Krzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiKrzysztof SibilskiWroclaw University Wroclaw University of Technology, Department of of Technology, Department of Aerospace Aerospace EngineeringEngineering

Air Force Institute of Technology Air Force Institute of Technology

MODELING AND SIMULATION OF MODELING AND SIMULATION OF

FLAPPING WINGS MICROFLAPPING WINGS MICRO--AERIALAERIAL--

VEHICLES FLIGHT DYNAMICS VEHICLES FLIGHT DYNAMICS

Micro Air VehicleMicro Air Vehicle -- MAVMAV

Technical Objectives:Technical Objectives: Develop flight enabling Develop flight enabling

technologiestechnologies..

Develop and demonstrateDevelop and demonstrateMicro Air Vehicles capable of Micro Air Vehicles capable of sustained flight and useful sustained flight and useful military missionsmilitary missions..

Military Relevance:Military Relevance:

Enhanced Situational Awareness for Enhanced Situational Awareness for

Small Units OperationsSmall Units Operations

Platoon level assetPlatoon level asset

Enables new missions in emergingEnables new missions in emerging

warfightingwarfighting environmentsenvironments

Urban operationsUrban operations

Potential users: Army, Marines, Air Potential users: Army, Marines, Air

Force, Navy, Special Operations Force, Navy, Special Operations

ForcesForces

Micro Air VehicleMicro Air Vehicle -- MAVMAV

Small air vehicle no larger Small air vehicle no larger than 15 cm in any than 15 cm in any dimension.dimension.

Capable of performing a Capable of performing a useful military mission at useful military mission at an affordable cost.an affordable cost.

Non Non Military Relevance:Military Relevance:

•• Outdoor NBC emergencyOutdoor NBC emergency reconnaissancereconnaissance

•• Crowd controlCrowd control

•• Suspect facilities surveillance Suspect facilities surveillance

•• Snap inspection of pollutionSnap inspection of pollution

•• Road accident documentationRoad accident documentation

•• Urban traffic managementUrban traffic management

•• Search for survivorsSearch for survivors

•• Pipeline inspectionPipeline inspection

•• High risk indoor inspectionHigh risk indoor inspection

•• Space explorationSpace exploration

MAV MissionsMAV Missions –– military applicationmilitary application

MAV HOST

MAV’s can deliverunattended

surface sensors

Interior Operationand Surveillance?

Interior Operationand Surveillance?Interior Operation?Interior OperationInterior Operation?

Sensor PlacementSensor PlacementSensor Placement

ReconnaissanceReconnaissanceReconnaissance Chemical CloudChemical CloudTracked by MAVTracked by MAV

Sensor detectsSensor detectsPPM PPM -- PPBPPB

MAV provides situational awareness,Provides beacon for rescue operations.

MAV provides situational awareness,MAV provides situational awareness,Provides beacon for rescue operations.Provides beacon for rescue operations.

Urban OperationsUrban Operations

MAV Assisted Pilot RescueMAV Assisted Pilot Rescue

BioBio--Chemical SensingChemical Sensing

““OverOver--thethe--hillhill”” ReconnaissanceReconnaissance

33

11

11

22

33

44

22

44

Miltary application – antiterrorist missionMiltary applicationMiltary application –– antiterrorist missionantiterrorist mission The Micro Air Vehicle Flight Regime The Micro Air Vehicle Flight Regime

Compared to Existing Flight VehiclesCompared to Existing Flight Vehicles

Speed

Hover

Agility

Covertness

High Degree of Integration and MultifunctionalityHigh Degree of Integration andHigh Degree of Integration and MultifunctionalityMultifunctionality

Range

Technical ChallengesTechnical Challenges

Low Re Aerodynamics and ControlLow Re Aerodynamics and Control

Lightweight Power and PropulsionLightweight Power and Propulsion

Autonomy navigation, Autonomy navigation,

guidance and controlguidance and control

UltraUltra--light sensorslight sensors

and communicationsand communications

IntegrIntegrationation of MAV systems of MAV systems

What isWhat is BiomimeticsBiomimetics??BiomimeticsBiomimetics is the abstraction a good design from Nature. is the abstraction a good design from Nature.

