility and versatility thatwould enable missions such as rapid flight beneath aforest canopy or within the confines of a building. Inorder to perform missions requiring extreme agility,MAV designs of the future may exploit flapping flight.The ability to vary wingbeat kinematics to generate largecontrol moments and to rapidly transition between flightmodes is a hallmark of nature’s most agile fliers.

Although a number of flapping mechanisms havebeen developed and demonstrated in a limited fashion,the creation of a practical ornithoptic MAV remains anelusive goal. Mechanical design, efficient actuation,power systems and control pose significant challenges tothe feasibility of an ornithoptic MAV concept. As a

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Figure 1. Several successful fixed-wing MAVs, from left to right, Aerovironment’s Black Widow, MLB’sTrochoid, and the University of Florida’s flexible wing design.

means of efficiently generating high-frequency flappingmotions, many natural flyers generate lift throughresonant excitation of an aeroelastically tailoredstructure: muscle tissue is used to excite a structurewhich exhibits a particular vibratory mode shape thatgenerates propulsive lift.9-11 Several research endeavorshave considered MAV concepts that would operate in asimilar fashion.12-14 Related research activities span abroad range of disciplines including ornithology,entomology, structures, materials, sensing, unsteady fluiddynamics and control. An extensive review of biologicaland aeronautical literature relevant to flapping flight wasprovided by Shyy15, and a highly multidisciplinaryconference on low Reynolds number fixed and flapping-wing flight was held at Notre Dame in 2000.1

Shown in Figure 2 are a number of flappingMAV concepts including Aerovironment’s Microbat,Vanderbilt’s Elastodynamic Ornithoptic Robotic Insect,and UC Berkeley’s Micromechanical Flying Insect. TheMicrobat was designed by Aerovironment in partnershipwith UCLA and Caltech under funding from DARPA.16

To create Microbat, the team drew upon advancementsin microstructures, miniature electronics, unsteady fluiddynamic modeling and multidisciplinary designoptimization. The vehicle was capable of brief radio-controlled flights, and its limitations provided greatinsight in terms of necessary directions for follow-onresearch activities.

However, one of the keys to agility in flapping flightis the ability to vary the wingbeat kinematics. TheMicrobat lacked this degree of control, relying instead on

a conventional tail and rudder arrangement to provideflight control functions. One of the goals of the currentinvestigation was to explore a more biologically inspiredrealization of the flapping wing apparatus that couldafford some degree of control over the wingbeatkinematics.

Also pictured in Figure 2 is a concept for anElastodynamic Ornithoptic Robotic Insect that wasstudied by Frampton and Goldfarb at Vanderbilt.17 Theconcept involved the mechanical amplification of smalldisplacements produced by piezoceramic wafer actuatorsto excite vibrating wing structures. The investigatorsperformed a parametric study of the impact of variouscombinations of bending and torsional wing stiffness onthe thrust production of flapping wings.

Perhaps the most multidisciplinary effort to createan ornithoptic MAV is being undertaken by theMicromechanical Flying Insect design team at UCBerkeley. This team is responsible for an impressiveseries of biological and engineering studies aimed atunderstanding natural insect fliers in the size range of2.5cm, and designing an artificial system capable ofemulating that behavior.18,19 A key element of theirresearch addresses the manner in which insects adjust thephasing between flapping and rotational motions of theirvibrating wing structures for the purpose of flightcontrol.

This paper describes an ongoing research activity inwhich resonant flapping MAV concepts are beingexplored in a small project at NASA Langley ResearchCenter. The study targets a MAV size range of 15-20cm.

Figure 2. Several ornithoptic MAV concepts, from left to right, Aerovironment’s Microbat, Vanderbilt’sElastodynamic Ornithoptic Robotic Insect, and UC Berkeley’s Micromechanical Flapping Insect.

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The research does not seek to develop a flapping MAVdesign, nor prove the feasibility of such an ornithopticsystem.§ Rather, the goal is to develop insight regardingbiologically-inspired structural approaches, mechanicalarrangements, actuation concepts, sensing, and wingbeatcontrol approaches that could contribute to the body ofknowledge required to create an agile MAV in whichresonant excitation of an aeroelastically tailored wingstructure is used to generate propulsive lift.

First, several insights and specifications are drawnfrom biological inspirations for flapping MAVs. Astructural concept that was applied to create wingshaving size, weight and planform similar to that of aparticular humming bird example is then described.Next, a biologically inspired arrangement of mechanicalcomponents is developed to provide control overvibratory wingbeat patterns, and results from a vibratorytestbed apparatus are presented. A feedback controlcircuit is described that automatically tunes the actuationdrive signal to the resonant flapping frequency of theflexible wing structures. A simple means of varying theactuator signals to generate wingbeat patterns thatapproximately match those exhibited by hummingbirdsin hover, cruise, and reverse flight is also presented.

