ABSTRACT
Title of thesis: DEVELOPMENT OF A TEST-BED FOR
CLOSED-LOOP MAV FLIGHT CONTROL
Nitin Kumar Gupta, Master of Science, 2006
Thesis directed by: Professor Inderjit Chopra
Department of Aerospace Engineering
A novel ground based test-bed for closed loop flight control of MAVs is developed.
The emphasis is on easy re-programability, measurement of internal states of the vehicle,
fail-safe features, and modular design so that control algorithms can be efficiently eval-
uated on a real MAV in flight. The sensors transmit data to the ground station using a
wireless link. All processing is carried out on the ground station, and the final commands
are up-linked back to the MAV. The control algorithm on the ground station is imple-
mented in LabVIEW. A microcontroller is used on the ground station to take care of the
time-critical tasks that cannot be handled by a PC. Starting with the early experiments on
yaw-control, this report presents the results for the 3-DOF attitude control experiments
done on an MAV using this test-bed. Three independent PID control loops are used to im-
plement automation. Ziegler-Nichols method is used for tuning the PID controller gains.
Simple proportional controllers in pitch and roll are shown to give good performance.
The roll and pitch attitudes are maintained within ?0.1 radians by the controller.
DEVELOPMENT OF A TEST-BED FOR
CLOSED-LOOP MAV FLIGHT CONTROL
by
Nitin Kumar Gupta
Thesis submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Master of Science
2006
Advisory Committee:
Professor Inderjit Chopra, Chair/Advisor
Professor Darryll Pines
Professor Sean Humbert
ACKNOWLEDGMENTS
I owe my gratitude to all the people who have made this thesis possible and who
have made my graduate experience one that I will cherish forever. First and foremost I
would like to thank my advisor, Professor Inderjit Chopra for giving me an opportunity
to work at the rotorcraft center at the University of Maryland. I am grateful to him for
being patient and understanding with me on several occasions and for his support and
encouragement.
I would like to thank Dr. Jayant Sirohi for his suggestions and advice on various
occasions during my graduate life. He has always made himself available for help and has
taken great pains to go through my work and suggest improvements. I am also grateful
to Joe for introducing me to several ideas, especially during the starting phase of my
research. Working with him for a couple of months was a great learning experience.
My colleagues at the graduate research office of the rotorcraft center have made
my graduate life a most enriching experience. In particular, I would like to thank Peter
who has been very closely associated with my research during the last six months and has
provided invaluable help in successfully conducting the flight experiments. It would have
taken me much much longer to finish, but for his help in fixing the Giant after every crash!
He also provided a great help by conducting experiments to validate the complementary
filter. I will always remember the lively discussions I have had with Vikram and Carlos
over the last year. Their keenness to explore different subjects and re-learn things starting
ii
from the basic principles, has greatly inspired me. I am thankful to Vikram for his help
during several experiments and theoretical derivations. John?s help as a pilot for the Giant
during initial experiments is gratefully acknowledged. His love for flying things turned
out to be quite contagious!
I am highly indebted to Abhishek who has always been there (both at work and
at home!) for guidance and help as an elder brother to me. I take this opportunity to
also thank Arun, Smita, Asitav, Anne, Sandeep, Shreyas, Sudarshan, and all others at the
rotorcraft center whose presence has made my graduate experience all the more lively and
enjoyable. I would also like to express my gratitude to Amardip, Chinna and Milind for
being such wonderful friends and house-mates.
I owe my deepest thanks to my family - my mother and father who have always
stood by me and encouraged me to do my best. Words cannot express the gratitude I owe
them. I shall always remain indebted to them for the many sacrifices they have made to
make me what I am.
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Contents
Table of Contents iv
List of Figures viii
List of Tables xiv
Nomenclature xv
1 Introduction 1
1.1 Micro Air Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 MAV Research Challenges . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Motivation and Challenge in Automation . . . . . . . . . . . . . . . . . 4
1.4 The Giant MAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Proposed Stability and Control Scheme . . . . . . . . . . . . . . . . . . 7
1.6 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 The Hardware Components 11
2.1 Sensors and their Operation . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Actuators and their Interface . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Working of a Servo . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 The Standard R/C Transmitter and Receiver . . . . . . . . . . . . 18
iv
3 Preliminary One DOF Experiments 23
3.1 Yaw Control Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 The Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Yaw Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.3 Yaw Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Issues Involved in Implementation of Free-Flight . . . . . . . . . . . . . 31
3.2.1 The Test Stand . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 The Avionics Package . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.4 Requirements for the MAV Control Test-bed . . . . . . . . . . . 33
4 Attitude Estimation 35
4.1 Attitude Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Euler Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.2 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Attitude Determination using Gyroscopes . . . . . . . . . . . . . . . . . 42
4.3 Attitude Determination using Accelerometers . . . . . . . . . . . . . . . 44
4.4 Complementary Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4.1 The Pendulum Experiment . . . . . . . . . . . . . . . . . . . . . 45
4.4.2 Design of Complementary Filter . . . . . . . . . . . . . . . . . . 48
4.4.3 Performance of Complementary Filter . . . . . . . . . . . . . . . 52
4.5 Position Determinition using INS . . . . . . . . . . . . . . . . . . . . . . 52
4.6 IMU Aiding and Kalman Filtering . . . . . . . . . . . . . . . . . . . . . 55
5 The Ground Based Setup 58
5.1 PID Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
v
5.2 Overview of the New Test-Bed . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Subsystems of the Setup (Hardware) . . . . . . . . . . . . . . . . . . . . 62
5.3.1 The Sensors and Telemetry . . . . . . . . . . . . . . . . . . . . . 62
5.3.2 The R/C Transmitter Interface . . . . . . . . . . . . . . . . . . . 64
5.3.3 The Virtual Instrumentation on PC . . . . . . . . . . . . . . . . . 66
5.4 Organization of the Virtual Instrument (Software) . . . . . . . . . . . . . 66
5.4.1 The Receiver Module . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4.2 The Processing Module . . . . . . . . . . . . . . . . . . . . . . . 70
5.4.3 The Transmitter Module . . . . . . . . . . . . . . . . . . . . . . 71
5.5 Implementation of the VI . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5.1 Initializing the IMU . . . . . . . . . . . . . . . . . . . . . . . . 73
5.5.2 State Estimation Loop . . . . . . . . . . . . . . . . . . . . . . . 74
5.5.3 Output Loop (PID controller) . . . . . . . . . . . . . . . . . . . 74
6 Results and Discussion 76
6.1 Vibrations and Sensor Saturation . . . . . . . . . . . . . . . . . . . . . . 76
6.2 Manual Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.3 Controlled Flight Results . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.3.1 Ziegler-Nichols PID Tuning . . . . . . . . . . . . . . . . . . . . 82
6.3.2 Perturbation Response . . . . . . . . . . . . . . . . . . . . . . . 109
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7 Conclusions and Future Work 116
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.3 The Future Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
vi
Appendices 124
A Gyroscope Drift 124
B Listing of Microcontroller Codes 130
C Implementing Digital Filters 138
D Setting up the Test-Bed 144
References 150
vii
List of Figures
1.1 Fixed-wing based MAVs developed by Aerovironment . . . . . . . . . . 2
1.2 Giant rotary-wing based MAV developed at the University of Maryland . 2
1.3 MIcro COaxial Rotor (MICOR) rotary-wing based MAV (UMD) . . . . . 3
1.4 Configuration of the Giant . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Subsystems involved in rotorcraft control . . . . . . . . . . . . . . . . . 7
1.6 Generic feedback control . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Internals of a typical gimballed inertial navigation system . . . . . . . . . 13
2.2 A typical gimballed inertial navigation system . . . . . . . . . . . . . . . 14
2.3 Internals of a typical strapdown inertial navigation system . . . . . . . . . 14
2.4 A typical strapdown inertial navigation system . . . . . . . . . . . . . . . 15
2.5 Schematic of strapdown inertial navigation system . . . . . . . . . . . . . 15
2.6 The standard servo used on R/C aircraft models . . . . . . . . . . . . . . 16
2.7 The internals of a standard servo . . . . . . . . . . . . . . . . . . . . . . 17
2.8 The PCM input signal to a servo . . . . . . . . . . . . . . . . . . . . . . 18
2.9 A typical R/C transmitter . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.10 A typical 4-channel micro R/C receiver . . . . . . . . . . . . . . . . . . 19
2.11 The motor driver circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.12 The PPM signal at the data port of an 8-channel transmitter . . . . . . . . 20
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2.13 The swashplate connections on a Blade-CP helicopter . . . . . . . . . . . 21
3.1 The yaw test stand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The yaw control scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 The MAG3 IMU from Memsense . . . . . . . . . . . . . . . . . . . . . . 25
3.4 The PIC 16F877A development board from CCS . . . . . . . . . . . . . 26
3.5 The hardware interfacing schematic for yaw control experiment . . . . . 26
3.6 The PD control scheme for yaw control . . . . . . . . . . . . . . . . . . 27
3.7 The yaw stabilization flowchart . . . . . . . . . . . . . . . . . . . . . . . 28
3.8 The flowchart for yaw control setup . . . . . . . . . . . . . . . . . . . . 30
3.9 The avionics package for 3 DOF onboard controller . . . . . . . . . . . . 32
4.1 Reference frames used in inertial navigation . . . . . . . . . . . . . . . . 36
4.2 The body fixed reference frame for the Giant . . . . . . . . . . . . . . . 37
4.3 The Euler angle transformations . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Determining gyro bias . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.5 Pendulum Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 Performance of accelerometer and gyro for attitude estimation (on axis) . 47
4.7 Performance of accelerometer and gyro for attitude estimation (off axis) . 48
4.8 The complementary filter schematic . . . . . . . . . . . . . . . . . . . . 49
4.9 Bode plot of the accelerometer filter transfer function (low pass) . . . . . 50
4.10 Bode plot of the gyroscope filter transfer function (high pass) . . . . . . . 51
4.11 Performanceofcomplementaryfilterforattitudeestimation(noaccelerom-
eter) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.12 Performance of complementary filter for attitude estimation (with ac-
celerometer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.13 Complementary filter performance (accelerometer saturation) . . . . . . . 55
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4.14 Complementary filter performance (free oscillations) . . . . . . . . . . . 56
5.1 Schematic of PID control for autonomous flight of Giant . . . . . . . . . 59
5.2 Schematic of attitude control loop (inner-loop) . . . . . . . . . . . . . . . 60
5.3 Architecture of the ground based test-bed . . . . . . . . . . . . . . . . . 61
5.4 The wireless IMU from Spark Fun Electronics [35] . . . . . . . . . . . . 63
5.5 The structure of a sensor data packet . . . . . . . . . . . . . . . . . . . . 64
5.6 The interface of the transmitter with the PC . . . . . . . . . . . . . . . . 65
5.7 The flowchart for the transmitter interface code . . . . . . . . . . . . . . 67
5.8 The 3 modules of the VI and their interfaces . . . . . . . . . . . . . . . . 68
5.9 The receiver module . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.10 The definition of stick positions . . . . . . . . . . . . . . . . . . . . . . 70
5.11 The implementation of the VI . . . . . . . . . . . . . . . . . . . . . . . . 73
5.12 The output loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.1 IMU mounted on the Giant with foam padding . . . . . . . . . . . . . . . 77
6.2 Angular rate about body x-axis during flight (gyro saturated) . . . . . . . 77
6.3 Angular rate about body x-axis during flight (gyro not saturated) . . . . . 78
6.4 Pitch attitude estimate during manual flight . . . . . . . . . . . . . . . . 79
6.5 Longitudinal cyclic during manual flight . . . . . . . . . . . . . . . . . . 79
6.6 Comparison of computed longitudinal cyclic with actual pilot command . 80
6.7 Dual-curve in throttle to reduce sensitivity near hover RPM . . . . . . . . 81
6.8 Pitch attitude vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . . . . 85
6.9 Roll attitude vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . . . . . 85
6.10 Longitudinal cyclic vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . 86
6.11 Lateral cyclic vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . . . . 86
x
6.12 Yaw attitude vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . . . . . 87
6.13 Vane command vs. time (KP? = 25,KP? = 25,KP? = 30) . . . . . . . . . 87
6.14 Pitch attitude vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . . . . 88
6.15 Roll attitude vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . . . . . 89
6.16 Longitudinal cyclic vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . 89
6.17 Lateral cyclic vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . . . . 90
6.18 Vane command vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . . . 90
6.19 Yaw attitude vs. time (KP? = 36,KP? = 25,KP? = 30) . . . . . . . . . . . 91