Scientists and engineers are increasingly turning to nature for Scientists and engineers are increasingly turning to nature for inspiration. The solutions arrived at by natural selection are oinspiration. The solutions arrived at by natural selection are often a ften a good starting point in the search for answers to scientific and good starting point in the search for answers to scientific and technical technical problems. Equally, designing and buildingproblems. Equally, designing and building bioinspiredbioinspired devices or devices or systems can tell us more about the original animal or plant modesystems can tell us more about the original animal or plant model.l.This lecture is focused onThis lecture is focused on BioinspirationBioinspiration && BiomimeticsBiomimetics in design of a in design of a new generation of flying vehicles sonew generation of flying vehicles so caaledcaaled Micro Aerial Vehicles Micro Aerial Vehicles ((MAVsMAVs).). MAVsMAVs are not a toys.are not a toys. MAVsMAVs are new generation of autonomous are new generation of autonomous flying robots.flying robots.Our research involved:Our research involved:

-- the study and distillation of principles and functions foundthe study and distillation of principles and functions foundin biological systems flight principles that have beenin biological systems flight principles that have beendeveloped through evolution,developed through evolution,-- application of this knowledge to produce novel and excitingapplication of this knowledge to produce novel and excitingbasic technologies and new approaches to solving scientificbasic technologies and new approaches to solving scientificproblems ofproblems of fligtfligt..

Insects Insects -- over 30 000 000 specimensover 30 000 000 specimens

Aerodynamically, the bumblebee can not fly.The bumblebee’s body is too heavy and its wings

span too small !!!

But it does not know that. That is why it flies.

Aerodynamically, the bumblebee can not fly.The bumblebee’s body is too heavy and its wings

span too small !!!

But it does not know that. That is why it flies.

Wais – Fogh mechanismWais Wais –– FoghFogh mechanismmechanism

Wais – Fogh mechanismWais Wais –– FoghFogh mechanismmechanism Wings rotation (rotational lift)Wings rotation (rotational lift)Wings rotation (rotational lift)

LEX vortexLEX LEX vortexvortex LEX LEX vortexvortex

Insects in flightInsects in flightEntomopter & insect wingsEntomopter & insect wings

Wing MotionWing Motion

Not simply up and down -much more complex!

Wingtip trajectoriesWingtip trajectories

Wing MotionWing Motion

Can consider as motion as Can consider as motion as being composed of three being composed of three different rotations flapping, different rotations flapping, lagging, and featheringlagging, and feathering

Three Hinges of the Wing Three Hinges of the Wing Apparatus.Apparatus.

Horizontal (flapping)Horizontal (flapping)Vertical (lagging)Vertical (lagging)TorsionalTorsional (feathering)(feathering)

EachEach insect insect hinge occurs at the intersection of a vein and foldhinge occurs at the intersection of a vein and fold

Helicopter articulated hub

Hinges of an entomopter wing

HingesHinges

The horizontal hinge The horizontal hinge -- 1 1 - occurs near the base of the wing occurs near the base of the wing next to the first next to the first axiliary scleriteaxiliary sclerite-- this hinge allow the wingthis hinge allow the wingto flap up and downto flap up and down

The vertical hinge The vertical hinge -- 2 2 -- located at the base of the located at the base of the radial vein near the second radial vein near the second axillary scleriteaxillary sclerite (2AX)(2AX)-- responsible for theresponsible for thelagging motion of the winglagging motion of the wing

The The torsionaltorsional hinge hinge -- 33-- more complicatedmore complicatedinteraction of interaction of scleritescleriteand deformable foldsand deformable folds

Insect wings

kinematics

Insect wings kinematicsInsect wings kinematicsInsect wings kinematicsEntomopter’s gears

Dr. Zbikowski Cranfield University

EntomopterEntomopter’’ss gearsgears

Dr.Dr. Zbikowski CranfieldZbikowski Cranfield UniversityUniversity

Entomopter gears Insect and bird enginesInsect and bird engines a) a) Insect Insect „„engineenginess””

b) anatomyb) anatomy

c) birds c) birds „„engineengine””

DD) ) entomopterentomopter engineengine

cc bb

aa

ddd

Unconventional propulsion –artificial muscels

From NASA websiteFrom NASA websiteFrom NASA website

RotorcraftRotorcraft primaryprimary

aerodynamic controlsaerodynamic controls

Fixed wing aircraft primaryFixed wing aircraft primary

aerodynamic controlsaerodynamic controls

Fixed & rotary wings aircraft aerodynamic controlsFixed & rotary wings aircraft aerodynamic controls