BIOLOGICAL INSPIRATION FOR ANORNITHOPTIC MAV

Although numerous examples of highly successfulflapping fliers exist in nature, perhaps the one that bestdemonstrates the characteristics we wish to possess in anagile MAV is the hummingbird. Hummingbird speciesbracket the size range of 6 inches and speed range of25 mph, used to define MAV-class vehicles. Winglengths range from about 33 mm (~2.5” total span) forone of the smallest species (Calliphlox amethystina), to135 mm (~10.5” total span), for the Giant Andean(Patagona gigas). Wind tunnel tests have revealed maxi-mum flight speeds as high as 27 mph for some species,compared to 8 to 10 mph for most fast-flying insects.21

The agility, precision, and flight mode variabilityexhibited by hummingbirds is astonishing, and thecreation of an artificial system that can perform similarlyis a lofty goal. Precise control of body axis rotation andtranslation during hover feeding is a necessity forhummingbirds. Transition from hover to cruise may beaccomplished in less than half a second, incurringaccelerations of roughly 5-gs. Despite their relativelyhigh power consumption during hovering flight,hummingbirds are able to cruise with considerableefficiency, and some species migrate across the Gulf ofMexico without feeding.

§ Such proof clearly exists in the form of natural fliers. Atissue, however, are the relative merits of rotary vs. flappingapproaches to MAV flight. Spedding examines this topic.20

In terms of size, weight, and Reynolds number,hummingbirds occupy a niche between insects and largerbirds, and their flight apparatus appears to represent ahybrid between the two approaches to flapping flight.Many insects employ a flight apparatus that relies uponresonant excitation of a relatively passive wing structureto produce a vibratory response that generates propulsivelift. Most birds, on the other hand, rely on highlyarticulated wing structures that move at the elbow andwrist as well as the shoulder joint. Their wingbeatkinematics are generally more complex, involving varia-tion of the wing planform geometry throughout theflapping cycle. Although birds tend to flap their wings atthe natural frequency of their biomechanical system,their highly articulated flapping motions cannot be fullydescribed merely as the vibratory response of a passivestructure. This additional degree of complexity wouldseem to endow birds with generally broader flightenvelopes and greater variability of function in terms offlight modes and behaviors.

Although the morphology of the hummingbird flightapparatus is distinctly avian, its mode of operation bearsa strong resemblance to insects. Unlike all other flyingbirds, a hummingbird's wing joints are fused at the elbowand wrist, so the wing planform does not change duringthe flapping cycle.21 Flapping motions are actuatedentirely from the shoulder joint, and wingbeat kinematicsof the upstroke and downstroke are markedly similar.The wing exhibits a vibratory motion much like that ofan insect wing: a non-articulated structure that isaeroelastically tailored to generate propulsive lift whenexcited at resonance. The relative simplicity of thehummingbird’s flight apparatus and wingbeat patterns,together with its remarkable precision and flight modevariability, make it an attractive source of inspiration formechanization and control concepts that may be appliedto an agile ornithoptic MAV.

In order to use the hummingbird as source of furtherinsight, it makes sense to develop specifications thatcharacterize those species in the size range of interest. Astudy by researchers at the University of Texas thatinvestigated the load carrying capacity of severalhummingbird species provides a useful starting point.22

Average characteristics for these species are presented inTable 1 from the study by Chai and Millard, which alsoprovides an assessment of wing and flight muscle mass.Note the wingbeat frequencies ranging from 23.3 Hz to51.7 Hz. Approximate wingbeat frequencies for allhummingbird species range from 10 Hz (P. gigas) to80 Hz (C. amethystina). 21 Parameters Pper and Pzero in thetable represent total mechanical power output of theflight muscle mass assuming perfect and zero elasticenergy storage, respectively.

