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