Entomopter vs. HelicopterEntomopter Entomopter vsvs. . HelicopterHelicopter

Analogies:-Control by change of thrust position and thrust magnitude

AnalogiesAnalogies::--Control Control byby change of thrust positionchange of thrust position and thrust magnitudeand thrust magnitude

Differences:

- aerodynamic loads are complex function of wings configuration and entomopter velocity

Differences:Differences:

-- aerodynamic loads are complex function of wings aerodynamic loads are complex function of wings configuration andconfiguration and entomopterentomopter velocityvelocity

Open loop wing motions that can generate: Open loop wing motions that can generate: (A)(A) pitch, (B) yaw, (C) roll torques. pitch, (B) yaw, (C) roll torques.

The arrows represent theThe arrows represent the instantaneous aerodynamic forcesinstantaneous aerodynamic forces acting on the wings.acting on the wings.The circles with a cross or with a dot correspond, respectivelyThe circles with a cross or with a dot correspond, respectively to the perpendicular to the perpendicular component of the force entering or exiting the stroke plane. Advcomponent of the force entering or exiting the stroke plane. Adv. and Del. stand for . and Del. stand for advancedadvanced and delayed rotation,and delayed rotation, respectively.respectively.

Flight stabilization mechanismFlight stabilization mechanism

Flight stabilization mechanismFlight stabilization mechanism

Global pitching moment generatedby different wing pitch reversals on both stroke endsGlobal pitching moment generatedby different wing pitch reversals on both stroke ends

Flight stabilization mechanismFlight stabilization mechanism

Control in rollCControlontrol in rollin roll

Flight stabilization mechanismFlight stabilization mechanism

Control in yawCControlontrol in yawin yaw

Coordinates systemCoordinates system

Coordinates systemCoordinates system Coordinates systemCoordinates system

Location of points, radius vectors,vectors of velocities and vectors of accelerationsLocation of points, radius vectorsLocation of points, radius vectors,,vectorsvectors of velocities and of velocities and vectorsvectors of of accelerationsaccelerations

MMMAAATTTHHHEEEMMMAAATTTIIICCCAAALLL MMMOOODDDEEELLL OOOFFF FFFLLLAAAPPPPPPIIINNNGGG WWWIIINNNGGGSSS

MMMAAAVVV MMMOOOTTTIIIOOONNN

The formalism of analytical mechanics allows to present dynamic

equations of motion of mechanical systems in generalised co-ordinates,

giving incredibly interesting and comfortable tool for construction of

equation of motion of aircraft. An example can be Gibbs-Appel equations.

Those equations have the following form:

Qq

=

∂

∂S

dt

d

(1)

where: q - is the vector of generalised co-ordinates

( )tS ,,, qqq

- is so called Appel function,

or functional of accelerations

Functional S for i-th element of the mechanical system is given by the eguation:

ii

V

idmS

i

vv ∫∫∫= 2

1

(2)

where:

iv means the vector of absolute acceleration

of elementary mass dmi of i-th body

of the considered dynamical system.

and:

( )iiiiiiiρωωρεvv ××+×+= 0000

(3)

Assuming that:

iiii333 rrrr +′+′′= (4)

and:

=

iO

i

Tiiii

m

mm

Jr

rIM

~

~

(5)