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Lampornisclemenciae

Eugenesfulgens

Archilochusalexandri

Selasphorusrufus

total mass, g 8.4 7.4 3.0 3.3wing mass, g 0.29 0.26 0.08 0.08flt muscle mass, g 2.44 2.01 0.87 0.96wing AR 8.2 8.4 7.1 7.4freq, Hz 23.3 24.0 51.2 51.7length, mm 85 79 47 42flap arc, deg 151 150 126 163Ut, m/s 10.4 9.9 10.5 12.3Re 11400 9800 7400 7400CL 1.46 1.67 1.42 1.41Pper, Watt 0.175 0.152 0.076 0.089Pzero, Watt 0.343 0.325 0.187 0.250 f l5/4 6014 5653 6301 5528 m/l3/2 0.0107 0.0105 0.0093 0.0121

Table 1. Data for several hummingbird species.22

Two species that lie within the relevant size rangeare the Blue Throat (Lampornis clemenciae), and theRivoli (Eugenes fulgens). These species are highlightedon the plot of wing length vs. total weight shown inFigure 3 for all hummingbird species. Also noted on thisplot is Aerovironment's ornithoptic MAV design, theMicrobat. An empirical fit to the hummingbird datasuggests that weight scales with wing length according tothe relation shown in equation (1).21 Greenwalt alsosuggests that hummingbird wing length and flappingfrequency scale according to equation (2).

m ∝ l3/2 (1)

f ∝ l−5 / 4 (2)

Figure 3. Plot of wing length vs. total weight for allhummingbird species.21

Using values of mass, wing length, flappingfrequency and flapping arc from Table 1 to computeaverage scale factors from these relations, it appears thata hummingbird-like MAV with wing length of 75 mmshould flap its wings through a 150-degree flapping arcat approximately 25 Hz and weigh only 7.5 grams. The

weight target for this conceptual vehicle represents anextreme challenge to the various subsystem technologiesof structures, power systems, actuation and miniaturizedelectronics. The realization of an artificial MAV withtruly bird-like agility would seem to hinge upon thedevelopment of such ultra-lightweight components.However, it is not only the availability of suitable systemcomponents, but the particular arrangement and mannerin which they are employed that will lead to a MAV withthe desired capabilities. The following sections presentconcepts for mechanization and control of a vibratingwing apparatus that could provide lift, thrust, andmaneuver moments for such a MAV if and when thenecessary component technologies emerge.

STRUCTURAL CONCEPT FORFLEXIBLE WINGS

To produce artificial wing structures with thedesired flexible characteristics, a structural concept wasadapted from the UF MAV design shown in Figure 1.Although it employs a fixed-wing and propellerarrangement, this vehicle incorporates a bat-like flexiblemembrane wing structure that is thought to provideimproved stall margins and handling characteristics. Thewing is constructed from a carbon-epoxy compositeframe that is covered with a thin latex membrane.6 Forthe present investigation, this structural concept wasapplied to wing designs inspired by hummingbirds. Winglayouts were developed from photographs of humming-birds with their wings extended that were scaled to havea single-wing length of 75 mm. An example of theresulting composite wing structure is shown in Figure 4,along with the photograph from which it originated. Theweight of the composite wing structure is 0.59 grams,compared to 0.26 grams for a natural wing of similar sizefrom Table 1. Several features in the structure of thehummingbird wing appear important to capture in theartificial wing design.

First, the quills of the primary flight feathers radiatefrom the shoulder region of the wing, rather thanemanating from the leading-edge spar as in theUniversity of Florida MAV. Radial orientation ofstructural wing members is a key element observed innatural fliers, and it has been found to greatly influencethe flexible behavior of their wings. A description of thecrucial role that such orientation plays in the resultingtorsional dynamics of insect wings is provided byEnnos.23 In the hummingbirds’ case, the radialorientation of quills provides the flexible wing withpartially reversible camber, enabling it to generate lift onboth the downstroke and upstroke segments of theflapping cycle during hovering flight, in which the strokeplane is nearly horizontal. This reversible characteristicof the wing is highly developed in hummingbirds, asillustrated by the hovering specimen shown in Figure 5.21

P. gigas

L. clemenciae

MicrobatE. fulgens

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Among avian species, hummingbirds possess proportion-ately the largest flight musculature associated with therearward portion of the flapping stroke. The reversibilityof their flexible wing structure along with their unusualflight musculature is largely responsible for thehummingbird’s prowess as a hovering flier.

Another critical feature required to generate theflexible behavior observed in Figure 5 is a wing surfacethat is capable of supporting compound curvaturewithout puckering. The extensible compliant latexmaterial used in the flexible wings of the University ofFlorida MAV has been shown in wind-tunnel tests to becapable of supporting such deformations.7

Figure 4. Extended hummingbird wing and a typicalwing created by applying UF structural concept tohummingbird-inspired wing designs.