6.20 Pitch attitude vs. time (KP? = 18,KP? = 130,KP? = 30) . . . . . . . . . . 92
6.21 Roll attitude vs. time (KP? = 18,KP? = 130,KP? = 30) . . . . . . . . . . 92
6.22 Pitch attitude vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . . . . . 93
6.23 Roll attitude vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . . . . . 93
6.24 Longitudinal cyclic vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . 94
6.25 Lateral cyclic vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . . . . 94
6.26 Yaw attitude vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . . . . . 95
6.27 Vane command vs. time (KP? = 18,KP? = 124,KP? = 30) . . . . . . . . 95
6.28 Pitch attitude vs. time (KP? = 36,KP? = 62,KP? = 30) . . . . . . . . . . 96
6.29 Roll attitude vs. time (KP? = 36,KP? = 62,KP? = 30) . . . . . . . . . . . 96
6.30 Pitch attitude vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . . . . 97
6.31 Roll attitude vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . . . . . 97
6.32 Longitudinal cyclic vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . 98
6.33 Lateral cyclic vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . . . . 98
6.34 Yaw attitude vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . . . . . 99
6.35 Vane command vs. time (KP? = 32,KP? = 62,KP? = 30) . . . . . . . . . 99
6.36 Pitch attitude vs. time (KP? = 16,KP? = 62,KP? = 30) . . . . . . . . . . 101
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6.37 Roll attitude vs. time (KP? = 16,KP? = 62,KP? = 30) . . . . . . . . . . . 102
6.38 Longitudinal cyclic vs. time (KP? = 16,KP? = 62,KP? = 30) . . . . . . . 102
6.39 Lateral cyclic vs. time (KP? = 16,KP? = 62,KP? = 30) . . . . . . . . . . 103
6.40 Pitch attitude vs. time (KP? = 20,KP? = 55,KP? = 30) . . . . . . . . . . 103
6.41 Longitudinal cyclic vs. time (KP? = 20,KP? = 55,KP? = 30) . . . . . . . 104
6.42 Lateral cyclic vs. time (KP? = 20,KP? = 55,KP? = 30) . . . . . . . . . . 104
6.43 Roll attitude vs. time (KP? = 20,KP? = 55,KP? = 30) . . . . . . . . . . . 105
6.44 Pitchattitudevs. time(KP? =14.4,KI? =12.3,KP? =55.8,KI? =55.8,KP? =
30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.45 Rollattitudevs. time(KP? =14.4,KI? =12.3,KP? =55.8,KI? =55.8,KP? =
30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.46 Longitudinal cyclic vs. time (KP? = 14.4,KI? = 12.3,KP? = 55.8,KI? =
55.8,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.47 Lateralcyclicvs. time(KP? =14.4,KI? =12.3,KP? =55.8,KI? =55.8,KP? =
30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.48 Pitchattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 108
6.49 Longitudinal cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . 109
6.50 Rollattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 110
6.51 Lateralcyclicvs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 111
6.52 Pitchattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 111
6.53 Longitudinal cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . 112
6.54 Rollattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 113
xii
6.55 Lateralcyclicvs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30) . . . . . . . . . . . . . . . . . . . . . . . . 113
6.56 Longitudinal cyclic with perturbation at 36 sec . . . . . . . . . . . . . . 114
6.57 Pitch attitude response to longitudinal perturbation . . . . . . . . . . . . 114
7.1 Hierarchical decomposition of autonomous control [41] . . . . . . . . . . 121
D.1 Communication settings in LabVIEW . . . . . . . . . . . . . . . . . . . 147
D.2 Control settings in LabVIEW . . . . . . . . . . . . . . . . . . . . . . . . 148
xiii
List of Tables
6.1 Ziegler-Nichols Tuning Method . . . . . . . . . . . . . . . . . . . . . . 82
6.2 Critical gain and period for pitch and roll . . . . . . . . . . . . . . . . . 100
6.3 Ziegler-Nichols Gains (Pitch) . . . . . . . . . . . . . . . . . . . . . . . . 100
6.4 Ziegler-Nichols Gains (Roll) . . . . . . . . . . . . . . . . . . . . . . . . 100
6.5 PID Controller Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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Nomenclature
?,?,? Pitch, roll and yaw attitudes, respectively (Euler angles)
e0,e1,e2,e3 The four Euler parameters
g Acceleration due to gravity
p,q,r (Euler) body rates along x, y, and z body axes, respectively
Ga(s) Transfer function for the low-pass filter (accelerometer branch)
Gg(s) Transfer function for the high-pass filter (gyroscope branch)
Ha(s) Accelerometer transfer function
Hg(s) Gyroscope transfer function
Kp Proportional gain
Ki Integral gain
Kd Derivative gain
Kcr Critical gain
KP?, K? Proportional gain for pitch axis
KP?, K? Proportional gain for roll axis
KP?, K? Proportional gain for yaw axis
KI? Integral gain for pitch axis
xv
KI? Integral gain for roll axis
KI? Integral gain for yaw axis
KD?, Kq Derivative gain for pitch axis
KD?, Kp Derivative gain for roll axis
KD?, Kr Derivative gain for yaw axis
Pcr Critical period
Td Derivative time
Ti Integral time
Abbreviations
A/D Analog to Digital
ASCII American Standard Code for Information Interchange
CCPM Cyclic Collective Pitch Mixing
DOF Degree-Of-Freedom
FIR Finite Impulse response
GPS Global Positioning System
IIR Infinite Impulse Response
IMU nomenInertial Measurement Unit
INS Inertial Navigation System
LiPo Lithium-Polymer
MAV Micro Air Vehicle
MEMS Micro Electro Mechanical Sensor
P Proportional control
xvi
PD Proportional-Derivative control
PI Proportional-Integral control
PID Proportional-Integral-Derivative control
PCM Pulse Coded Modulation
PPM Pulse Position Modulation
PWM Pulse Width Modulation
R/C Radio Control
RPM Rotations Per Minute
SISO Single Input. Single Output
VI Virtual Instrument
xvii
Chapter 1
Introduction
1.1 Micro Air Vehicles
MicroAirVehicles(MAVs)aredefinedbyDARPAassix-degree-of-freedomaerialrobots
measuring less than 15 cm in length, width or height [1]. Such aircraft are expected to
be small, inexpensive and expendable. These can be used for surveillance and measure-
ment missions in urban environments and other situations, where larger vehicles are not
practical. Their applications range from small unit battlefield surveillance, mapping out
chemical/radiation spills or viral outbreaks to more routine applications such as, mon-
itoring crops or wildlife distributions. With the ever-decreasing size and weight of the
payload components that can include video cameras, chemical sensors, electronics, and
communication devices, such applications are becoming more achievable.
In the last decade, several concepts for MAVs have been developed. These can be
broadly classified into fixed-wing based MAVs, like Black Widow, Hornet and Wasp [2?4]
(Fig. 1.1), and rotary-wing based MAVs, like Giant [5] (Fig. 1.2) and Micor [6] (Fig. 1.3).
1
CHAPTER 1. INTRODUCTION
Figure 1.1: Fixed-wing based MAVs developed by Aerovironment
Figure 1.2: Giant rotary-wing based MAV developed at the University of Maryland
Rotary-wing based MAVs have capabilities that may allow missions to be performed that
cannot be considered for fixed-wing MAVs. In order to generate enough lift to sustain
weight, the fixed-wing MAVs have to fly fairly fast. Rotary-wing based MAVs, on the
other hand, can hover, and can take off and land vertically. This allows them to operate in
more confined environments, such as, small indoor spaces and dense urban settings.
2
CHAPTER 1. INTRODUCTION
Figure 1.3: MIcro COaxial Rotor (MICOR) rotary-wing based MAV (UMD)
1.2 MAV Research Challenges
The small size requirements of MAVs generate a variety of challenges in their develop-
ment, not seen in their full-scale counterparts. For the rotary-wing based MAVs, these
challenges fall into two main categories: (1) improving aerodynamic efficiency or figure
of merit, and (2) achieving stability and control [7]. Solutions for improving figure of
merit of these vehicles are currently been developed in the form of design of rotor blades
suitable for low Reynolds number flight, ducted rotors, and other novel concepts [8?11].
AsahumanpilotisnotpresentonboardtheMAVs, eitheraremotepilotoranautonomous
controllerisrequiredinordertoflythesevehicle. EvenifaremotepilotcontrolstheMAV,
a basic stability-augmentation system is desired to reduce pilot workload. Design of a
3
CHAPTER 1. INTRODUCTION
test-bed to implement and evaluate closed-loop control during flight, and development of
an attitude stabilization system using this test-bed are discussed in this thesis.
1.3 Motivation and Challenge in Automation
Traditionally, the UAVs and MAVs were tele-operated by remote human-pilots. These
UAVs were sometimes equipped with onboard cameras and other sensors to assist the
human pilot by providing visual cues on his monitor [12]. Recently there has been much
research effort to automate MAVs, which would not only eliminate the remote human
pilotbutalsoallowhigherdegreeofmaneuverabilitytoaccomplishmissionswhichwould
be extremely difficult, if not impossible, to fly for a remote human pilot. An important
requirementofsuchautomationsystemsistoaugmentstability. Thisisexpectedtoenable
untrained pilot to operate an MAV by issuing high-level commands.
The smaller size and lower inertia, relative to the available thrust, of rotary-wing
based MAVs makes them more maneuverable and agile than the full-scale helicopters.
ThisalsomakesthecontrolandstabilizationofMAVsamorechallengingtaskthanthatof
full-scale helicopters. Additional requirements like control and navigation in constrained
environments, and low weight and size of the avionics package makes this problem even
more involved [13]. Previous work on autonomous flight control of model helicopters
has investigated outdoor flight of much larger models (5 feet rotor diameter and above)
with higher payload carrying capability [14?18]. This research has resulted in successful
autonomous flight of these large helicopter models. Typical payload carrying capability
of MAV is around 20 grams. The design of an avionics package that is both light and
4
CHAPTER 1. INTRODUCTION
provides reliable state estimation is still a challenge.
1.4 The Giant MAV
We propose to use the Giant MAV (Fig. 1.4), developed at the Micro Air Vehicles Lab-
oratory of University of Maryland, as the test-bed for our MAV control experiments be-
cause it is representative of the dynamics of a typical hover-capable rotary-wing MAV,
and still has a sufficient payload carrying capacity to lift the avionics package designed
using commercial off-the-shelf components. This enables us to focus on issues related to
implementation and algorithms related to flight stability and control.
The Giant consists of a single fixed pitch rotor, with a set of vanes in the downwash
of the rotor to provide the required anti-torque. The main rotor has a diameter of 25 cm.
It is a two bladed rotor with a teetering hinge and a Bell/Hiller servo-paddle. Giant is
powered by a brushless DC motor, and a 700mAh Lithium-polymer battery pack gives
it an endurance of about 10 minutes. Yaw control is achieved by aerodynamic control
surfaces in the vanes and lateral control is achieved by a swashplate connected to the
servo-paddle. The Giant is equipped with an off-the-shelf gyro that provides automatic
vane inputs in order to stabilize the vehicle in yaw. The entire system weighs 250 grams
and has a payload carrying capacity of about 30 grams.
The actuator configuration of the Giant is very similar to a conventional helicopter.
It has four controls: the lateral and longitudinal cyclic inputs control the swashplate or the
roll and pitch moments produced by the rotor; the thrust (rotor RPM) is controlled by the
throttle input; the yaw input controls the angle of the vanes, thereby providing the anti-
5
CHAPTER 1. INTRODUCTION
Figure 1.4: Configuration of the Giant
torque to counter the rotor torque. Thus the controls have a direct effect on the Giant?s
roll and pitch attitude rate, vertical velocity, and the heading rate, respectively.
The pilot does not control Giant?s position and velocity directly. These are con-
trolled through a chain of effects as follows. The cyclic control inputs result in control
moments about the rotor hub via a tilting motion of the rotor tip-path-plane. The rotor
control moments produce a fuselage rolling or pitching motion. The tilting of the tip-
path-plane produces horizontal thrust components. For example, holding a constant pitch
angle, the Giant will accelerate until the aerodynamic drag force balances the horizontal
thrust component. In the steady state, a pitch or roll angle translates into a steady longi-
tudinal or lateral velocity. Figure 1.5 shows a block diagram of the subsystems involved
in the longitudinal-lateral control problem.
Of course, different cross couplings also need to be compensated, such as the effect
6
CHAPTER 1. INTRODUCTION
Rotr
Fuselage
Rotor
Dynamics
Angular
Dynamics
Translational
Dynamics
Gust
Pilot
Cycli
Inputs
Rotr
Forces
Rotr
Moments
Rol and Pitch
Rotrcaft
Atitude
Rotrcaft
Velocity
Figure 1.5: Subsystems involved in rotorcraft control
of the translation or rotational fuselage motion on the rotor and fuselage attitude dynam-
ics, or the secondary effects of the controls. For example, when the Giant is pitched, the
vertical thrust component will decrease, requiring an increase in the thrust magnitude to
maintain altitude. This increase in thrust, however, will produce a reaction torque at the
rotor shaft and thus vanes will need adjustment to provide more anti-torque. The Giant
because of its relatively small size, is also quite sensitive to atmospheric disturbances that
affect the rotor and fuselage dynamics.
1.5 Proposed Stability and Control Scheme
WeproposetoimplementfeedbackcontrolinordertostabilizeandcontrolanMAV.Basic
architecture of such a control scheme is shown in figure 1.6.
7
CHAPTER 1. INTRODUCTION
-
+
Actuators
Sensors and 
Filter Algorithms
Control
Algorithm
Vehicle
Dynamics
Desired
Stats
Control
omands
Estimate of Curent
Vehicle States
Figure 1.6: Generic feedback control
The sensors (attached to the vehicle) and the associated filter algorithms give us
an estimate of the current states of the vehicle. These states are dictated by the control
algorithm and the control objective. For 6 DOF control (3 rotational and 3 translational
degrees-of-freedom) of the vehicle, the states would typically be the attitude and position
ofthevehicle. Thecontrolalgorithmthenusesthisinformationtocomputethecommands
for the actuators in order to stabilize and control the vehicle as desired. These actuators
act on the vehicle and influence its motion. The sensors, in turn, again estimate the new