+

+=

000

200

~~~

~~

ωJωvωr

rωωh

iO

iii

iiii

m

mm

(6)

where: mi - mass of the i-th element, JO

i tensor of inertia of the i-th element,

ωωωω0000 - vector of the angular velocity, v0

i - vector of the velocity of the i-th element,

[ ]Taaa ςηξ ,,=awhere if where if where if thanthanthan

0

0

0

a a

a a

a a

ς η

ς ξ

η ξ

−

= − −

a

The term (2) can be expressed in the following matrix form: The term (2) can be expressed in the following matrix form:

( ) ( )

+

+=

−− iiiiT

iiiiS hMvMhMv11

2

1

Defining matrixes for all k bodies of the system:

= kdiag MMMM ...,,..., 21

(8)

( ) ( ) ( )

TTkTT

= vvvv ...,,...,

21

(9)

( ) ( ) ( )

TTkTT

= hhhh ...,,..., 21

(10)

(7)(7)(7)

Functional S for the whole mechanical system is given by the equation:

( ) ( )hMvMhMv

11

2

1 −− ++= T

S (11)

Assuming that q is vector generalised coordinates of mechanical system, the

relations between q and v are given by equation:

( ) ( )tt ,, qfqqDv += (12)

hence:

( ) ( )tt ,,, qqφqqDv += (13)

where:

fqD +=ϕϕϕϕ

Therefore the Appel function can be expressed by following relation:

( ) ( ) ( )hqDMhqDqqq11111111 ΜΜΜΜϕϕϕϕΜΜΜΜϕϕϕϕ −− ++++=

TtS

2

1,,,

(14)

Assuming, that:

MDDM Tg = and ( )hMDh += ϕϕϕϕ

Tg

and remembering, that:

( ) 11 −−= MDMDDD TT

the equation (14) can be expressed in the form:

( ) ( ) ( )gg

T

ggtS hqMhqqqq11111111 ΜΜΜΜΜΜΜΜ

−− ++=

2

1,,,

(15)

Vector of generalised co-ordinates has following form

[ , , , , , , , , , , , ]T

s s s R L R L R Lx y z β β ζ ζ θ θ= Φ Θ Ψq (16)

vector of quasi-velocities can be expressed by the following equation

[ , , , , , , , , , , , ]T

R L R R R Lu v w p q r β β ζ ζ θ θ=w (17)

For the holonomic dynamical system the relation between generalized velocities

[ ]1 2, ,........T

nq q q=q and quasi velocities [ ]1 2 3, ,........T

w w w=w

is following:

( )T=q A q w (18)

The matrix AT has a construction:

G

T T

=

A 0 0

A 0 C 0

0 0 I (19)

From (18) we have the following relation:

( ) wAwqAq TT += (20)

Finally, the Appel function has following form:

( ) ( ) ( )www

T

wwtS hMwMhMwwwq11*

2

1,,,

−−++=

where ( ) TqTTw AMAqM = , and: ( ) ( )qTq

TTw hAMAwqh += ,

Gibbs-Appel equations of motion, written in quasivelocities has the following

form:

( ) ( ) ( )tttw

S

w

SSww

T

k

T

,,,,,..,,......... **

1

**

wqQwqhwqMw

=+=

∂

∂

∂

∂=

∂

∂

(21)

Mathematical model for Mathematical model for nonlinearnonlinear flight simulationflight simulation

( ) C CΩ Ω Ω Ω Ω+ + + + = +MV M J J J R MJ R MJ F G

( )( ) ( ) 0

2R L w w

B B R B L s S S S

R R L L

B B R B B L B C

Ω

Ω Ω Ω

+ + + + + + +

+ + + + + = + ×

J Ω J O J O J J J J J V

J J J O J J J O J J Ω M R G

where: M=mI, m – mass of MAV, I – unit matrix,

F=[Fx, F

yF

z]T– vector of aerodynamic forces,

M0=[L,M,N]T – vector of aerodynamic moments,

V=[U,V,W]T – velocity vector;

ΩΩΩΩ=[P,Q,R]T – vector of angular velocity,

- vector of right wing angular rates,

- vector of left wing angular rate;

Rc=[x

c, y

c, z

c]T vector of the center of mass

, ,T

R P Q Rβ θ = − + O

, ,T

L P Q Rβ θ = + + O

Mathematical model for Mathematical model for nonlinearnonlinear flight simulationflight simulation

SSxx,, SSyy,, SSzz- static moments static moments of of entomopterentomopter without wings; without wings;

-- matrix of static moments ofmatrix of static moments of MAVMAV’’ss wing; wing;

JJBB -- inertial moment of MAV without wings;inertial moment of MAV without wings;

-- inertial moments of right and left wing.inertial moments of right and left wing.

The control vector is defined as follows: The control vector is defined as follows:

where: β - flapping angle of wings;

φ - feathering angle of wings,

ω - frequency of wing motion respect to the body;

ψ - phase shifting between feathering and flapping;