Figure 5. A hummingbird in hovering flight illustratesthe reversible camber exhibited by its flexible wingstructure (Eutoxeres aquila).21

GENERATION OF VIBRATORYFLAPPING MOTION

If the motivation for pursuit of a flapping flightmechanism is bird-like agility, then a crucial goal is toprovide some degree of control over the wingbeat kine-matics as a means of changing flight modes or generatingmaneuvers. In order to achieve variability in wingbeatbehavior, a vibratory flapping system was designed thatincludes a ball and socket joint at the shoulder. Thedesign of the system represents an attempt to applyinsights from the basic arrangement of skeletal andmuscular components that drive a typical bird wingshown in Figure 6, which is drawn from Freethy, 1982.24

The storage of elastic energy has been found to be animportant factor in the arrangement and operation of thissystem. We shall drastically simplify and then crudelymodel these components as an elastodynamic system,while attempting to retain the basic function of thearrangement. The simplified mechanical system shownin Figure 7 provides a basis for development of themodel. The following paragraphs describe the variouscomponents and the rationale for their arrangement.

In Figure 6, a ball-and-socket joint connects thecoracoid to the humerus, constituting the shoulder of thebird. At point h in Figure 7, this component isrepresented as a 3-degree of freedom ball-and-socketconnection between a fixed rigid test stand and a rigidbeam element having length L1 and mass m, representingthe humerus. The use of a rigid beam element in thiscapacity means that the flexible dynamics of the wingstructure itself are neglected for the time being.

Two reference frames are defined consisting ofbody-fixed axes {b} and wing-fixed axes {a}, bothhaving their origin at the shoulder joint, h. Control overthe relative amplitude and phasing of angular rates ofrotation between these two coordinate systems willenable the arrangement to generate changes in thevibratory wingbeat pattern. (The shoulder joint of insectsis also designed to permit such control, but the insect’sshoulder anatomy resembles a series of hinges that hasbeen compared to the articulated rotor hub of ahelicopter.25 It differs markedly from the ball-and-socketshoulder joint found in birds.)

Located distance L2 from the shoulder joint h is theapplication point, f, for a pair of tendons that connect thebeam element to points c and d, which represent theattachments of the depressor muscle, pectoralis, to thesternum and scapula in Figure 6, respectively. Thetendons are able to contract, thereby generating forces F1

and F2 that act upon the beam at point f. In Figure 6, thepectoralis muscle serves to draw the wing down througha stroke plane having an inclination to the bird’s bodyaxis that may be varied by changing the relativemagnitudes of muscular contraction that generate the

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Figure 6. Basic arrangement of skeletal and muscularcomponents comprising the avian flapping system.24

Figure 7. Simplified arrangement of mechanicalcomponents used to approximate the natural systemshown in Figure 6.

sternum-humerus and scapula-humerus resultant forces.As a simplification in the model, these tendons attach tothe beam at equal and opposite angles to the a2 -a3 planewith magnitude λ.

Located a distance L3 from the shoulder joint is theattachment point, g, for a vertical spring that representsthe elevator muscle, supracoracoideus, which raises thewing. The justification for representing this muscle witha single spring element is that the supracoracoideuspasses through a small notch that permits it to travelaround and over the top of the coracoid before reversingdirection and attaching to the sternum, as shown inFigure 6. This notch constrains the line of action of theelevator muscle to pass through a point at the top of thecoracoid, much as the force generated by the springshown in Figure 7 acts through point i. The use of thespring element collectively represents the elastic storagepotential that has been attributed to the sternum andscapula arrangement.

SIMULATION MODELA simulation model of the mechanical arrangement

shown in Figure 7 was programmed in MatlabTM toevaluate the potential for the system to generate wingtip

trajectories similar to those exhibited by hummingbirds.Using notation from Smith (1996),26 two referenceframes are defined consisting of body-fixed axes {b} andwing-fixed axes {a}, both having their origin at theshoulder joint, h. The body axis system {b} represents aninertial frame of reference fixed to the stationary teststand. In order to predict wingtip trajectories thesimulation must generate time histories for the vector re

b,relating the position of tip of the rod, e, in the body-fixedcoordinate system {b}. This vector is given by:

reb=[Tab]

T rea

Where rea is the position of e in the wing-fixed

coordinate system {a}, given by rea =[0 L1 0]T. The

Euler angle rotation sequence ( ) relates thecoordinate systems {a} and {b} via the direction cosinematrix Tab such that {a}=Tab {b} where:

Tab

=cos cos cos sin − sin

sin sin cos −cos sin sin sin sin +cos cos sin cos

cos sin cos +sin sin cos sin sin −sin cos cos cos

The Euler rotations ( ) are respectively referredto as folding, feathering and flapping in describing thewingbeat kinematics of natural fliers. The kinematicdifferential equations relating the Euler angle rates andthe angular rotation rates (p q r) of {a} relative to {b} are:

˙ = p + (qsin + r cos ) t a n˙ = q cos − r sin˙ = (qsin + r cos ) / c o s

Several assumptions serve to simplify thesimulation. First, representation of the humerus with arigid homogenous beam element having shoulder joint,actuator and spring attachment points all lying along thecenterline means that the feathering degree of freedom isneither driven by actuator inputs nor excited by inertialcoupling. Furthermore, let the mechanical attachment atpoint f be defined such that feathering motion of thebeam is prohibited. Thus theta dot is identically zero,implying q= r tan .