values of the states, and the entire cycle is repeated.
The first step in implementing this scheme is the selection of a control algorithm.
This decision is based on the kind of vehicle, its dynamics, availability of its flight dy-
namics model, the actuator configuration, and of course the control objective. The states
required by the control algorithm will dictate the sensors and the filter algorithms to be
used. The sensor selection is also constrained by payload carrying capability of the vehi-
cle, onboard power available and other operational constraints (e.g., GPS cannot be used
if the vehicle has to operate indoors). If no suitable sensors and filter algorithms could be
8
CHAPTER 1. INTRODUCTION
found to provide the states required by the chosen control algorithm, we need to select a
different control algorithm for which suitable sensors and filter algorithms exist.
The control algorithms can be broadly classified into modern model-based con-
trol techniques and the classical techniques. Given a highly accurate vehicle dynamics
model of a vehicle, the model-based techniques, like the H-infinity control, would have
significantly better performance than a classical controller, like the PID (Proportional-
Integral-Derivative) control [19]. While a PID based controller is expected to achieve
basic automation, it will not be optimal, and will not be able to fully utilize the available
degree of maneuverability of the vehicle. As there does not exist a sufficiently accurate
model for the Giant and developing such a model for any rotorcraft-based vehicle is a
challenging task in itself, we opt to first implement a classical PID based control and
demonstrate the working of the generic test-bed developed to enable this implementa-
tion. Such a test-bed can later be used for implementing a model-based controller when
required.
1.6 Overview of the Thesis
This thesis presents the development of an innovative test-bed for closed loop MAV flight
control experiments. The basic concepts from control theory, state estimation and an
overview of hardware components used for this setup is given in Chapter 2. Chapter 3
descibes the preliminary experiments performed to develop understanding of these basic
concepts. The yaw-control experiment and development of a complete onboard stabiliza-
tion system are discussed in detail. The software and hardware aspects of the final test-
9
CHAPTER 1. INTRODUCTION
bed developed to overcome the shortcomings of the onboard stabilization system form the
subject of Chapter 4. The results of the 3-DOF hover control experiment are discussed
in Chapter 5. Chapter 6 presents the conclusions and recommendations for future work.
A quick guide to setting up the test-bed for future experiments and solutions to common
problems encountered are documented as an appendix to this thesis.
10
Chapter 2
The Hardware Components
2.1 Sensors and their Operation
Inertial measurement unit (IMU) provides one of the most established methods for es-
timating the motion (change in attitude and position) of a vehicle [20, 21]. This is a
self-contained system and does not need information from external source, like GPS, to
determine position.
An accelerometer measures acceleration along a single axis. Its output can be inte-
grated to get velocity. The second integration gives the position, or change in position. If
the direction of travel is known, the current position with respect to the original position
can thus be obtained. The inertial navigation system (INS) is a form of ?dead reckon-
ing?, that is, it gives the present position with respect to the initial position, and it cannot
directly find the absolute position in the inertial frame.
Three accelerometers can be put together with orthogonal sensing directions to give
a measure of displacement in the three-dimensional space. In order to maintain the ori-
11
CHAPTER 2. THE HARDWARE COMPONENTS
entation of these accelerometers when the vehicle maneuvers, the accelerometers are sus-
pended in a set of three gimbals which are gyro-stabilized to maintain the direction. Such
an arrangement forms the ?gimballed? configuration of the inertial navigation system.
The gyros, used in the gimballed inertial navigation system are of a type known
as ?integrating? gyros, that is, they give output proportional to the angle through which
they have been rotated (about their sensing axis). They serve as the sensing elements in
the null-seeking servos. The output of each gyro drives the servo motor connected to the
appropriate gimbal, thus keeping the gimbal in a constant orientation in inertial space.
The gimbals are a set of three rings, each with a pair of bearings, initially at right
angles (fig. 2.1). Each gimbal also consists of a motor, built around one of the bearings,
and at the other end a synchro (an electromagnetic angle-measuring device) [22]. The
innermost gimbal always maintains its orientation in inertial space, irrespective of how
the vehicle maneuvers. The synchro on the innermost gimbal thus measures the azimuth
(heading), the synchro on the middle gimbal measures the pitch, and the one on the outer
gimbal measures roll.
The innermost gimbal provides a ?stable platform? which holds the gyros and the
accelerometers. The entire system is called a ?gimballed platform?. Figure 2.2 shows the
Marconi FIN1000 inertial platform, which is used in virtually all the RAF?s combat air-
craft and many others world-wide. Such systems can measure vehicle?s position, velocity,
acceleration, attitude, and heading. Over the last 30 years, the gimballed inertial naviga-
tion technology has fully matured and very reliable and accurate IMUs are available.
The gimballed arrangement is mechanically very complex. It contains delicate
sliprings, the motors dissipate power; mechanical resonances are unavoidable. Due to
12
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.1: Internals of a typical gimballed inertial navigation system
high part count, these are too heavy and bulky to be carried by MAVs.
Research in the direction of simplifying the complexity of these systems lead to the
development of ?strapdown? systems. These do away with the gimbal altogether and the
gyros and accelerometers are mounted on the platform directly. The gyros are used to
measure the rotations in space instead of null-seeking sensors. Using the gyro informa-
tion, thesystemknowswhichdirectiontheaccelerometeraxisispointinginatanyinstant.
Thus, the mechanical gimbals are replaced by a ?mathematical gimbal set? (fig. 2.3, 2.4).
Realizationofsuchasystembecamepossibleduetorecentadvancesinlightweight,
powerful and cheap digital computers (or microcontrollers), and MEMS (Micro Electro-
Mechanical Sensor) technology. A software solution is used to keep track of the orien-
tation of the IMU (and vehicle) and transform the measurements from the body frame
to the navigational frame. This method overcomes the problems encountered with the
gimbaled system, and most importantly reduces the size, cost, power consumption, and
complexity of the system. The strapdown INS measures the orientation of a vehicle by
13
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.2: A typical gimballed inertial navigation system
Figure 2.3: Internals of a typical strapdown inertial navigation system
14
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.4: A typical strapdown inertial navigation system
Rate Gyros
Acelrometrs
Orientation
Integration
Inital
Orientation
Transform to
Localy-Levl
Navigation Frame
Subtract g
From Vertical
Acelration
Velocity
Integration
Positon
Integration
Inital
Velocity
Inital
Positon
,
xyz
!
,!"#
vPositon of
the vehicle
Atitude of
the vehicle
Figure 2.5: Schematic of strapdown inertial navigation system
integrating the angular rates from three orthogonal angular rate sensing gyroscopes (rate
gyros) strapped down to the frame of the vehicle. To get position, 3 accelerometers, also
affixed to the orthogonal axes of the moving body, measure the total acceleration vector
of the body relative to the inertial space. This acceleration vector can be converted from
the body coordinates to inertial coordinates using the known instantaneous orientation of
the body determined by the gyros. Position is then obtained by subtracting the effect of
gravity from the measured acceleration and then performing double integration starting
from a known initial position (fig. 2.5).
15
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.6: The standard servo used on R/C aircraft models
2.2 Actuators and their Interface
The actuators used on the Giant are the standard servos used on most commercially avail-
able radio-controlled (R/C) aircraft models (fig. 2.6). A Servo is a small device that has
an output shaft. This shaft can be positioned to specific angular positions by sending
the servo a coded signal. As long as the coded signal exists on the input line, the servo
will maintain the angular position of the shaft. As the coded signal changes, the angular
position of the shaft changes. These servos although quite small, can generate very high
torque. The servos used on the Giant are rated at 10 oz-inch.
2.2.1 Working of a Servo
Aservoworksontheprincipleofnegativefeedback. Figure2.7showstheinternalpartsof
a servo. Here, the current to the motor is provided by a potentiometer that is itself driven
by the same motor. This potentiometer also serves as the output shaft. The motor when
turned on, drives the potentiometer till the potentiometer provides no more current to the
16
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.7: The internals of a standard servo
motor. A circuitry allows for changing this zero-current position of the potentiometer,
based on the input signal. So, when a new position of the potentiometer (or output shaft)
is desired, this zero position is altered by the circuitry (based on input signal) and the
motor turns the potentiometer till this zero position is reached.
The angle is determined by the duration of a pulse that is applied to the control wire.
This is called Pulse Coded Modulation (PCM). The servo expects to see a pulse every 20
milliseconds (.02 seconds). The length of the pulse determines how far the motor turns.
A 1.5 ms pulse, for example, will make the motor turn to the 90-degree position (often
called the neutral position). If the pulse is shorter than 1.5 ms, then the motor will turn
the shaft to closer to 0 degrees. If the pulse is longer than 1.5 ms, the shaft turns closer
to 180 degrees (fig. 2.8). The position of a servo can therefore be theoretically updated
not more than 50 times per second (20 ms for each update). This imposes a fundamental
limit on the servo bandwidth besides the mechanical performance issues.
17
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.8: The PCM input signal to a servo
2.2.2 The Standard R/C Transmitter and Receiver
Giant canbe flown manuallyby ahuman pilot usingthe standard radio-controltransmitter
and receiver. The radio-control transmitter (fig. 2.9) converts movements of the control
sticks and switches into a coded radio signal, which is transmitted by radio to the radio-
control receiver (fig. 2.10) installed on Giant. The signal is received and then decoded by
the micro-controller on the receiver into the servo-control signals.
Giant needs a transmitter and a receiver with at least 4 channels, one each for con-
trolling longitudinal cyclic, lateral cyclic, rotor RPM and yaw-control vanes. While lon-
gitudinal cyclic, lateral cyclic and yaw-control vanes are directly driven by the servos
(which are connected to different channels on the receiver), the rotor RPM is controlled
through a motor-driver circuit (fig. 2.11), which converts the servo-control signals into
high frequency PWM signals.
Radio-control transmitters are usually provided with a data port. The signals being
18
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.9: A typical R/C transmitter
Figure 2.10: A typical 4-channel micro R/C receiver
19
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.11: The motor driver circuit
Figure 2.12: The PPM signal at the data port of an 8-channel transmitter
sent by the transmitter, corresponding to the stick positions can be read on the output
pin of this port. This port also has an input pin, and any desired signal can be written
to this pin for transmission to the receiver. The input and output signals on this port
follow a modulation very similar to the servo-control signal. The normal state of the pin
is high. Each frame has a width of 20 ms and has as many inverted-pulses as the number
of channels. The width of the first pulse (inverted pulse) corresponds to the position of
first servo, and so on as shown in figure 2.12. This modulation is called the inverted Pulse
Position Modulation (PPM) as different channels are represented by different positions of
the pulses in each frame.
It is important to note that although usually each stick corresponds to one servo
channel (as in case of Giant), there maybe configurations where each stick movement
20
CHAPTER 2. THE HARDWARE COMPONENTS
Figure 2.13: The swashplate connections on a Blade-CP helicopter
may lead to changes in more than one servo channel. For example, in a typical CCPM
(Cyclic/Collective Pitch Mixing) type of RC helicopter (like, Blade-CP [23]), the swash-
plate is controlled by three servos (fig. 2.13). The motion of all three servos is affected
even if only one of the two cyclic or collective controls is applied. Therefore, although
pilot moves only one stick at a time, the width of all three pulses corresponding to swash-
plate servos changes.
The hardware components described in this chapter are all commercial off-the-shelf
components. These enable the Giant to be flown manually by a human pilot. The next
task is to use the knowledge of the protocols and internal working of these components to
interface these (along with sensors) with a processing element (microcontroller or a PC)
21
CHAPTER 2. THE HARDWARE COMPONENTS
in order to automate the flight of the Giant.
22
Chapter 3
Preliminary One DOF Experiments
3.1 Yaw Control Experiment
As the first step, in order to explore the requirements of a stability augmentation system,
a yaw stabilization experiment was conducted on the Giant. For this purpose, a test stand
that allowed only one degree-of-freedom (yaw) was prepared, and the Giant was mounted
on it, as shown in figure 3.1.
A single degree of freedom PD (proportional-derivative) control scheme as shown
in figure 3.2, in conjunction with a commercial off-the-shelf IMU, was implemented for