and: ,

0

0

0

R Q

R P

Q P

− = − −

ΩJ

0

0

0

z y

S z x

y x

S S

S S

S S

−

= − −

J

w

SJ

R L

B B,J J

[ ], , ,T

=u β φ ω ψ

0 sin tβ β ω=0sin ( )t= +φ φ ω ψ

Mathematical model for nonlinear flight simulationMathematical model for nonlinear flight simulation

In those equations:In those equations:

2

0

1( ( , ), ( , )) ,

2x x L D

F V SC C Cρ α α= u u

2

0 0

1( , ),

2x l

M V SbCρ α= u

2

0

1( ( , ), ( , )) ,

2y y L DF V S C C Cρ α α= u u

2

0

1( ( , ), ( , )) ,

2z z L DF V S C C Cρ α α= u u

2

0 0

1( , ),

2y mM V SbCρ α= u

2

0 0

1( , ).

2z nM V SbCρ α= u

Distribution of instantaneous forcesDistribution of instantaneous forces aalong a long a wingbeatwingbeat cycle:cycle:

Important to stabilise the flight.

FundamentalFundamental kinematickinematic parametersparameters:

flapping angle of wingsflapping angle of wings β.β.β.β.β.β.β.β.

feathering angle feathering angle of of wingswings φφφφφφφφ

frequency of wing motion respect frequency of wing motion respect

to the bodyto the body ωωωωωωωω,,,,,,,,

phase phase shifting between feathering shifting between feathering

and flappingand flapping ψψψψψψψψ,,,,,,,,

mean strokemean stroke ηηηηηηηη, ,

angle of attack angle of attack αααααααα

Large and impulsive forces at the Large and impulsive forces at the

wing reversals.wing reversals.

Aerodynamic model - Blade Element Method (BEM) Aerodynamic model - Blade Element Method (BEM)

( ) ( ) ( )

( )( )( ) ( )( )

( )

3

3

cos cos sin sin sin cos sin sin sin cos sin cos

cos sin cos cos sin sin

sin cos cos sin sin sin sin cos sin cos cos cos cos cos

sin cos cos sin sin

ti M M M

ni M

U U V W

P Q R z

P Q R y

U U

β ζ β θ ζ β ζ β θ ζ β θ

θ ζ θ ζ θ ζ θ

β ζ β θ ζ β ζ β θ ζ β θ γ ζ θ β

β ζ β θ ζ

= + + − + − +

+ − + − − +

+ − + + + + +

= −

( )

( ) ( )( )( )

3

3

sin sin cos sin cos cos cos

cos cos sin sin sin cos sin sin sin sin sin cos cos cos sin

cos sin cos cos sin sin

M MV W

P Q R z

P Q R x

β ζ β θ ζ β θ

β ζ β θ ζ β ζ β θ ζ β θ θ β ζ θ β

β ζ θ ζ θ ζ δ

+ + + +

+ + + − − + − +

− − + − −

sin cosi Xi i Zi i

T P Pθ θ∆ = −∆ + ∆ cos sini Xi Zi i

Q P Pθ θ∆ = −∆ − ∆

θ γ α= −

21( )

2Xi i Xi i iP cU C bρ α∆ = ∆ ( )21

2Zi i Zi i iP c U C bρ α∆ = ∆

arc tan ni ii

ti

U V

Uα

−=

Modeling of aerodynamic loadsModeling of aerodynamic loads steady steady state model state model -- BEMBEM Aerodynamic model – quasi unsteady approachAerodynamic model – quasi unsteady approach

Stroke angle

Rotation angle

Lift

Wing

thrust (drag)

BEMBEM: results of simulations: results of simulations

Pressure force:

Translational

Pressure force:

Roto-translational

Neuromotor Control in Insects

compound eyes allow insects completelyto survey the surroundings|compound eyes allow insects completelyto survey the surroundings|

Flight-related sensors of the housefly Musca domestica: - the large compound eyes dominate the head;- ocelli are three light-sensitive sensors on top of the head;- halteres appear on the thorax and beat in anti-phase to the wings, sensing rotary

motion

Ocelli like light-sensitive sensors applied to stabilization of MAV flight

α

XB

yB

Z B

P1

P4

P2

P3

eb3

A 3

Four photoreceptors are fixed

with respect to the insect’s body frame

Four photoreceptors are fixed

with respect to the insect’s body frame

Promieniowanie podczerwone

fotodiody

R V1

V2

x

y

z

α

Schematics of ocelli designSchematics of ocelli design

Ocelli and halters like light-sensitive sensors applied to stabilization of MAV flight

sin cos

sin sin

cos

p

p

p

x r

y r

z r

θ ψ

θ ψ

θ

=

=

=

2 2

1 2

2 2

3 4

1 ,0, , 1 ,0,

0, 1 , , 0, 1 ,

T Tb b

T Tb b

P h h P h h

P h h P h h

= − = − −

= − = − −

1 2 1 2

( ) ( , ) ( )

( ) ( )

I P I I

I I

ψ θ θ

θ θ θ θ

= =