Having eliminated the ˙ q equation by a kinematicconstraint, the remaining portion of the moment equationmay be written as:

J˙ p

˙ r

= M A + M R + MD

where J is the inertia matrix having diagonal elementsequal to (mL1

2)/4 and MA, MR, and MD respectivelyrepresent moments due to actuating forces, restoringforces, and damping acting on the beam. Momentsarising from actuator force inputs are given by:

MA =−L2 cos cos −L2 cos cos

−L2 sin cos L2 sin cos

F1

F2

m

K

F1F2

c

d

h

e λ λ

fg

i b1

b2

b3

a1

a2

a3

Scapula

Depressor muscle Pectoralis

Elevator muscleSupracoracoideus

Coracoid

Humerus

Sternum

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where F1 and F2 are time varying force inputs generatedby linear actuators located at points c and d in Figure 7.Moments arising from restoring forces provided by thespring are given by:

MR =sin cos

sin

−KL3

2{ }Moments arising from aerodynamic damping and frictionof the shoulder joint are expressed as:

MD =C1 0

0 C2

p

r

where C1 and C2 are estimated constants. As a furthersimplification, attachment points f and g for the springand actuator tendons representing the elevator anddepressor muscles were co-located, so L2 = L3. Valueswere chosen for L1 and m based on the actual compositewing length and weight. A tendon attachment location,L2, and spring constant, K, necessary to produce a naturalfrequency of 25 Hz were then selected where:

n =L2

0.5L1

K

m

The simulation was implemented in Matlab’sSimulinkTM with a step size of 1ms using the ODE4(Runge-Kutta) integration solver with the followingparameter values: C1 & C2 = 10e-5 N/cm/s, L1 = 7.5cm,L2 & L3 = 0.5cm, K= 8.19N/cm, m= 0.59gm, = 40deg.

Figure 8. Example waveforms used to control vibratorywingtip trajectory produced by the dynamic simulation.

By providing periodic inputs F1 and F2 at the resonantflapping frequency of 25 Hz, the element representingthe wing humerus can be made to undergo a large-amplitude vibratory flapping motion. Factors that affectthe relative amplitude, phasing, and waveform of F1 andF2 can be used to control various aspects of the wingtiptrajectory. Examples of actuator input waveforms andresulting wingtip trajectories are shown in Figure 8.

VIBRATORY TESTBED APPARATUS

Based on the promising simulation results, avibratory flapping apparatus was constructed using thebiologically inspired component arrangement fromFigure 7. The goal was to create a benchtop testbedcapable of generating vibratory wingbeat patterns similarto those observed in hummingbirds. Dispensing withcomponent weight limitations levied by the need for aflight-capable design led to the testbed shown in Figure9. A crucial component of the apparatus is the 3-dofpinned ball-and socket used for the shoulder joint. Thisjoint permits a limited range of feathering and foldingrotations, and unconstrained flapping rotation. Thepinned ball-and-socket was resorted to after attemptswith a true ball-and-socket repeatedly resulted in the balldeparting from the socket when the system was excitedat resonance. Nylon line connects the main spar of thewing, representing the humerus, to two linear actuatorsthat provide input forces F1 and F2, representing thepectoralis. Two Labworks ET-126A electrodynamiclinear shaker actuators driven by Labworks PA-138-1power amplifiers were used in this capacity. Thesupracoracoideus was represented by a spring that wasattached to a point 10.5 cm above the shoulder joint. Theflexible wing structure, itself, consisted of the carbonprepreg and latex composite described previously.

Figure 9. Shaker-actuated testbed designed to providecontrol of vibratory wingbeat patterns.

0 0.05 0.1 0.15 0.2-1.5

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Figure 10. Strobed photographic images illustratingvibratory flapping motion and wingtip trajectories tracedout by LEDs at resonant wingbeat frequency (~25Hz).