stabilization. The yaw angle is measured and the yaw-vanes on the Giant are controlled
in a way so as to maintain the same yaw attitude.
3.1.1 The Hardware
After an exhaustive search, the MAG3 IMU from Memsense [24] was selected for the
sensor. This IMU (fig. 3.3) has 3 gyroscopes each with a range of ?150 deg/sec, 3
23
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Giant MAV
IMU
Bearing
allows only
Yaw DOF
Vice
Microcontroller
Figure 3.1: The yaw test stand
Figure 3.2: The yaw control scheme
24
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Figure 3.3: The MAG3 IMU from Memsense
accelerometers each with a range of?2g and 3 magnetometers each with a range of?1.9
gauss. All sensor outputs are available as analog voltages varying from zero to five volts.
This is one of the smallest and lightest IMUs available, weighing only 5 grams and having
a size of 0.7 in x 0.7 in x 0.4 in.
A development board (fig. 3.4) based on Microchip PIC 16F877A microcontroller
[25] was obtained from Custom Computer Services, Inc. (CCS) [26] to serve as an in-
terface between the sensors and the actuators, and to carry out the control computations.
16F877A microcontroller from PIC is an 8-bit microcontroller running at 20 MHz, and
has 256 bytes of EEPROM data memory. It has 2 capture/compare/PWM functions, sup-
port for I2C bus and 8 channels of 10-bit Analog-to-Digital (A/D) converter. The de-
velopment board from CCS gives easy access to all these input/output pins, provides an
interface to easily program the microcontroller and has a potentiometer connected to one
of the A/D channels. Figure 3.5 shows the interface between different hardware compo-
nents.
3.1.2 Yaw Stabilization
The numerical integration of yaw-rate (to get yaw angle), PD controller and servo com-
mand generation are implemented on the microcontroller as shown in figure 3.6. Here the
25
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Figure 3.4: The PIC 16F877A development board from CCS
Figure 3.5: The hardware interfacing schematic for yaw control experiment
26
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Figure 3.6: The PD control scheme for yaw control
analog output from yaw gyro is continuously sampled. This is then added to a counter,
which is initialized to zero in the beginning of the code, to give a quantity proportional
to the yaw angle (determination of exact yaw angle is not important). The output angle
of the vanes is computed using the value of this angle and the angular rate at that instant.
A separate interrupt routine generates appropriate signal for the vane servo, based on this
desired angle of vanes, once every 20 ms (as explained in section 2.2.1). It is important
to use interrupt routine for this task as it is time critical. The microcontroller suspends all
other tasks, once every 20 ms, and generates the servo signal. The flowchart for this is
given in figure 3.7 and the code is attached as an appendix to this report.
The proportional and derivative gains (K? and Kr, respectively) used for the compu-
tation of output angle of vanes are experimentally determined. Here, the HighTime equa-
27
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Figure 3.7: The yaw stabilization flowchart
28
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
tion represents the PD controller. This controller continuously moves the vanes (changes
the value of HighTime) so as to hold a constant yaw attitude when the main rotor is spun
or its RPM changed.
3.1.3 Yaw Control
The setup is later modified for yaw control (from yaw stabilization). A potentiometer
provided on the CCS development board is used to command the desired yaw angle.
The code is upgraded to sample the analog voltage from the potentiometer and use it for
computation of the vanes angle. The interrupt routine in this case remains the same as
that for the previous case. On turning the potentiometer, the vehicle is observed to follow
the command and turn by the desired yaw angle.
In the next step, this setup is further modified and was interfaced with an RC re-
ceiver (discussed in section 2.2.2). This way the human-pilot can command the desired
yaw angle remotely using the R/C transmitter. This is different from normal radio control,
as in the normal case, the pilot would control the angle of the vanes, which would change
the torque, and hence the yaw acceleration. By using the yaw attitude controller, he can
however directly command the desired yaw angle using the knob on the R/C transmitter.
The controller now continuously adjust the vanes to achieve and maintain that yaw atti-
tude. The new flowchart is given in figure 3.8. This uses two interrupt routines, one to
generate the servo signal and other to read the signal from the R/C receiver. The code is
listed as an appendix to this report.
29
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Figure 3.8: The flowchart for yaw control setup
30
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
3.2 Issues Involved in Implementation of Free-Flight
The goal of this project is to enable controlled free-flight of the MAV, that is, the Giant
should not be constrained to the yaw-stand. The electronics therefore needs to be pack-
aged and mounted on the vehicle. The source of power for this electronics should also
be carried on the vehicle. Once the yaw-control is demonstrated in free-flight, it would
be desirable if the same setup can later be modified for additional pitch and roll control,
along with yaw control. The setup used for yaw control in the previous section (section
3.1.3) had all the basic components required for the 3-DOF control; it had an appropriate
sensor package (with 3 gyros, 3 accelerometers and 3 magnetometers), a microcontroller
to do the computations, and it was interfaced with the RC receiver so that control com-
mands can be sent to it remotely. The microcontroller used here is on a development
board which is designed for ease of use and not for least weight and size.
3.2.1 The Test Stand
The test stand used in the yaw control experiment allowed the use of microcontroller
development board (bulky but easy to use), as only the IMU and the servos were directly
mountedonthevehicle; restofthehardwarewaskeptonthetablejustbelowtheGiantand
was connected to the sensors and the actuators using long wires. A wireless telemetry link
was not required for this experiment as the vehicle was not free to fly. The development of
the miniature onboard stabilization system to enable free-flight of the Giant is discussed
in this section.
31
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
Intel Mote
One communication module used for this research is the Intel iMote, shown in figure 12. The iMote consists
of an ARM 7TDMI 32-bit microprocessor operating at 12 MHz, a wireless Zeevo Bluetooth radio capable of
700 Kbps on a 2.4 GHz frequency, and on-board data logging memory, and is capable of I
2
C, UART (serial),
and GPIO wired communications. The entire unit weighs 6.4 grams. This particular mote was chosen for
its powerful processor and high-bandwidth radio.
Transceiver Module
Figure 13. Transceiver Module.
An additional transceiver module, seen in figure 13, has been developed to complement the Intel Mote.
This module utilizes a serial-to-wireless module from Radiotronix, along with the required external com-
ponents. The maximum range of this module is approximately 500 meters, but has a lower maximum
bandwidth and does not include multi-node networking as advanced as the Intel Mote. For long range
vehicle communication outdoors, this module is the preferential communications module.
System Integration Configurations
The possibilities for system integration can be seen in figure 16. The arrows in figure 15 define components
that can be connected to share information. The modularity inherent in the design allows for several
configurations to suit a desired level of functionality. The actuator module includes the optional capability
to interface with a traditional RC receiver, should the Intel Mote bi-directional bandwidth be unnecessary.
A configuration for attitude control would include the IMU daughterboard, the actuator module, and a
communications board, which weighs a total of approximately 25 grams, seen in figure 14. The Actuator
module can be omitted to create a 15 gram remote inertial sensing and telemetry module, seen in figure 15.
IMU/Actuator/Intel Mote Combo
Figure 14. IMU/Actuator Board/Comm Board Configuration.
11 of 14
American Institute of Aeronautics and Astronautics
Figure 3.9: The avionics package for 3 DOF onboard controller
3.2.2 The Avionics Package
An avionics package (fig. 3.9) consisting of an IMU, three PIC 18F6722 microcontrollers
and a transceiver, designed by Conroy [27], is used for onboard control implementation.
This package, including the IMU and all other components weighs 30 grams. It consists
of 3 boards (sensor board, actuator board and the transceiver board) that can be snapped
together in different configurations.
3.2.3 System Performance
The autonomous yaw stabilization with pilot controlling the other degrees of freedom
was successfully demonstrated on the Giant in free-flight using this setup. The 3 DOF
attitude control, although based on the same basic principle as the yaw control setup, has
several significant differences. The main issue is that of sufficiently accurate estimation
of attitude states. The control can only be as good as the state estimation. While minor
errors in estimation of yaw heading are not critical, relatively small errors in pitch and roll
32
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
estimation are not acceptable, as the vehicle would then develop large linear velocities
and cease to hover. The 3 DOF system also involves the transformation of information
from body to navigation frame (section 4.1). This was not required for the yaw control
experiment as only one DOF was involved. We therefore need to work towards filter and
transformation algorithms before a 3 DOF control can successfully be implemented.
3.2.4 Requirements for the MAV Control Test-bed
The experience with the onboard avionics package helped in the evolution of a list of
features required in a setup for effective development of control laws and evaluation of
different algorithms. The test-bed is required to have the following basic features:
? Visibility of states; easy to debug: The main problem with the onboard avionics
package is that sufficient data is not being sent back to ground. It is therefore
difficult to locate the problem and to debug the system. It is required that the test-
bed allows several more intermediate states (e.g., raw sensor data, filtered data,
pilot inputs, servo commands generated) to be continuously monitored for faster
and effective evaluation of an algorithm.
? Easy re-programability: Re-programming the different microcontrollers on the
avionics package is a very time consuming job. Firstly, all the algorithms need to
be programmed in PIC-C (a variant of standard C language) and then optimized
for execution on a microcontroller. Secondly, a number of wires need to be con-
nected from the avionics package to the computer and power supply, each time a
microcontroller has to re-programmed. This makes the entire process very cumber-
33
CHAPTER 3. PRELIMINARY ONE DOF EXPERIMENTS
some and significantly reduces the number of different cases that one would like to
experimentally evaluate.
? Moreprocessingpower: The microcontrollers have very limited processingpower
andotherresources. Theprogramsthereforeneedtobecarefullyoptimizedtomake
sure they are executed as desired. Most of the times, it becomes difficult to locate
if the source of error is in the algorithm itself or in the way it has been coded for
the microcontroller. In order to first evaluate the algorithm, we would like to use a
test-bed with much more processing power.
? Safety features: The design of onboard avionics package did not incorporate suf-
ficient safety features. In case of malfunction of any electronics, there was no way
to bypass the setup and take over manual control of the vehicle. This resulted in
at least one major accident that led to some serious damage to Giant. It is there-
fore important that the test setup for such experiments incorporates better safety
features.
34
Chapter 4
Attitude Estimation
In order to implement a 3 DOF attitude stabilization and control system, the primary
task is to correctly determine and represent the attitude of the vehicle. The rotations in
three dimensional space are not commutative. It is therefore important to be consistent
with the conventions. Further, the attitude can be estimated using both the accelerometers
and the gyroscopes; but both have their limitations and therefore filtering algorithms are
necessary to get reliable attitude information. These issues are discussed in detail in this
chapter.
4.1 Attitude Representation
Inertial navigation uses several reference frames [28], which are shown in figure 4.1. We
restrict our discussion to the earth fixed navigation frame and the body fixed frame.
The origin of the navigation frame is located on the surface of the earth such that
the Oze axis is directly towards the center of the spherical Earth. The Oxe axis points
35
CHAPTER 4. ATTITUDE ESTIMATION
Figure 4.1: Reference frames used in inertial navigation
towards the local north and Oye points towards the local east to form a right-hand system.
The location of the origin of this coordinate is chosen so that it lies beneath the vehicle
at t = 0. Such a system is useful for defining the position of the vehicle with respect to
the launch point and orientation of the vehicle, and with respect to the gravity vector and
local north.
ThebodyaxessystemontheGiantisdefinedinaccordancewithstandardaerospace
convention. The center of gravity of the Giant is the origin of this system. The Oxb axis
goes out the nose of the vehicle, the Oyb axis is perpendicular to the Oxbzb plane and
points towards the right side, as shown in figure 4.2. The Ozb axis is the symmetry
axis and points downwards so as to form a right-hand system. Since the vehicle is axi-
symmetric about Ozb axis, an orange sticker is placed on one side of the vehicle and nose
is defined as being directly opposite to this orange sticker, as shown in figure 4.2.
36
CHAPTER 4. ATTITUDE ESTIMATION
Figure 4.2: The body fixed reference frame for the Giant
Since we do not plan to use a magnetic heading sensor for initial experiments, we
need not associate the Oxe and Oye axes with north and east directions. At t = 0, the