< ⇒ >1 1 2

2 3 4

( ) ( )

( ) ( )

a a

a a

y I P I P

y I P I P

= −

= −α

XB

yB

Z B

P1

P4

P2

P3

eb3

A 3

( )( )

( )( )1 22 2

1 33 31 33 311 1dI dI

y I hr r h I hr r hd d

ξ ξ

θ θ

= + − − − −

( ) ( )[ ] ( )[ ] ( )[ ] zyxl tmftfmtfmtF ωωαωα 211 2cos2sin2 −+−=

( ) ( )[ ] ( )[ ] ( )[ ] zyxr tmftfmtfmtF ωωαωα 211 2cos2sin2 +++=

Ocelli like light-sensitive sensors applied to stabilization of MAV flight

(Paparazzi autopilot)

Stabilization of hovering flight -Nonlinear Inverse Dynamics (NID) approach

Stabilization of hovering flight -Nonlinear Inverse Dynamics (NID) approach

( ) ( )f g= +x x x u ( )y = h x

( ) ( )-1 u = D x v - N x-1

( )

0

0

rj

z j

j=

∑v = P y - P y

1 11 1

1 1 1 1

1 1

1

h , ..., h

... ... ...

h , ..., hm m

r r

r r

m m m

L L L L

L L L L

− −

− −

=

G T G T

G T G T

D

h hL = ∇F F ( ) ( )[ h ]jr

jL= FN x x

Averaging Theory:

If forces change very rapidly relative to body If forces change very rapidly relative to body

dynamics, only dynamics, only meanmean forces and torques determineforces and torques determine

this this body body motionmotion

Averaging: system with inputs

How do we choose the T-periodic function w(v,t) ?

- Geometric control

- BIOMETICS: mimic insect wings trajectory

How can we compute ?

- For insect flight this boils down to computingmean forces and torques over a wingbeat period:

Simulations Force platform

How small must the period T of the periodic input be?

- Wingbeat period of all insects is good enough

How do we choose the THow do we choose the T--periodic function w(v,t) ?periodic function w(v,t) ?

-- Geometric control Geometric control

-- BIOMETICS:BIOMETICS: mimic insect wings trajectorymimic insect wings trajectory

How can we computeHow can we compute ??

-- For insect flight this boils down to computingFor insect flight this boils down to computingmeanmean forces and torquesforces and torques over aover a wingbeatwingbeat period:period:

Simulations Simulations Force platformForce platform

How small must the period T of the periodic input be?How small must the period T of the periodic input be?

-- WingbeatWingbeat periodperiod of all insects is good enoughof all insects is good enough

How doing it ? 3 IssuesHow doing it ? 3 Issues

( ) ( ) ( ) ( ), w ,f s S= = +x x u x x u u

Parameterization of wings motionParameterization of wings motion

( )( )( )

,w ,

,

b

a

b

a

=

F u uu u

M u u

( )

( )( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( )0 0

,

1 1, , , , ,

T T

f

f g t dt s S w g t g t dtT T

s S

= =

= = + =

= +

∫ ∫

.

x x v

x v x x v v

x x w v

Parameterization of wings motion

( ) ( ) ( )( )0

1, , ,

T

w w g t g t dtT

= ∫v v v

( ) ( ) ( )1 1,t g t g tφφ = +v v ( ) ( ) ( )2 2,t g t g t= +v vηη

( )2

cos3

g t tT

φ

π π =

( )

2cos

4g t t

Tη

π π =

( )1

2cos

15g t t

T

π π =

( ) ( )2 1g t g t=

Parameterization of wings motionHovering flight stabilization - NID aproach

( ), , ,R L R L

=u φ φ η η

( ) ( ) ( ),v t t t= +0u g G v

( )1 1 2 2, , ,R L R L

v v v v=v

1

1

0

2

2

0 0 0

0 0 0,

0 0 0

0 0 0

g g

g g

g g

g g

= =

g G

φ

φ

η

η

ParametrizationParametrizationof wings motionof wings motion

Block diagram of Block diagram of DynamicsDynamics ModuleModule

Block diagram of Aerodynamic Block diagram of Aerodynamic MModuleodule Algorithm Flow Chart:Algorithm Flow Chart:

Simulation of Simulation of

hovering flighthovering flight

(uncontrolled (uncontrolled

motionmotion))

Stabilization of hovering flight (NID)

Stabilization of hovering flight (NID) Stabilization of hovering flight (NID)

Rφ

Rη

Rφ

Lη

Conclusions