Several experimental techniques have proven usefulin assessing the performance of this apparatus. The firstis the use of a tunable strobe light, which permits thecreation of an aliased slow-motion video image of thehigh frequency periodic motion. The use of the strobegreatly improves the ability to qualitatively assess thebehavior of the flexible wing structure. Another effectivetechnique is the placement of small LED devices at thetips of the wings to trace out the entire wingtip trajectoryin a single photographic image. By combining thesemethods, it is possible to generate images that illustratethe large-amplitude vibratory flapping motion of thewings at resonance, as shown in Figure 10.

As in the dynamic simulation model, control inputsto the apparatus consist of scale factors on the relativeamplitude, phasing and waveform of commands to thetwo electrodynamic actuators. These provide a degree ofcontrol over the wingtip trajectory, enabling the systemto approximate wingbeat patterns exhibited byhummingbirds in various flight modes. A comparison ofwingtip trajectories produced by the testbed withhummingbird wingtip trajectories documented byGreenwalt is shown in Figure 11. The factors that areapproximately matched in these figures include thestroke plane inclination to the body axis of the bird (ortestbed), amplitude of the flapping arc, approximategeometry of the wingtip trajectory, and sense of rotationabout that trajectory. Note that in forward flight, thewing travels clockwise about the trajectories shown inFigure 11, while in reverse flight the wing travels in acounter-clockwise sense. Transition between wingbeatpatterns has been accomplished in as little as fourflapping cycles (0.16 seconds). These results suggest thatthe biologically inspired mechanical arrangement inFigure 7 provides sufficient control over the vibratorywingbeat pattern to enable the flight mode variabilitythat would be required by an agile ornithoptic MAV.

Figure 11. Comparison of wingtip trajectories producedby the vibratory flapping testbed with those exhibited byhummingbirds in various flight modes.21

The apparatus provides control over the wingtiptrajectory as defined by a particular combination offolding and flapping motions. However, the featheringcomponent of the vibratory wing motion produced by thetestbed is uncontrolled. Many insects use the phasingbetween feathering and flapping motions as a steeringmechanism, implying some degree of control overfeathering rotations via moments generated at theshoulder joint.18 But entomologists have also found thatinsects rely heavily upon inertial and aerodynamicloading to affect rotation of the wing.27 The degree towhich hummingbirds exercise direct actuation andcontrol of wing feathering rotations for steering purposesis uncertain. Although the feathering rotation is notdirectly actuated or controlled in the current mechanicalarrangement, some degree of control may be achieved byintroducing offsets between various tendon attachmentpoints at the humerus in Figure 7. This is a topic forfurther research.

It is important to distinguish between wing torsionand feathering motions. The former refers to structuraldeformation of the wing about the torsional axis, whilethe later is the rigid-body component of wing rotationabout the a2 axis. A similar distinction exists for bendingand flapping components of wing motion. It is clear fromFigure 10 that the experimental wing undergoesconsiderable bending and torsion at resonance. Thisbehavior is strongly influenced by the stiffnessdistribution of the wing lay-up (dictated by ply number,membrane thickness, and dimensions of compositemembers.) Ideally, a prescribed mode shape, consistingof a particular combination of wing bending and torsionthat has been tuned to generate propulsion and lift, wouldbe designed into the wing structure at the desiredresonant frequency by appropriately tailoring thecomposite lay-up. Aeroelastic tailoring of the wingstructure is another topic for further research.

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CONCEPT FOR RESONANT TUNING

A means of sensing the flexible behavior of thevibrating wing structure was found in the form of thinfilm piezoelectric strain rate sensors made ofpolyvinylidene fluoride (pvdf). These commerciallyavailable sensors, manufactured by MeasurementSystems, Inc. (MSI), employ the piezo effect to producea voltage output in response to strain rate. The thinnestdevices available consist of a 28µm x 15mm x 40mmlayer of “metalized” pvdf material. These sensors areeasily bonded to the composite wing structure using athin coat of spray adhesive, as shown in Figure 12. Inthis arrangement the sensor responds to a broad range ofdeformations, including the overall bending and twistingmotions of the wing as well as individual batten andmembrane vibrations. The voltage output of the sensorwas found to be easy to use and quite repeatable. Sensorswere applied to both wings of the testbed apparatus.

An RMS sensor output signal may be computed toprovide a gross indication of the amplitude of vibrationthe flexible wing experiences at a given excitationfrequency. It is then possible to experimentally ascertainthe fundamental resonant flapping frequency of the wingstructure by conducting an input frequency sweep andplotting RMS sensor output against input frequency.Such a plot is shown in Figure 13 for a flexible wingstructure that resonates at approximately 24 Hz.