vehicle is on ground and is stationary. Hence, Ozb axis is aligned with Oze. Therefore,
to simplify interpretation of results, the Oxe axis is defined to be parallel to Oxb axis at
t = 0; similarly, Oye axis is defined to be parallel to Oyb at t = 0.
As the sensors are strapped to the body of the vehicle, the raw data is obtained in
the body frame. This needs to be converted into navigation frame in order to determine
the current position and attitude with respect to the initial states in earth-fixed reference
frame. There are two main methods of carrying out this transformation: (1) using Euler
angles, and (2) using quaternions (Euler parameters).
37
CHAPTER 4. ATTITUDE ESTIMATION
Figure 4.3: The Euler angle transformations
4.1.1 Euler Angles
The orientation of a given reference frame can be related to another reference frame by
three Euler angles: ?,?,?, or, the roll, pitch and yaw angles, respectively (fig. 4.2). In the
present application, Euler angles give the orientation of the Giant in space with respect to
the Earth. ? is called the heading or yaw angle, ? the inclination or pitch angle, and ? the
roll or bank angle. The orientation change is divided into three consecutive rotations, first
about the body z-axis by angle ?, then about the new body y-axis by angle ?, and finally
about the newer still body z-axis by angle ?. In figure 4.3 the x,y,z are the original body
axes, xprime,yprime,zprime are the new body axes after first rotation, xprimeprime,yprimeprime,zprimeprime are the new still body
axes after second rotation, and xprimeprimeprime,yprimeprimeprime,zprimeprimeprime are the final body axes after third rotation.
We now derive the transformation matrix for such a sequence of rotations. Before
the first rotation, the body-referenced coordinates match those of the navigation frame,
i.e.,vectorx0b =vectorx. For first rotation, yaw about z-axis by angle ?, the rotation matrix is given
38
CHAPTER 4. ATTITUDE ESTIMATION
by.
vectorx1b =
?
??
??
??
?
cos? sin? 0
?sin? cos? 0
0 0 1
?
??
??
??
?
vectorx0b = R(?)vectorx0b (4.1)
The transformation about z-axis does not modify the z-coordinate of the point. Other axes
are modified according to the basic trigonometry. Now apply the second rotation, pitch
about the new y-axis by angle ?.
vectorx2b =
?
??
??
??
?
cos? 0 ?sin?
0 1 0
sin? 0 cos?
?
??
??
??
?
vectorx1b = R(?)vectorx1b (4.2)
Finally, rotate (roll) the system about the newest x-axis by ?:
vectorx3b =
?
??
??
??
?
1 0 0
0 cos? sin?
0 ?sin? cos?
?
??
??
??
?
vectorx2b = R(?)vectorx2b (4.3)
This represents the location of the original point in the fully-transformed body-reference
framevectorx3b (henceforth called justvectorxb). The equivalent transformation can be written as:
vectorxb = R(?)R(?)R(?)
=
?
??
??
??
?
cos?cos? cos?sin? ?sin?
?sin?cos?+sin?sin?cos? cos?cos?+sin?sin?sin? sin?cos?
sin?sin?+sin?cos?cos? ?cos?sin?+sin?sin?cos? cos?cos?
?
??
??
??
?
vectorx
= R(?,?,?)vectorx (4.4)
All the transformation matrices including R(?,?,?) are orthonormal, i.e., their inverse is
39
CHAPTER 4. ATTITUDE ESTIMATION
equal to their transpose [28]. Therefore we can get the inverse transform as:
vectorx = R?1vectorxb = RTvectorxb (4.5)
Similarly, a transformation matrix for angular rates can be derived. Given the angular
rates in the body frame, the Euler rates can be computed using the current Euler angles as
follows [28]: ?
??
??
??
?
??
??
??
?
??
??
??
?
=
?
??
??
??
?
1 sin?tan? cos?tan?
0 cos? ?sin?
0 sin?cos? cos?cos?
?
??
??
??
?
?
??
??
??
?
p
q
r
?
??
??
??
?
(4.6)
The most significant drawback of Euler angle scheme is the existence of singularity when
pitch angle is ? 90 degrees, since at this angle both roll and yaw have similar effects.
Thus, in applications where one has to encounter high values of pitch angle, a different
way of measuring orientation is required.
4.1.2 Quaternions
Quaternions present a practical alternative to the Euler angles for attitude representation.
These have the advantage that no singularity is encountered for any orientation. Funda-
mental to this method is Euler?s theorem that body frame can be made to coincide with
navigation frame by a single rotation D about a fixed axis in space making angles A, B, C
40
CHAPTER 4. ATTITUDE ESTIMATION
with the navigation frame [28]. Four parameters can be defined, e0,e1,e2,e3 as follows:
e0 = cos D2 (4.7)
e1 = cosAsin D2 (4.8)
e2 = cosBsin D2 (4.9)
e3 = cosCsin D2 (4.10)
It can be verified that these four parameters are constrained by:
e20 +e21 +e22 +e23 = 1 (4.11)
The transformation matrix in equation (4.4) can now be written as:
R(?,?,?) =
?
??
??
??
?
e20 +e21?e22?e23 2(e1e2 +e0e3) 2(e1e3?e0e2)
2(e1e2?e0e3) e20?e21 +e22?e23 2(e2e3 +e0e1)
2(e0e2 +e1e3) 2(e2e3?e0e1) e20?e21?e22 +e23
?
??
??
??
?
(4.12)
The relation between Euler angles and Euler parameters can be derived as [28]:
e0 = cos?2 cos?2 cos?2 +sin?2 sin?2 sin?2 (4.13)
e1 = cos?2 cos?2 sin?2 ?sin?2 sin?2 cos?2 (4.14)
e2 = cos?2 sin?2 cos?2 +sin?2 cos?2 sin?2 (4.15)
e3 = ?cos?2 sin?2 sin?2 +sin?2 cos?2 cos?2 (4.16)
41
CHAPTER 4. ATTITUDE ESTIMATION
The rate equations for the four quaternion parameters, given the present value of these
parameters are [28]:
?e0 = ?12(e1p+e2q+e3r) (4.17)
?e1 = 12(e0p+e2r?e3q) (4.18)
?e2 = 12(e0q+e3p?e1r) (4.19)
?e3 = 12(e0r+e1q?e2p) (4.20)
4.2 Attitude Determination using Gyroscopes
The gyroscopes are strapped to the body and they give a direct measure of angular rates in
bodyframe, i.e., p, qandr. Thesebodyratesaretransformedintonavigationframe(Euler
rates) using equation (4.6). For this computation step, the values of Euler angles at the
previous instant are used (dead-reckoning) and the result is then numerically integrated to
obtain the new Euler angles. The algorithm is initialized with zero Euler angles when the
vehicle is on ground, to start with.
Gyro bias, defined as the output produced by gyro at rest, leads to drift in determi-
nation of orientation. Fixed bias, if uncompensated, leads to a constant rate of drift after
integration. However, the startup bias can be measured before take-off and corrected.
What matters then is bias stability. The typical drift performance of a ring laser gyro is
about 0.001 deg/hr, which is sufficient to get accurate position within about a mile for one
hour [29]. On the other hand, the recently developed very low cost and miniature Coriolis
vibratory gyroscopes (CVGs) have drift rates ranging from several degrees per hour to a
42
CHAPTER 4. ATTITUDE ESTIMATION
2.107
2.104
2.103
2.102
2.101
2.100
2.099
2.098
2.097
2.106
2.105
150010005000
Time (seconds)
Output (volts)
5 sec
30 
1 
Figure 4.4: Determining gyro bias
degree per second!
A gyro at rest is sampled for a period of time and the average of all the samples
collected gives the bias of the gyro. An experiment to demonstrate non-constant gyro bias
was conducted. The ADXRS150 gyroscope [30] from Analog Devices is used for this
experiment. Figure 4.4 shows three different lines corresponding to the averages taken
over 5, 15 and 30 seconds repeatedly in order to estimate bias. The gyro is sampled at a
rate of 100 samples per second using a 12 bit analog-to-digital converter. The calibration
factor for the gyroscope is 60 degrees per volt. This data is collected after the sensor has
been on for over 2 hours so that a stable temperature has been reached. This shows that it
is not possible to assign a single exact value to gyro bias as the output for zero angular rate
keeps changing over the time. Any choice of gyro bias will lead to drift in the integrated
43
CHAPTER 4. ATTITUDE ESTIMATION
result. Further discussion on the sources of gyro drift is included in the appendix to this
report.
4.3 Attitude Determination using Accelerometers
The accelerometers, strapped to the vehicle, measure the tilt by registering changes in
the component of gravity along their axes. Assuming, linear accelerations are negligible
compared to the acceleration due to gravity, the pitch and roll angles can be computed
from the accelerometers. Using transformation equations 4.4, 4.5, we get:
ax = ?gsin? (4.21)
ay = gsin?cos? (4.22)
az = gcos?cos? (4.23)
We therefore get:
? = sin?1 ?axg (4.24)
? = tan?1 aya
z
(4.25)
where, ax, ay and az represent the accelerations (due to gravity) measured by the three
orthogonal accelerometers aligned along the body x, y and z axes, respectively, and g
represents the acceleration due to gravity.
Aserious drawbackofthe accelerometeris itssensitivityto vibrations. Toeliminate
this, a low frequency filter is required which limits the bandwidth of the accelerometers
and introduces a phase delay in the filtered result.
44
CHAPTER 4. ATTITUDE ESTIMATION
4.4 Complementary Filter
We have seen that either gyroscopes or accelerometers can be used to determine atti-
tude. However, each sensor has serious limitations when used alone; a gyroscope has
long term divergence problem due to drift (bad for measuring low frequency rates) and
an accelerometer has bandwidth problem due to low pass filter (bad for measuring high
frequency rates). These limitations are demonstrated by the results of the experiments
described in the next section.
4.4.1 The Pendulum Experiment
A thin aluminum beam is suspended from the rotational axis of a potentiometer to form
a pendulum. The potentiometer used is a contactless Hall effect based angle sensor [31].
This potentiometer gives analog output proportional to the pendulum angle within a range
of ?40 degrees. The output of the potentiometer is nonlinear outside this range. The
IMU discussed in section 5.3.1 is mounted on the aluminum beam 4.5. The data from the
gyroscope is integrated to get the attitude. We also get attitude from the accelerometers
using equation 4.24. The data from the accelerometers and gyroscopes on the IMU can
now be compared with the attitude given by the potentiometer (the true angular position
of pendulum).
The IMU is setup with the bluetooth transmission of sensor data. The potentiometer
is sampled separately at a rate of 500 Hz using a 12-bit analog-to-digital converter. All
data is displayed on a chart in LabVIEW. To filter the noise, 5 potentiometer readings are
read at a time and averaged. Similarly, a moving average of last 10 samples is used on
45
CHAPTER 4. ATTITUDE ESTIMATION
Figure 4.5: Pendulum Experiment Setup
the accelerometer data. The angle data from the gyroscopes is quite smooth because of
integration; so no filtering is required for the gyroscope.
In the first case, the IMU is mounted on the axis of rotation. This makes sure
that the accelerometer is not subjected to any linear accelerations and it thus measures
only the change in the component of gravity along its axis (hence the angular position of
pendulum). The pendulum is now given a push by the hand and the data from 3 different
sensors, i.e., the potentiometer, the gyroscope and the accelerometer is recorded. This is
shown in figure 4.6. The accelerometer data shows a good match with the potentiometer
data. The attitude from the gyroscope is seen to drift away from the true attitude (from
potentiometer) with time.
The IMU is placed at a distance of 14 inches away from the axis of rotation on the
pendulum for the second test. The results for this test are shown in figure 4.7. When the
pendulum is held at some attitude with hand, the accelerometer is seen to give correct
attitude, but when in motion, it is no longer able to give correct attitude estimate. This
is because now it is subject to linear acceleration along with changes in the magnitude
of gravity along its axis. In fact, when the pendulum is allowed to swing freely, the ac-
46
CHAPTER 4. ATTITUDE ESTIMATION
! " # $ %
&?(
&)!
&)(
&!
(
!
)(
)!
*+,-./0-12
3456-.
/7-52
89:-4:+9,-:-;
311-6-;9,-:-;
<=;9019>-
Figure 4.6: Performance of accelerometer and gyro for attitude estimation (on axis)
celerometer does not measure any angle. This is because the linear accelerations exactly
cancel the change in the magnitude of the gravity along its axis (in the linear approxi-
mation, both equal to g? in different directions; where ? is the angle of the pendulum
with the vertical). The attitude from the gyroscope is again seen to drift away from the
true attitude with time. The pendulum was given large oscillatory perturbations by hand
towards the end of experiment (as seen towards the right end of figure 4.7). We therefore
notice that the attitude form the accelerometers is way off during such situations, i.e., in
the presence of high linear accelerations, or vibrations.
47
CHAPTER 4. ATTITUDE ESTIMATION
! "# "! $# $! %# %!
&?#
&(#
&)#
&$#
#
$#
)#
(#
*+,-./0-12
3456-.
/7-52
89:-4:+9,-:-;
311-6-;9,-:-;
<=;9019>-
Figure 4.7: Performance of accelerometer and gyro for attitude estimation (off axis)
4.4.2 Design of Complementary Filter
The complementary filter is used to fuse the outputs of different sensors with comple-
mentary noise characteristics [32]. In this case, rate gyros provide a good high frequency
estimate of attitude and the accelerometers provide a good low frequency estimate, as
discussed before. The best estimate of the orientation is thus obtained as the sum of the
signals from two measurement branches as shown in figure 4.8. The accelerometers feed
output signal into the filter Ga(s), which provide the contribution of the accelerometer
branch to the low frequency estimate of attitude. The output of rate gyros is fed into the
filter Gg(s), which provides the high frequency estimate of attitude.
In order to have constant amplification of the entire system, the filter transfer func-
48
CHAPTER 4. ATTITUDE ESTIMATION
Acelrometr
Ha(s)
Rate Gyro
Hg(s)
Filter
Ga(s)
Filter
Gg(s)
+
!
!
& Estimate
Plant
Figure 4.8: The complementary filter schematic
tions Ga(s) and Gg(s) must be chosen according to [32]:
Ha(s)Ga(s)+sHg(s)Gg(s) = 1 (4.26)
where, Ha(s) and Hg(s) denote transfer functions of the accelerometer and gyro respec-
tively. We assume the sensors to be ideal and hence use:
Ha(s) = Hg(s) = 1 (4.27)
This is assumption is valid because the dynamics of sensors is much faster than that of
the vehicle itself. Therefore, equation (4.26) is reduced to:
Ga(s)+sGg(s) = 1 (4.28)
A second order filter with a double pole is now selected:
Ga(s) = 4s+1(2s+1)2 (4.29)
Gg(s) = 4s(2s+1)2 (4.30)
Here, the transfer function Ga(s) works as a first order low-pass filter (-20 db per
decade) on the signal coming from the accelerometer (fig. 4.9). The other transfer func-
tion, Gg(s) works as a second order high pass filter with respect to the orientation (-40 db
per decade), on the signal from the gyroscope (fig. 4.10).
49
CHAPTER 4. ATTITUDE ESTIMATION
M
a
g
n
i
t
u
d
e
 