Fixed wing MAV technology seems to be an almost ready solution fFixed wing MAV technology seems to be an almost ready solution for or applications requiring high airspeed and long endurance. applications requiring high airspeed and long endurance. MicrohelicoptersMicrohelicopters can supplement fixed wing designs if hovering is can supplement fixed wing designs if hovering is required, but more work has to be done to increase their enduranrequired, but more work has to be done to increase their endurancece..

CConcepts oncepts entomoptersentomopters seem to be the most promising, because their seem to be the most promising, because their successful application would provide high successful application would provide high manoeuvrability manoeuvrability and and efficiency in hover. efficiency in hover.

TThe highly nonlinear nature of the he highly nonlinear nature of the entomoptersentomopters’’ss mathematical model mathematical model caused, that caused, that the use of linear control schemesthe use of linear control schemes is rather impossibleis rather impossible. . As As solution it is possible to apply solution it is possible to apply fuzzy controllers, fuzzy controllers, oror genetic algorithms genetic algorithms and neural networksand neural networks..

The The GurGur Game, an algorithm for selfGame, an algorithm for self--optimization and selfoptimization and self--organization organization for distributed nonlinear systems, for distributed nonlinear systems, also can be applied.also can be applied.

The results demonstrate that flexible membranes improved lift anThe results demonstrate that flexible membranes improved lift and thrust d thrust performance not by maximizing the positive force peaks, but rathperformance not by maximizing the positive force peaks, but rather by er by minimizing the negative peaks.minimizing the negative peaks.

TThese performance gains arose from localized areas of the wing duhese performance gains arose from localized areas of the wing during ring very short time periods of the overall flapping cycle. The physivery short time periods of the overall flapping cycle. The physical cal mechanism for these gains was that wing deformation due to incremechanism for these gains was that wing deformation due to increased ased flexibility caused a favorable tilting of the overall force vectflexibility caused a favorable tilting of the overall force vector, thereby or, thereby reducing the negative force componentsreducing the negative force components

… or alternative solution …„Computer Electronics Meet Animal Brains”… or alternative solution …„Computer ElectronicsComputer Electronics Meet Animal BrainsMeet Animal Brains””

COMPUTER, January, 2003;

Published by the IEEE Computer Society © 2003 IEEE

COMPUTERCOMPUTER, , JanuaryJanuary,, 20032003;;

Published by the IEEE Computer Society Published by the IEEE Computer Society ©© 2003 IEEE2003 IEEE

Chris Diorio

Jaideep Mavoori

University of Washington

Chris Chris DiorioDiorio

Jaideep MavooriJaideep Mavoori

UniversityUniversity of Washingtonof Washington

Computer Electronics Meet Animal BrainsComputer ElectronicsComputer Electronics Meet Animal BrainsMeet Animal Brains

Neurochip functional block diagram. Solid lines show required components,dashed lines show some optional components

NNeurochipeurochip functional block diagram.functional block diagram. Solid lines show required components,Solid lines show required components,

dashed lines show some optional componentsdashed lines show some optional components

ComputerElectronicsMeetAnimal Brains

ComputerComputerElectronicsElectronicsMeetMeetAnimal BrainsAnimal Brains

Integrative biology using neurochips. A neurochip can splice into neuromuscular pathways to unravel the internal biological circuitry.Neurochips armed with recording and stimulation channels will help neurobiologists understand the complex interactions amongthemoth’s various neural control systems.