Figure 12. Thin film pvdf strain-rate sensor devicebonded to flexible wing structure.

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Figure 13. Plot of the RMS strain-rate sensor output vs.input frequency showing resonant peak at 24 Hz.

The frequency response plot suggests the potentialfor a feedback control circuit that would automaticallytune the actuator input frequency to the resonantfrequency. The inspiration for such a tuning circuit

derives from a recent text on the biomechanics of insectflight by Dudley.9 This reference notes that certaindome-shaped sensory organs (campaniform sensillae)identified within the structure of locust wings have beenfound to respond specifically to wing deformation. Theseorgans tend to be concentrated near the base of thewings, where bending is greatest. Feedback signals fromthese “stretch receptors” are used to drive the primaryflight musculature within in the locust’s body. Suchfeedback directly stimulates and phase-locks thoracicmotor neurons at the wing oscillation frequency. In fact,the vibratory motion of the wing itself is both necessaryand sufficient to generate the neural stimulus to themuscle tissue that sustains the oscillation. Hence, thebiomechanical vibratory system simply containsneuromuscular feedbacks from the flexible wingstructure that cause it to operate at resonance whenactivated.

It is possible to devise a feedback circuit thatemploys the thin film strain rate sensor in a capacitysimilar to that of the locust’s campaniform sensillae. Thesimplicity of deriving such a circuit becomes obviousupon consideration of the forced response of a 2nd ordersystem with positive rate feedback:

˙ ̇ + 2 n˙ + n

2= F (4)

let F = G ˙

˙ ̇ + (2 n − G ) ˙ + n

2= 0 (5)

Let represent the generalized modal coordinatefor the first bending mode shape of the wing, and the ratesignal, ˙ , represent output of the strain rate sensor (anidealization which assumes that the sensor responds onlyto the first bending mode of the structure). Let Frepresent a generalized force input to the wing structurethat is generated by a command to the electrodynamicactuators under the condition F1 = F2. Setting the forcingfunction equal to feedback gain, G, times the strain ratesensor output, ˙ , yields equation (5). The linear systemis dynamically unstable for sufficiently high feedbackgain, G > 2 n , resulting in a divergent oscillation ofthe vibrating structure. However, insertion of a saturationnonlinearity on the strain-rate feedback signal prior tomultiplying by gain G, causes the system to exhibit alimit-cycle oscillation at the resonant frequency of the 2nd

order system, rather than a divergence. The saturationrepresents a limit on the power used to drive actuators,preventing the force input from increasing withoutbounds. The amplitude of the limit cycle may becontrolled by varying G, which is equivalent to scalingthe power used to drive the actuators. Increasing Gresults in greater flapping amplitude, generating greaterpropulsive lift while maintaining the same flappingfrequency – a convenient throttle control for the resonantflapping system.

AIAA 2003-5345


This resonant tuning circuit was implemented for thevibratory test stand using dSpaceTM hardware-in-the-loopsimulation equipment. A predictable obstacle wasencountered as a result of a basic assumption employedin the preceding development: the output of the strainrate sensor does not only represent the derivative of thefirst bending mode generalized coordinate (whichconstitutes the fundamental flapping motion we wish toexcite). Instead, the signal also includes higher frequencycontributions from batten and membrane vibratorymodes. As a result, the closed-loop system performsunpredictably, often tuning to a much higher frequencythan desired. Examination of the signal from the strainrate sensor revealed that, although there did indeedappear to be considerable high frequency content, thepredominant signal content reflected the fundamentalbending mode. The result was that zero crossings of thesignal occurred at the frequency of the fundamentalmode. Such an outcome is greatly influenced by theorientation of the sensor relative to wing the structure. Ifthe sensor is positioned to respond predominantly to thefundamental bending mode, then it is likely that zerocrossings may provide an indication of the fundamentalmode frequency for the tuning circuit.

To examine this possibility, the feedback portion ofthe block diagram was changed to a simple scalar factoron the sign of the strain rate signal, resulting in a squarewave at a frequency that depends solely on the zerocrossing of the strain rate sensor output. This approachhad the benefit of simplicity, and did not risk theintroduction of excessive phase loss that could resultfrom applying a band-pass filter to the sensor signal. Themodified algorithm was implemented and functioned asdesired. Although the sharp corners of the square wavecreate an input with high frequency content, the output ofthe strain rate sensor is dominated by the fundamentalbending mode, and so the zero crossings occur at thedesired frequency. No repositioning of the sensor wasnecessary to achieve this result, although sensororientation is presumably an important factor to theproper operation of the circuit, and may be a subject forfurther experimentation. Time histories of the output ofthe strain-rate sensor plotted with the input signal to theactuator when the tuning circuit is engaged are shown inFigure 14 for a system that resonates at 24 Hz. Using abell-jar apparatus, several experiments have beenperformed to verify that the closed-loop system tracksthe variation in resonant frequency in response toambient pressure changes.