(
d
B
)
P
h
a
s
e
 
(
d
e
g
)
Frequency (rad/sec)
Figure 4.9: Bode plot of the accelerometer filter transfer function (low pass)
50
CHAPTER 4. ATTITUDE ESTIMATION
M
a
g
n
i
t
u
d
e
 
(
d
B
)
P
h
a
s
e
 
(
d
e
g
)
Frequency (rad/sec)
Figure 4.10: Bode plot of the gyroscope filter transfer function (high pass)
51
CHAPTER 4. ATTITUDE ESTIMATION
4.4.3 Performance of Complementary Filter
The pendulum experiment described in section 4.4.1 is now repeated with the comple-
mentary filter designed above. The results for this case are shown in figure 4.11 (no
accelerometer data) and figure 4.12 (with accelerometer data). We see that although the
attitudes from both the accelerometer and the gyroscope do not match very well with the
true attitude (potentiometer), for some or the other region of the chart, the attitude from
the complementary filter shows a very good match for all regions. It takes care of both
the drift in the gyros (low frequency phenomenon) and the linear accelerations in the ac-
celerometers (mostly due to vibrations, a high frequency phenomenon). Close-up views
of of different regions of this plot are shown in figures 4.13, 4.14.
4.5 Position Determinition using INS
Linear position determination is a much harder problem than attitude estimation. Firstly,
there are accelerometer instrument errors such as bias stability, scale factor stability, non-
linearity and misalignment. Inertial grade accelerometers must keep these errors to a few
micro-g to get an accuracy of 1 mile/hr. Since position is obtained by double integrating
acceleration, leads to a position drift error that grows quadratically in time. It is there-
fore especially critical to accurately estimate and eliminate any persistent bias errors. The
second critical cause of error in position measurement is error in the orientation deter-
mined in the gyros. Since the INS interprets the direction of the measured acceleration
according to the computed orientation of the platform, and error in this computer orienta-
tion will cause it to integrate the accelerations in the wrong direction, thus deviating from
52
CHAPTER 4. ATTITUDE ESTIMATION
!" #" $" %" &" ?" ("
)!""
)&"
"
&"
!""
*+,-./0-12
3456-.
/7-52
89:-4:+9,-:-;
<9,=6-,-4:>;?.@+6:-;
A?;9019=-
Figure 4.11: Performance of complementary filter for attitude estimation (no accelerom-
eter)
53
CHAPTER 4. ATTITUDE ESTIMATION
!" #" $" %" &" ?" ("
)!""
)&"
"
&"
!""
*+,-./0-12
3456-.
/7-52
89:-4:+9,-:-;
<9,=6-,-4:>;?.@+6:-;
311-6-;9,-:-;
A?;9019=-
Figure 4.12: Performance of complementary filter for attitude estimation (with ac-
celerometer)
54
CHAPTER 4. ATTITUDE ESTIMATION
!" !# !! !$ !%
&?""
&("
"
("
?""
)*+,-./,01
2345,-
.6,41
789,39*8+,9,:
;8+<5,+,39=:>-?*59,:
200,5,:8+,9,:
@>:8/08<,
Figure 4.13: Complementary filter performance (accelerometer saturation)
the true course of the vehicle. More importantly, the cancellation of gravity will be per-
formed imperfectly by the navigation computer. This will cause a horizontal acceleration
component to be erroneously added to the navigation-frame acceleration vector. Thus,
even gyros have a more critical accuracy requirement in order to get an accurate position
estimate using INS.
4.6 IMU Aiding and Kalman Filtering
Although figure 2.5 shows how IMU is theoretically self-sufficient for the purpose of both
attitude and position determination, we now realize that practically it can only be reliably
used for attitude determination (provided linear acceleration are negligible compared to
55
CHAPTER 4. ATTITUDE ESTIMATION
!! !" !# !$ %&
?"&
?!&
&
!&
()*+,-.+/0
1234+,
-5+30
678+28)7*+8+9
:7*;4+*+28<9=,>)48+9
1//+4+97*+8+9
?=97./7;+
Figure 4.14: Complementary filter performance (free oscillations)
56
CHAPTER 4. ATTITUDE ESTIMATION
acceleration due to gravity). Therefore, IMUs are normally one component of a naviga-
tion system. Other systems such as GPS (used to correct for long term drift in position),
a barometric system (for altitude correction), or a magnetic compass (for attitude correc-
tion) compensate for the limitations of an IMU [33]. Note that most other systems have
their own shortcomings which are mutually compensated for.
In case of accelerometers and gyroscopes, there is a clear distinction in the fre-
quency range where each gives a reliable estimate of attitude. We are therefore able to
exploitthispropertyanddeviseacomplementaryfilter. Wheremanydifferentsystemsare
used, the region of reliability can always not be marked as clearly in terms of frequency or
magnitude. Such situations need more advanced filtering algorithms, like Kalman filter,
that can optimally fuse all the available data, utilizing sensor and their noise characteris-
tics [34].
57
Chapter 5
The Ground Based Setup
5.1 PID Configuration
We need to find a suitable control algorithm that can be used for autonomous flight of the
Giant, and then build a test-bed for its implementation and performance evaluation. A hu-
man pilot applies lateral cyclic in order to control the roll degree-of-freedom. Similarly,
one applies longitudinal cyclic or vane input to control pitch or yaw degrees-of-freedom,
respectively. For a full-envelope flight, it is important to consider coupling between dif-
ferent axes and nonlinear dynamical effects; thus a SISO (single input, single output) PID
framework is clearly not suitable. But, for a near-hover flight, roll, pitch and yaw can
be treated as uncoupled and a linear SISO PID controller is expected to give satisfactory
results [19]. The schematic of the PID control scheme that we plan to implement on the
Giant is shown in figure 5.1.
The inner attitude-control loop (higher bandwidth) forms the core of the controller
anddirectlyinteractswiththevehicletoachievetherequiredattitudes. Theoutertranslation-
58
CHAPTER 5. THE GROUND BASED SETUP
Helicopter/MAV 
Dynamics
Sensors
u,v,w
p,q,r
ref
!
,!"#
pd
u
long
lat
!
Attitude 
Control 
Loop
(Inner)
x,y,z
Translation
Cotrol
Lop
(Outer)
Desired
Positon
Desired
Velocity
+
Velocity Estimate
Body Rates stiate
Atitude Estimate
Positon stiate
PID Control
Figure 5.1: Schematic of PID control for autonomous flight of Giant
control loop (lower bandwidth) is the secondary controller, which takes translation com-
mands from the user and generates equivalent attitude commands for the inner loop
(which in turn controls the vehicle).
Next, we need to look for appropriate sensors to implement these two control loops.
The attitude-control loop needs the sensors that can provide information regarding the 3-
DOF attitude of the vehicle, and the translation-control loop additionally requires the
3-DOF position information. In the present work, we focus on the attitude control loop of
the controller and discuss in detail how to obtain a good estimate of attitude of the vehicle
using low cost sensors. The detailed schematic of this controller is shown in figure 5.2.
59
CHAPTER 5. THE GROUND BASED SETUP
Helicopter/MAV 
Dynamics
Sensors
p
q
r
ref
!
!
ref
ref
q
K
!
!
p
r
K
!
ped
u
long
lat
u
Figure 5.2: Schematic of attitude control loop (inner-loop)
5.2 Overview of the New Test-Bed
The design of the new test-bed, incorporating the features listed in section 3.2.4, is now
discussed. This is a ground based setup with the main idea to do minimal work onboard
and to transfer all the complex jobs to the ground station. Ground station can employ
much faster processors and can help graphical monitoring of much more data than what
can be done using onboard microcontrollers. The architecture for such a system is shown
in figure 5.3.
Here, only the sensors and the actuators are placed on the vehicle. The sensors send
the raw sensed data to the ground station using a wireless transmitter. All the processing
is done on ground and the final command are linked back to the vehicle using the wireless
equipment.
60
CHAPTER 5. THE GROUND BASED SETUP
Receiver
Computer
(Processing)
Transmitter
Receiver
Sensors and
Telemetry
The Flying Platform
Wireless
Downlink
Wireless
Uplink
The Ground Station
Figure 5.3: Architecture of the ground based test-bed
61
CHAPTER 5. THE GROUND BASED SETUP
One of the most important requirement for such a system is redundancy. That is,
should the control system fail, the Giant should revert back to normal manual controls.
The wireless links employed need to be very reliable, as any communication failure could
lead to loss of computer control of flight. Since the standard R/C transmitter-receiver
is known to provide very reliable communication, is inexpensive, easily available and
redundancy can be easily built using it, hence it was decided to use the same for uplinking
the commands from the ground station. As mentioned earlier in section 2.2.2, the input
pin on the data port of the transmitter can be used to transmit data received from a source
external to transmitter. The servos and the speed controller on the Giant (or any other
MAV in use) are connected to the same R/C receiver as in the case of normal manual
flight configuration.
5.3 Subsystems of the Setup (Hardware)
This setup consists of 3 main subsystems (fig. 5.3); first, consisting of the onboard sensors
and the wireless transmission of this data; second, reception of this data on ground and
its processing to generate the commands for the actuators; and third, consisting of the
interface with the R/C transmitter to uplink these commands to the Giant and to read pilot
inputs.
5.3.1 The Sensors and Telemetry
A sensor-board with Bluetooth data transmission capability was obtained from Spark Fun
Electronics [35]. It consists of a MMA7260Q single IC triple axis accelerometer [36]
62
CHAPTER 5. THE GROUND BASED SETUP
The 3 orthogonal 
ADXRS150 Gyros
The MMA7260Q
triple-axis
 accelerometer
 BlueSMiRF 
Bluetooth
transceiver
Figure 5.4: The wireless IMU from Spark Fun Electronics [35]
from Freescale and three ADXRS150 gyroscopes [30] from Analog Devices, mounted
along three orthogonal axes as shown in figure 5.4. This sensor-board weighs about 22
grams. The analog data from these six sensors is sampled by PIC16F88 microcontroller
and it transmitted to ground through an onboard BlueSMiRF Bluetooth transceiver [37].
The firmware on microcontroller allows for selection of appropriate data channels
to be sampled and the range for accelerometers, as described in the datasheet [38]. Six
channels corresponding to sampled data from the 3 accelerometers and 3 gyroscopes are
selected from the firmware menu. A range of ?2g is selected for accelerometers. The
gyroscopes have a range of ?150 deg/sec. All the analog channels are sampled using a
10-bit ADC. Therefore, each sample consists of 2 bytes in the data-stream. The lower
10 bits are occupied by the sample and the upper 6 bits read as zeros. Each data packet,
consisting of one sample each from all 6 channels, starts with an ?A, then has 12 bytes
corresponding to readings from 6 sensors and concludes with an end byte ?Z. Therefore,
14 consecutive bytes, starting with an ?A? and ending with a ?Z?, make a packet. The
63
CHAPTER 5. THE GROUND BASED SETUP
0 00 00 0X X
X X   XX   X XX X
Head
?A?
Tail
?Z?
1 sensor eading
Upper 
Byte
Lower 
Byte
? readings from 5 other sensors?
The uper 6 bits
(zero)
The 10 bit sensor dat
Figure 5.5: The structure of a sensor data packet
structure of the packet is illustrated in figure 5.5. A data rate of about 230 packets/second
is achieved using the 57.6 kbps bluetooth wireless link. A bluetooth dongle is used on the
ground station PC to receive the data from the wireless IMU.
5.3.2 The R/C Transmitter Interface
The generation and sampling of high frequency pulses, as required by the transmitter for
communication(discussedin section2.2.2), istimecritical andcannotbedirectlydoneby
a PC running a normal non-real-time operating system (e.g., MS Windows, Linux, or Mac
OS). We, therefore, either need a PC with real-time operating system, or a microcontroller
to interface the transmitter with a PC running a non-real-time operating system. The latter
option is chosen, as it simplifies application development using LabVIEW and is also
faster and cheaper to implement. The microcontroller communicates with the PC using
serial port (RS232) and with the transmitter using PPM pulses (fig. 2.12), as shown in
figure 5.6.
64
CHAPTER 5. THE GROUND BASED SETUP
PPM Signals
?00101001?
Serial Data (RS232)
PC with LabVIEW
MicrocontrollerTransmitter
Figure 5.6: The interface of the transmitter with the PC
The radio control system used has 6 channels. Therefore, each frame of PPM (dis-
cussed in section 2.2.2) consists of 6 pulses corresponding to each of these channels. The
system can easily be modified to use transmitters with 4, 8 or any other number of chan-
nels. The transmitter is used both for sending commands to the vehicle, as well as, as an
input device, i.e., to get pilot inputs through the sticks. Therefore, the microcontroller in
this interface does two jobs:
1. Writing data to transmitter: The PC sends a stream of six 8-bit numbers to the
microcontroller over the serial port, corresponding to the width of each of the six
pulses in a PPM frame. For servos to hold position and for the effective working
of the system, a new frame is required every 20 ms. The microcontroller is pro-
grammed to continue to repeat the same PPM frame till data for a new frame is
received from the PC. In order to synchronize, the decimal number ?255? (a byte
with all 1?s) is sent by the PC before every frame. Once the microcontroller receives
this synchronization byte, the next 6 bytes are read as data corresponding to the 6
channels, respectively.
2. Reading data from transmitter: The data from the transmitter is continuously
65
CHAPTER 5. THE GROUND BASED SETUP
sampled and the width of each pulse in a frame is calculated by the microcontroller.
This data is then sent to the PC as six 8-bit numbers over the serial port, corre-
sponding to each of the six channels. A pulse of width larger than 2.5 ms marks the
beginning of a new frame. For communication with PC, the microcontroller first
sends a byte with all bit as 1?s (for synchronization) and then 6 bytes corresponding
to the 6 channels of data, in order.
Figure 5.7 shows the flowchart for the microcontroller code. The PIC-C code is included
in the appendix to this report.
