Dynamic Model and System

Identification Procedure for

Autonomous OrnithopterBharani Malladi , Roman Krashanitsa, Dmitry Silin, and Sergey Shkarayev

The University of Arizona

Tucson, AZ, USA

This work is sponsored by AFRL, Eglin AFB

September, 2007

Outline

• Motivations

• UA MAVs

• Dynamic model for an ornithopter

• Parameters identification procedure

• Ornithopter design

• Integration of the autopilot

• Flight data analysis

• Conclusions

Motivations

• Advancement of knowledge on flapping-

wing flight

• Design of automatic controls for flapping-

wing MAV

UA MAVs

– Autonomous MAV Dragonfly

– VTOL MAV

– Small radio-controlled ornithopters

Current Studies

• Development of a dynamic model for an

ornithopter

• Identification of stability and control parameters

of the ornithopter

• Designing robust ornithopters capable of

sustained and controlled flight

• Integration of the autopilot into an ornithopter

– Selection of attitude sensors

– Analysis of flight telemetry data

Dynamic Model for an Ornithopter

are aerodynamic moments, and

are aerodynamic forces applied at the aerodynamic centers of wing,

tail, and fuselage of the ornithopter

Equations of motion2

1 1 W22 2 2 R ( ) (R R )( )

W W W

B T W TO

TO G a a a g W XYZ iW x y z W

W

dm r F F F F r r dm

dt

W T

W T B W T B

G G G W G G G G G G G G GM M M m r a H r a H H

aerodynamic forces gravitational forces

w w w

W W W W

G A G a G G g AM r F r F M

T T T

T T T T

G A G a G G g AM r F r F M

B B B

B B B B

G A G a G G g AM r F r F M

w

W

AMT

T

AMB

B

AM W

aF T

aF B

aF

Lift and drag coefficient definitions

1 2 1 21 1

0 1 2 0 1 2

1 1 1( ) ( ) ( ) ( )

2 2 2

W u d u d

a L L D DF T C q t ldt C q t ldt C q t ddt C q t ddt

-Average values of the aerodynamic force for flapping period

-Define coefficients for up-stroke and down-stroke

2

2

0

1( ) ( , ) ( )

2

b

q t V t y c y dy is the instantaneous dynamic pressure

Aerodynamic coefficients

approximation

Ee

u u u u u

L L L L e LC C C C C E

e

d d d d d

L L L L e EC C C C C E

min

2( )u u u

D D LC C K C

min

2( )d d d

D D LC C K C

Are functions of average angle of attack, , elevator deflection,

and stiffness of wing spars, Ee

0 em m m m m eC C C C C

where x is a state vector, u is a control vector, and A and B are system

matrices. The state vector for the longitudinal mode is

Perturbed state model

0C A Bx x u

1 1

0 0C A C Bx x u

' 'A Bx x u

[ , , , ]Tu w qx

From the aerodynamic forces and moments, the stability and control

derivatives are obtained and the longitudinal equations of motion are cast

into the following linear state-space model

where s is the current set of parameters for the state-space model

Inverse problem is solved in a least-squares sense by minimizing a

real-valued scalar objective function

is a solution of the direct problem for the current set of

parameters;

represents experimental data; and t1 and t2 are time

domain of integration.

Use a direct search “nonlinear simplex” method by Nelder and Mead (1965)

2

1

2( ) ( , ) ( )

t

t

s x s x d

( , )x s

( )x

Parameter identification

Ornithopter mechanical designParameter Value

Wingspan 1 m

Wing Area 0.1571 m2

Mass 369g

Wing root chord 200 mm

Autopilot integration

• Paparazzi autopilot board Tiny 0.99 using Phillips ARM7 microprocessor

• Attitude sensor – subject to study

• GPS U-Blox LEA-4P with 18mm patch antenna

• Medium-range wireless modem XBeePro for bidirectional link

Attitude sensing

• Two solutions considered– IMU with a 3-axis accelerometer and 2-axis gyro with

Kalman-filtered attitude output

– 2-axis IR sensor for direct angle sensing based on infrared emission contrast of ground and sky