The control algorithm was implemented using adSpaceTM model DS1005 480 MHz Power PC 750processor with a model DS2003 16-bit A-to-D converterboard and a model DS2103 14-bit D-to-A converterboard. The real time process was implemented with aframe rate of 1KHz.

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Figure 14. Time histories of strain-rate sensor output andsquare wave input with tuning circuit engaged.

CONCLUDING REMARKS

Today’s fixed-wing MAVs have already demon-strated the potential to function as rapidly deployableautonomous aerial reconnaissance platforms. Suchvehicles were confined to the realm of conceptual designonly a decade ago, and to the realm of imagination adecade prior to that. Perhaps fifteen years hence, thecurrently infeasible hummingbird-like MAV concept willenjoy a similar liberation. An extremely agile ornithopticMAV design would challenge the current state-of-the-artin control for vehicles with highly transient flightcharacteristics. Developing methods required to modeland control a highly agile flapping MAV will promotethe understanding of unsteady and nonlinear dynamicphenomena in general, and could generate technologieshaving broader application to full-scale aircraft.

This work has contributed to an emerging body ofmultidisciplinary knowledge in the area of biologicallyinspired micro-scale flight. The research activity seeks togain and apply an understanding of the function of highlyagile natural fliers in the size range of the micro aerialvehicle class. A key factor in this endeavor has been todesign and control a vibratory wingbeat apparatus usinginsights provided by bird, insect, and bat morphologies.Results were presented from a benchtop testbed used toexplore a vibratory system that embodied such insights.

A structural concept from an existing MAV designwas adapted to create wings having size, weight andplanform based on an appropriately scaled hummingbirdexample. The structure consisted of a carbon-epoxycomposite frame covered by a thin layer of latex similarto the battened membrane structure of a bat wing. Thewings exhibited a vibratory resonance at the flappingfrequency of an equivalently sized hummingbird.

A mechanization concept was developed for abiologically inspired vibratory flapping testbed thatprovided control over wingtip trajectories generated bythe system. A means of varying the testbed actuationsignals to generate wingbeat patterns that approximatelymatched those exhibited by hummingbirds in hover,cruise, and reverse flight was implemented.

AIAA 2003-5345


A feedback control circuit inspired by locustmorphology was also developed and implemented thatautomatically tunes the actuator drive signal to theresonant flapping frequency of the flexible wingstructure. The circuit relies upon a strain-rate feedbacksignal from a thin film sensor applied to the wing.

ACKNOWLEDGEMENT

Biological insights provided by Dr. Robert Dudleyof the Department of Integrative Biology at UC Berkeleyare gratefully acknowledged.

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IEEE International Conference on Micro ElectroMechanical Systems, Miyazaki, Japan, 23-27 Jan 2000.

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18. Dickinson M. H., Lehmann F., Sane S. P.: WingRotation and the Aerodynamic Basis of Insect Flight.Science, June 1999, v.284, pp.1954-1960.

19. Schenato L., Deng X., Sastry S.S.: Flight ControlSystem for a Micromechanical Flying Insect:Architecture and Implementation. IEEE InternationalConference on Robotics and Automation, 2001.

20. Spedding G.R., Lissaman P.B.S., 1998: TechnicalAspects of Microscale Flight Systems, Journal of AvianBiology, v.29, pp 458-468.

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22. Chai P., Millard D., 1997: Flight and Size Constraints:Hovering Performance of Large Hummingbirds UnderMaximal Loading. Journal of Experimental Biology,1997, v.200, pp.921-929.

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24. Cummins J.: Avian Anatomy webpage, April 1 1996,resketched from Freethy R., 1982: How Birds Work, AGuide to Bird Biology. 1st ed. Poole: BlanfordPress.(http://numbat.murdoch.edu.au/Anatomy/avian/shoulderl.GIF)

25. Lasek M., Pietrucha J., Zlocka M., Sibilski K.:Analogies Between Rotary and Flapping Wings fromControl Theory Point of View. AIAA 2001-4002,AIAA Atmospheric Flight Mechanics Conference,6-9 August 2001, Montreal, Canada.

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27. Ennos A.R., 1988: The Inertial Cause of Wing Rotationin Diptera. J. Experimental Biology, v.140, pp.161-169.

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