5.3.3 The Virtual Instrumentation on PC
The Virtual Instrumentation (VI) on the PC, using the National Instrument?s LabVIEW
software [39], forms the core of this experimental setup and the rest of discussion will
primarily concentrate on its implementation. The sensor data is received, processed and
commands for the transmitter are generated through this VI. Almost all the processing is
therefore done on the ground station PC using this VI. This provides a very efficient way
to make changes to the controller and conduct different experiments.
5.4 Organization of the Virtual Instrument (Software)
The in-house developed VI can be divided into 3 distinct modules as discussed below.
These modules communicate using a set of well-defined protocols, i.e., the type and for-
mat of input to, and output from each module is defined. This allows for replacement or
up-gradation of any of the module without disturbing the working of rest of the VI. Figure
66
CHAPTER 5. THE GROUND BASED SETUP
Figure 5.7: The flowchart for the transmitter interface code
67
CHAPTER 5. THE GROUND BASED SETUP
Receiver 
Module
Sensor Data
from Receiver
Control 
Module
Transmitter 
Module
3 body rates and 3
body accelerations
The 4 ?stick?
positions
The actual servo
positions required
Fixed Protocol
To
Transmitter
Figure 5.8: The 3 modules of the VI and their interfaces
5.8 shows a schematic of the interface between these modules.
5.4.1 The Receiver Module
The receiver module is coded as a separate sub-VI. It reads the data from the Bluetooth
receiver via serial port. The data is received as a packet of 14 bytes (discussed in section
5.3.1). The receiver module makes use of the packet delimiters, ?A? and ?Z?, to check for
validity of data. If the packet does not have appropriate delimiters, it is discarded and
the module waits for next valid packet. After successful validity check, the 12 middle
bytes of a packet are fused together, taken 2 at a time to retrieve the 6 sensor readings
of 10-bit each. The raw sensor data thus obtained is converted into meaningful physical
quantities, i.e., angular body rates in radians per second and linear accelerations in gs,
using the calibration data, and passed on to the processing module. The working of the
receiver module is shown in figure 5.9.
68
CHAPTER 5. THE GROUND BASED SETUP
Fuse 2 bytes at a time
to get sensor readings
Use calibration to get
 physical quantities
Read Data
from serial port
Is it valid?
Pass these to
Processing Module
Yes
No
Figure 5.9: The receiver module
69
CHAPTER 5. THE GROUND BASED SETUP
100
100100
1000
0 0
0
Throttle
Longitudinal Cyclic
(Pitch)
Lateral Cyclic
(Roll)
Vane (Yaw)
Figure 5.10: The definition of stick positions
5.4.2 The Processing Module
The processing module first transforms the data received from the receiver module into
the navigation frame (section 4.1). The transformed data is then used to obtain the body
attitude using a complementary filter. Finally, a PID controller computes the desired
stick positions, or the amount of cyclic and anti-torque, and passes on this information to
the transmitter module. The value of stick positions correspond to the physical positions
where the sticks of the transmitter should be in order to generate the desired output. These
are normalized on a scale of 0 to 100; 0 corresponding to one extreme position of stick
and 100 to the other extreme. The convention adopted is that the increase in the value of
stick position should lead to increase in thrust or yaw, pitch, roll attitudes of the vehicle,
as shown in figure 5.10
The stick positions discussed above may or may not have a one-to-one relation
with servo channel pulse-widths, as explained in section 2.2.2. The distinction between
70
CHAPTER 5. THE GROUND BASED SETUP
servo positions and stick positions is important. The idea is that the controller (or human
pilot) is interested in issuing generic lateral cyclic, longitudinal cyclic, collective and anti-
torque commands. The vehicle dynamics or controller design does not depend on how
these commands are conveyed to the vehicle or how the servos are actually connected
to the swashplate. Therefore, the processing module essentially remains the same even
when different MAVs or transmitters are used. These effects are isolated in the form of
transmitter module. The transmitter module takes care of the variations in the way these
commands are actually implemented on a certain design of an MAV.
5.4.3 The Transmitter Module
The transmitter module sub-VI converts the stick positions received from the processing
module into actual commands for different servo channels and writes it to the transmitter
via the microcontroller connected to the serial port (section 5.3.2). This sub-VI also reads
the pilot inputs (the servo positions from the transmitter output), translates them into stick
positions and communicates these back to the processing module. The transmitter is thus
used both as an input and an output device.
Once the transmitter is transmitting information received on the data port through
the microcontroller, it (obviously) stops transmitting the stick positions directly. Very
often, it is required that the pilot still control one or more channels manually, when selec-
tive channel autonomy is implemented (semi-autonomous vehicle). For example, in our
experiments, the throttle stick position is controlled manually by the pilot and is not au-
tonomously controlled because of lack of altitude sensor. This is implemented by reading
71
CHAPTER 5. THE GROUND BASED SETUP
thethrottlestickpositionfromthetransmitterandsendingthatdatabacktothetransmitter
as output by the processing module. The same concept is also used for implementing the
?throttle curve?, limits on motion of the cyclic servos, and to receive attitude commands
from the pilot (via the cyclic sticks) in the attitude follow mode of control.
5.5 Implementation of the VI
The sensor data is received and processed (complementary filter) at a much higher sam-
pling frequency (230 Hz) than the output frequency or the servo bandwidth (50 Hz). Two
parallel loops are therefore used in the implementation of the VI (fig. 5.11); one for read-
ing sensor data and state estimation, and the second for PID controller and RC transmitter
interface. While the first loop is a ?while loop? running at the maximum possible rate,
determined by the sampling rate of sensor data, the second loop is a ?timed loop? and runs
once in every 20 ms as the servo update is required only at that rate. This makes sure
that the processing resources are optimally utilized. These two loops are analogous to the
state equation and the output equation in the state-space form of control. It is therefore
appropriate to refer to the first loop as the ?state estimation loop? and to the second as the
?output loop?.
The code can thus be divided into 3 sections, i.e., 1) tasks done outside both these
loops for initialization, 2) the tasks done under the first loop, and 3) the tasks done under
the second loop.
72
CHAPTER 5. THE GROUND BASED SETUP
Initialize the IMU
Send ?g? to IMU,
Estimate bias
State Data
(Attitudes and Rates)
State Estimation Loop
(?while lop? at ~230Hz)
Has nsr module and
Compleentary filter
Output Loop
(?timed lop? at 20Hz)
Has PID cntroler and
Transmiter mdule
Used only once
Two parlel ops
 run contiuosly
Figure 5.11: The implementation of the VI
5.5.1 Initializing the IMU
The first task of the VI is to send the command to the IMU to start sending data. The
ASCII character ?g? is sent to the IMU, as specified in the IMU datasheet [38]. The data
from 6 sensors is now made available by the sensor module. The MEMS sensors are quite
sensitive to temperature. It is therefore important to wait for the temperature of sensors to
stabilize before bias estimation. Every time the IMU is powered on, the analog-to-digital
convertors, and other electronics need some time to stabilize. The first 5000 data packets
received are thus discarded.
Accurate determination of gyroscope bias (the gyro output for zero angular rate) is
critical, as any error in this will lead to large drift in the estimation of attitude over long
time (without filtering). The bias of a gyroscope is not constant between different runs.
Therefore, the bias needs to be estimated every time before the experiment. The IMU is
73
CHAPTER 5. THE GROUND BASED SETUP
kept stationary and the next 5000 samples from each of the 3 gyros are averaged to get
their biases. Further discussion on gyro bias is presented in the appendix to this report.
5.5.2 State Estimation Loop
State estimation loop is responsible for continuously sampling the IMU, and then filtering
the raw sensor data to provide the output loop with required states, viz. the roll, pitch and
yaw attitudes. The sensor data is read through the sensor module (described above), and
the angular rates and translational accelerations are made available in navigation frame.
The angular rates are then converted into inertial frame (section 4.1) and the accelerations
into roll and pitch attitudes (section 4.3). These are finally processed by the complemen-
tary filter (section 4.4) to provide the attitudes.
5.5.3 Output Loop (PID controller)
The output loop uses the transmitter module to read the pilot inputs (via the sticks). The
attitudes and body rates are made available by the state estimation loop. The pilot inputs
and attitudes are then used along with the user supplied gains to generate output based on
the selected mode, as shown in figure 5.12. The 3 modes of operation are as follows:
1. Loop-back mode: In this mode all the data received through the transmitter module
(pilot stick positions) is directly wired back to the transmitter module. It is useful
to check if the transmitter interface is working correctly.
2. Attitude hold mode: This mode uses the gains supplied by the user to generate the
cyclic and tail-rotor commands in order to keep the attitudes close to zero (PID
74
CHAPTER 5. THE GROUND BASED SETUP
Angular body rates of GiantAtitude of the Giant
State dat from ?state stimation lop? 
The mode of Operation
Proprtional nd 
derivative gains
Pilot stick inputs
(throtle, desired atitude)
User Inputs
PID Controller and low-pass filter
Transmiter Module
Figure 5.12: The output loop
controller). The Giant is thus expected to hover in this mode.
3. Attitude control mode: It is similar to the attitude hold mode, except that the pilot
can now demand roll and pitch attitudes through the cyclic sticks on the transmitter.
The controller will make the Giant follow those attitude commands.
The gains can be adjusted by the user anytime during the experiment. The servos
have a limited bandwidth. The frequency of the output signal should be below 5Hz for
effective working of servos. A low pass filter is therefore incorporated in the output of
PID controller.
75
Chapter 6
Results and Discussion
6.1 Vibrations and Sensor Saturation
The IMU is mounted on the Giant as shown in figure 6.1. During the initial test flights, the
vibrations were found to lead to saturation of gyroscopes aligned with the body x and y
axes as shown in figure 6.2. The reliability of attitude estimation is severely affected due
to saturation of sensors. The vibrations are isolated from the IMU by proving a padding
between the LiPo battery and the IMU. Different blade geometries are also seen to affect
the vibration level. Typical gyro data with no saturation is shown in figure 6.3
6.2 Manual Flight
In order to fly the Giant with PID controller, it is first required to get an estimate of the
gains required. In order to gain confidence in the system and obtain an estimate of gains
required, a manual instrumented hover flight is conducted. The data from the IMU and
76
CHAPTER 6. RESULTS AND DISCUSSION
LiPo Batery
Foam Pading
IMU
Figure 6.1: IMU mounted on the Giant with foam padding
Double-click 
here to edit 
text.
Gyroscope (x-axis)
Figure 6.2: Angular rate about body x-axis during flight (gyro saturated)
77
CHAPTER 6. RESULTS AND DISCUSSION
Gyroscope (x-axis)
Figure 6.3: Angular rate about body x-axis during flight (gyro not saturated)
the pilot stick inputs are recorded during the flight. Figure 6.4 shows the pitch attitude
as estimated by the accelerometers, gyroscopes and the complementary filter. We see
that the attitude is maintained within ? 0.1 radian. The time history of pilot longitudinal
cyclic inputs during this flight is shown in figure 6.5.
From this data, it can be seen that the pilot effectively uses a gain of around 20%
to 25% stick range per radian. It can also be seen that cyclic is applied at a maximum
frequency of about 2Hz by the pilot. Based on the complementary filter data, output
proportional to the attitude, with a gain of 25% stick range per radian is computed and
plotted in figure 6.6. A low-pass filter is also incorporated in the output of controller so
that the servos are actuated at a frequency similar to that used by a human pilot.
78
CHAPTER 6. RESULTS AND DISCUSSION
Figure 6.4: Pitch attitude estimate during manual flight
Figure 6.5: Longitudinal cyclic during manual flight
79
CHAPTER 6. RESULTS AND DISCUSSION
Figure 6.6: Comparison of computed longitudinal cyclic with actual pilot command
6.3 Controlled Flight Results
The results for the controlled hovering flight of the Giant are presented next. The roll,
pitch and yaw of the vehicle are controlled by the autonomous controller. Throttle is the
only input provided by the pilot. A dual slope is used on the throttle curve to reduce the
sensitivity near the hovering RPM of rotor. Once the throttle exceeds 60% stick range, a
slope of 0.4 is used in place of unity, to enable finer control of rotor RPM. As can been
seen in figure 6.7, both the pilot-input and the controller-output match when throttle is
below 60% stick range, but the controller output increases by only 40% of pilot-input
beyond that.
Yaw control is provided by both the onboard (off-the-shelf) gyro as well as the
control system. The off-the-shelf gyro provides the basic derivative control and it is as-
sisted by a proportional control implemented in LabVIEW. The off-the-shelf gyro is left
80
CHAPTER 6. RESULTS AND DISCUSSION
0
10
20
30
40
50
60
70
80
2 32 42 52 62 72
Time (sec)
T
h
r
o
t
l
e
 