• Pros and cons– IMU is faster that IR sensor

– IMU calibration is not sensitive to IR emission or reflectivity of ground surface

– IMU output is more susceptible to external forces and vibrations

Guidance and control• Difference from conventional airplane

– Flapping wings generate thrust and lift

– V-tail controls ornithopter in lateral and longitudinal directions

Channel Function

Guidance

Heading

Altitude

via roll

via flapping frequency

Control

Pitch

Roll

Flapping

frequency

tail control surfaces

tail control surfaces

motor rotational frequency

Proportional control gain coefficients

Aircraft type Span, m Roll Pitch

Zagi 1.01 0.4 1.28

Ornithopter 1.03 0.16 0.83

Zagi 0.58 0.090 0.83

Dragonfly 0.3 0.092 1.24

Static flapping frequency

Throttle setting f (Hz)

25% 2-2.5

50% 4.5-5

75% 5.5-6

100% 7-7.5

A range of 30-40% throttle is used for cruise flight

In-flight telemetry data

• Trajectory with respect to the ground-

fixed coordinate frame

• Velocity in the ground-fixed coordinate

frame

• Roll and pitch

, ,E E EX Y Z

, ,E E EX Y ZV V V

,

Flight trajectory

- No pilot input on the elevator and aileron controls

- Throttle was held constant at a cruise flight setting of 35%.

Flight altitude data

The flight altitude data was smoothed for the purposes of velocity calculations.

Measured climb rate for the duration of the test flight was no higher than 0.4 m/s.

Angle of attack

A dynamic behavior of the ornithopter

similar to the short-period oscillatory

motion was observed with the time

period of about 1 sec and time required

for the oscillations in angle of attack

and pitch to decay to one-half of initial

amplitude of about 2 sec (2 – 5 sec

time period)

Spectral analysis of pitch data

The recorded data were analyzed using FFT.

A peak can be seen in the range of 1-1.25 Hz that corresponds to

the noticed short period oscillations

Conclusions

• A multi-body dynamic model of the ornithopter was developed

• A procedure for the estimation of the parameters of this model was proposed

• The experimental ornithopter was built and the autopilot controller was integrated into the vehicle.

• Flight tests showed that the ornithopter is capable of a controlled sustained flight in the autonomous mode.

• In-flight telemetry data were collected and initial analysis was conducted.

Acknowledgments

This work has been sponsored by the grant from

AFRL, Eglin AFB

Program Manager Dr. Gregg Abate

f

System Identification

• Form equations of motion– Currently only longitudinal motion is

modeled:

3 equations of motion

– Wing motion is averaged over a flapping half-period

• Define model input and output –data supplied and what model produces– Control input is supplied, and forces

and moments acting on the ornithopter center of gravity are produced

Model

V

IR sensor and IMU comparison

• Accelerometer-based IMU is not

applicable to the attitude sensing on

ornithopters even while used with a

Kalman filter

• Suggested attitude sensing solution on

ornithopters is infrared-based unit being

inherently insensitive to any displacements

Results and discussion

IR sensor and IMU

• IMU 3-axis accelerometer ADXL330 and 2-axis gyro ADG300

• IR 2-axis MLX-based differential sensor board

Hardware used

Filter techniques used

• Kalman filter and moving average filter for the IMU

• Moving average filter for the IR sensor

Results based on performance on the ornithopter

• IMU and Kalman filter – the work is in progress

• IR sensor is not affected by vibrations

IMU performance for ornithopter

application

(a) (b)

(c)

(a) Low energy motion in

vertical or horizontal plane;

slow rolling motion

(b) Medium energy motion in

vertical and horizontal plane;

rapid rolling motion

(c) High energy motion in

vertical and horizontal plane;

no rolling motion