Dynamic Model and System Identification Procedure for Autonomous Ornithopter Bharani 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 flappingwing flight • Design of automatic controls for flappingwing 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

Equations of motion mTO rG FaB 2 FaT 2 FaW FgTO 2 R 1 (rW ) XYZ W

aerodynamic forces

M GW

M GT M GB

d2 (R1R W )(riW ) xW yW zW dmW 2 dt

gravitational forces

mW rGW G aG H GW rGT G aG H GT H GB

M GW

rAwG FaW

rGwG FgW

M WAw

M GT

rAT G FaT

rGT G FgT

M ATT

M GB

rABG FaB

rGBG FgB

M ABB

M WAw M ATT M ABB are aerodynamic moments, and FaW FaT

FaB

are aerodynamic forces applied at the aerodynamic centers of wing, tail, and fuselage of the ornithopter

Lift and drag coefficient definitions

12

FaW T

CLu 0

d 1 q(t )ldt CL 2

1

u 1 q(t )ldt CD 2 12

12

0

d 1 q(t )ddt CD 2

1

q(t )ddt 12

-Average values of the aerodynamic force for flapping period -Define coefficients for up-stroke and down-stroke

q(t )

1 2

b2

V (t , y ) 2 c( y )dy 0

is the instantaneous dynamic pressure

Aerodynamic coefficients approximation CLu

CLu

CLu  CLu

CLd

CLd

CLd  CLd

CDu

CDumin

K (CLu )2

CDd

CDdmin

K (CLd )2

Cm

Cm0

Cm

e

e

Cm 

Are functions of average angle of attack, and stiffness of wing spars, E

e

CLuE E

e

CEd E

Cm

e

e

, elevator deflection,

e

Perturbed state model 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

C0 x

Ax Bu

x C0 1 Ax C0 1 Bu x

A ' x B 'u

where x is a state vector, u is a control vector, and A and B are system T matrices. The state vector for the longitudinal mode is x [u, w, q, ]

Parameter identification Inverse problem is solved in a least-squares sense by minimizing a real-valued scalar objective function t2

2

x( s, ) x( ) d

( s) t1

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

x(s, ) x ( )

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)

Ornithopter mechanical design Parameter

Value

Wingspan

1m

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 XBee Pro 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

via roll

Altitude

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

0.3

0.092

1.24

Dragonfly

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 groundfixed coordinate frame X E , YE , Z E

• Velocity in the ground-fixed coordinate frame VX E , VYE , VZ E

• Roll and pitch ,

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

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

f

V

IR sensor and IMU comparison Results and discussion

• 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

IR sensor and IMU Hardware used • IMU 3-axis accelerometer ADXL330 and 2-axis gyro ADG300 • IR 2-axis MLX-based differential sensor board 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)

(c)

(b) (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