(
%
 
s
t
i
c
k
 
r
a
n
g
e
)
Controler Output
Pilt Iput
Figure 6.7: Dual-curve in throttle to reduce sensitivity near hover RPM
in place, because in case the flight mode is switched to manual (or if there is a failure
of autonomous control), it would not be possible to control the Giant without some level
of yaw stabilization. A fixed gain of 30% stick range per radian is used for the yaw axis
for all experiments. It is important to note that from the Euler-angle transformation point
of view, the yaw attitude is not important as it does not affect the roll or pitch attitudes
(this is not true for roll and pitch though; roll affects both pitch and yaw, and pitch affects
yaw (see equation 4.6)). However, dynamics in yaw may still influence the roll and pitch
motion due to the presence of coupling terms in the dynamics of the Giant.
We follow the Ziegler-Nichols method of tuning the PID controller [40]. Ziegler
andNicholssuggestedrulesfortuningPIDcontrollersbaseonexperimentalstepresponse
or based on the value of proportional gain that results in marginal stability when only
proportional control action is used. Ziegler-Nichols tuning rules give an educated guess
81
CHAPTER 6. RESULTS AND DISCUSSION
Type of Controller Kp Ti Td
P 0.5Kcr ? 0
PI 0.45Kcr 11.2Pcr 0
PID 0.6Kcr 0.5Pcr 0.125Pcr
Table 6.1: Ziegler-Nichols Tuning Method
for the gain values and provide a starting point for fine tuning, rather than give the final
settings for the gains in a single shot. We use the second Ziegler-Nichols method, i.e., the
one based on the value of proportional gain that results in marginal stability, for tuning
the PID controller for autonomous flight of Giant [40].
6.3.1 Ziegler-Nichols PID Tuning
According to the Ziegler-Nichols second method of PID gain tuning [40], we we increase
the proportional gain, Kp, upto a critical value Kcr at which the output exhibits sustained
oscillations or marginal stability. Once the critical gain Kcr and the corresponding period
Pcr areexperimentallydetermined, ZieglerandNicholssuggestedthatwesetthevaluesof
the proportional gain Kp, integral time Ti, and derivative time Td according to the formula
given in table 6.1.
The resulting controller, Gc(s), in s-domain is given by:
Gc(s) = Kp
parenleftbigg
1+ 1T
is
+Tds
parenrightbigg
(6.1)
In terms of gains, the resulting controller action (in time domain) is:
Gc(t) = Kpe(t)+Ki
Z t
0
e(?)d?+Kd dedt (6.2)
82
CHAPTER 6. RESULTS AND DISCUSSION
where, e(t) is the error signal given by:
e(t) = setpoint?measurement(t) (6.3)
We therefore see that the integral gain, Ki, and derivative gain, Kd, are related to the
integral time, Ti, and derivative time, Td, as follows:
Ki = KpT
i
(6.4)
Kd = KpTd (6.5)
Determining Critical Gain and Critical Period
As required for the Ziegler-Nichols gain tuning method, we first conduct experiments to
determinethecriticalgainandthecorrespondingcriticalperiod. Asmentionedbefore, we
are primarily interested in tuning the roll and pitch loops. For simplicity, the yaw gain is
keptfixedforallexperiments. Thecriticalgainsforboththerollandpitchaxesisexpected
to be different because of the non-symmetric servo-swashplate assembly, i.e., the two
swashplate servos need to be deflected by different amounts to get equal longitudinal and
lateral cyclics. We apply the Ziegler-Nichols method to this two axes system as follows.
The idea is to keep the system well-tuned in one axis at a time, and marginally stable in
the other. This way, the first axis will have minimal influence during determination of
critical gain and period of the other axis. The same process is then repeated with the axes
swapped, in order to determine the other set of critical gain and period.
We first determine approximate gains for which the vehicle is stable in both axes.
We then keep one gain fixed at this value and increase the other till it becomes marginally
83
CHAPTER 6. RESULTS AND DISCUSSION
unstable. This value of second gain gives us a first approximation of critical gain for that
axis. We now fix the second gain to half of this value and change the first gain (which was
kept fixed earlier) till the vehicle again becomes marginally unstable to get approximation
of critical gain for first axis. The second gain is reduced to half of critical value because
accordingtotable6.1,halfofcriticalgainisexpectedtogiveawelltunedsystem. Wenow
iterate till consistent results are obtained, i.e., the system becomes marginally unstable
whenweusecriticalgainforoneaxisandhalfofcriticalgainfortheother. Wethusobtain
critical gains for both the axes that can be used to tune the proportional (P), proportional-
integral (PI) and proportional-integral-derivate (PID) controllers.
From the analysis of manual flight (section 6.2), we expect the vehicle to be stable
for proportional gains of around 25% stick range per radian for both roll and pitch axes.
The pitch and roll attitudes during the autonomous flight for these values of gains are
shown in figures 6.8 and 6.9, respectively. The corresponding control inputs are shown
in figures 6.10 and 6.11, respectively. Figures 6.12 and 6.13 show the roll attitude and
corresponding controller inputs, respectively. The large peaks in all these plots at T ?48
seconds corresponds ot the landing of the vehicle. The vehicle can be seen to diverge
much more in yaw than roll or pitch. This is because of relatively much lower inertia in
yaw. As mentioned before, for simplicity, a fixed gain was used in yaw as any errors in
yaw do not affect pitch and roll estimation.
We now increase the pitch gain. The system is found to reach the critical condition
for a gain of 36% stick range per radian in pitch (the roll gain is kept fixed at 25% stick
range per radian). The pitch and roll attitudes for this case are shown in figures 6.14 and
6.15, respectively. Although only the pitch gain was increased, the instability in pitch
84
CHAPTER 6. RESULTS AND DISCUSSION
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! " # $
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Figure 6.9: Roll attitude vs. time (KP? = 25,KP? = 25,KP? = 30)
85
CHAPTER 6. RESULTS AND DISCUSSION
4
45
46
47
48
49
50
51
52
53
10 20 30 40 50 60 70
Time (sec)
L
o
n
g
i
t
u
d
i
n
a
l
 
C
y
c
l
i
 
(
%
 
s
t
i
c
k
 
r
a
n
g
e
)
Controler Output
Pilt Iput
Figure 6.10: Longitudinal cyclic vs. time (KP? = 25,KP? = 25,KP? = 30)
45
47
49
51
53
5
57
59
61
63
65
10 20 30 40 50 60 70
TIme (sec)
L
a
t
e
r
a
l
 
C
y
c
l
i
 
(
%
 
s
t
i
c
k
 
r
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e
)
Controler Output
Pilot Input
Figure 6.11: Lateral cyclic vs. time (KP? = 25,KP? = 25,KP? = 30)
86
CHAPTER 6. RESULTS AND DISCUSSION
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
10 20 30 40 50 60 70
Time (sec)
Psi 
(rad)
Psi
Figure 6.12: Yaw attitude vs. time (KP? = 25,KP? = 25,KP? = 30)
25
35
45
5
65
75
85
95
10 20 30 40 50 60 70
Time (sec)
V
a
n
e
s
 
(
%
 
s
t
i
c
k
 
r
a
n
g
e
)
Controler Output
Pilot Input
Figure 6.13: Vane command vs. time (KP? = 25,KP? = 25,KP? = 30)
87
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
? % ) * ( " ( ? ( %
+ ,-./01.23
+4.56/07683
Figure 6.14: Pitch attitude vs. time (KP? = 36,KP? = 25,KP? = 30)
is reflected also in roll due to coupling. The corresponding cyclic inputs are shown in
figures 6.16 and 6.17. The vane control inputs and yaw attitude are shown in figures 6.18
and 6.19, respectively.
We now reduce the proportional gain in pitch to 18% stick range per radian (half
of estimated critical value) and increase the roll gain till the system becomes marginally
stable. At a gain of 130% stick range per radian in roll, the system is found to be unstable
as shown in figures 6.20 and 6.21. The gain is then reduced and marginal stability is
found at the gain of 124% stick range per radian in roll (with 18% stick range per radian
in pitch). The pitch and roll attitudes for this flight test are shown in figures 6.22 and
6.23, respectively. The longitudinal and lateral cyclics provided by the controller for
same flight are shown in figures 6.24 and 6.25, respectively. The yaw attitude and the
vane input provided by the controller are shown in figures 6.26 and 6.27, respectively.
88
CHAPTER 6. RESULTS AND DISCUSSION
!"#$
!"#%
!"#&
!"#?
!"#(
"
" # (
" # ?
" # &
" # %
" # $
? % ) * ( " ( ? ( %
+ , - . / 0 1 . 2 3
45,/06783
Figure 6.15: Roll attitude vs. time (KP? = 36,KP? = 25,KP? = 30)
!"
#$
#"
%$
%"
"$
""
&$
&"
! % & ? ($ (! (%
)*+,-./,01
2345*678*49:-;<0:*0-.=-/6*0>-?945,1
; 3 4 6 ? 3 : : , ? - @ 7 6 A 7 6
B*:36- C4 A76
Figure 6.16: Longitudinal cyclic vs. time (KP? = 36,KP? = 25,KP? = 30)
89
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
# "
# #
$ "
$ #
% ! $ & ? " ? % ? !
( ) * + , - . + / 0
123+425,
67/58/,
-9,
.38/:,
42;<+0
6=;34=55+4, >?3@?3
A85=3, );@?3
Figure 6.17: Lateral cyclic vs. time (KP? = 36,KP? = 25,KP? = 30)
! "
# $
# "
% $
% "
& $
& "
" $
" "
? $
? "
# & ? ( ! $ ! # ! &
)*+,- ./,01
2
3
4
,
/
-
.
5
-
/
6
*
0
7
-
8
3
4
9
,
1
: ; 4 6 8 ; < < , 8 - = > 6 ? > 6
@ * < ; 6 - A 4 ? > 6
Figure 6.18: Vane command vs. time (KP? = 36,KP? = 25,KP? = 30)
90
CHAPTER 6. RESULTS AND DISCUSSION
! "
!#$%
! #
!&$%
&
& $ %
#
# $ %
"
" ? ( ) # & # " # ?
* + , - . / 0 - 1 2
30+.
/4562
Figure 6.19: Yaw attitude vs. time (KP? = 36,KP? = 25,KP? = 30)
The large spikes towards the end of all these plots corresponds to the touch down of the
Giant.
We now check if the system is marginally stable for a pitch gain of 36% stick range
per radian and roll gain of 62% stick range per radian. If this is found to be marginally
stable, then the estimates of critical gains for the two axes is correct, else we need to
iterate. The system was found to be unstable for these gains as shown by the pitch and roll
attitudes in figures 6.28 and 6.29, respectively. We now reduce the pitch gain to 32% stick
rangeperradiantogetthemarginalstabilitycondition. Thepitchandrollattitudesforthis
case are shown in figures 6.30 and 6.31, respectively. The longitudinal and lateral inputs
for the same flight are shown in figures 6.32 and 6.33, respectively. Figures 6.34 and 6.35
show the yaw attitude and vane servo commands given by the controller, respectively.
The critical gains and period are thus obtained as shown in table 6.2.
91
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
( " ( $ ? " ? $ & "
)*+,- ./,01
)2,34-
.5461
Figure 6.20: Pitch attitude vs. time (KP? = 18,KP? = 130,KP? = 30)
!"#$
!"#%
!"#&
!"#?
!"#(
"
" # (
" # ?
" # &
" # %
" # $
( " ( $ ? " ? $ & "
) * + , - . / , 0 1
23*-
.4561
Figure 6.21: Roll attitude vs. time (KP? = 18,KP? = 130,KP? = 30)
92
CHAPTER 6. RESULTS AND DISCUSSION
!"#$
!"#%
!"#&
!"#?
!"#(
"
"#(
"#?
"#&
"#%
"#$
?" ?$ &" &$ %"
)*+,- ./,01
)2,34-
.5461
Figure 6.22: Pitch attitude vs. time (KP? = 18,KP? = 124,KP? = 30)
!"#$
!"#%
!"#&
!"#?
!"#(
"
" # (
" # ?
" # &
" # %
" # $
? " ? $ & " & $ % "
)*+,- ./,01
23*-
.4561
Figure 6.23: Roll attitude vs. time (KP? = 18,KP? = 124,KP? = 30)
93
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
! $
% &
% !
% "
% #
% $
" &
? ( ? " ! ( ! " % (
)*+,- ./,01
2
3
4
5
*
6
7
8
*
4
9
:
-
;
<
0
:
*
0
-
.
=
-
/
6
*
0
>
-
?
9
4
5
,
1
; 3 4 6 ? 3 : : , ? - @ 7 6 A 7 6
B * : 3 6 - C 4 A 7 6
Figure 6.24: Longitudinal cyclic vs. time (KP? = 18,KP? = 124,KP? = 30)
!
" !
# !
$ !
% !
& !
? !
( !
) !
* !
" ! !
#! #& $! $& %!
+ , - . / 0 1 . 2 3
4
5
6
.
7
5
8
/
9
:
2
8
;
2
/
0
<
/
1
6
;
2
=
/
7
5
>
?
.
3
9@>67@88.7/ AB6CB6
D ; 8 @ 6 / , > C B 6
Figure 6.25: Lateral cyclic vs. time (KP? = 18,KP? = 124,KP? = 30)
94
CHAPTER 6. RESULTS AND DISCUSSION
!"
! # $ %
! # $ &
! # $ ?
! # $ (
#
# $ (
# $ ?
# $ &
# $ %
"
( # ( ) * # * ) ? #
+,-./ 01.23
41,/
05673
Figure 6.26: Yaw attitude vs. time (KP? = 18,KP? = 124,KP? = 30)
!"
#$
#"
%$
%"
"$
""
&$
&"
! $ ! " # $ # " % $
?()*+ ,-*./
012*-+
,3+
-4(.5+
6127*/
892469::*6+ ;<4=<4
> ( : 9 4 + ? 2 = < 4
Figure 6.27: Vane command vs. time (KP? = 18,KP? = 124,KP? = 30)
95
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
? $ & " & $ % " % $
) * + , - . / , 0 1
)
2
,
3
4
-.
5
4
6
1
Figure 6.28: Pitch attitude vs. time (KP? = 36,KP? = 62,KP? = 30)
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
? $ & " & $ % " % $
)*+,-./,01
2
3
*
-.
4
5
6
1
Figure 6.29: Roll attitude vs. time (KP? = 36,KP? = 62,KP? = 30)
96
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
( " ( $ ? " ? $ & "
) * + , - . / , 0 1
)2,34-
.5461
Figure 6.30: Pitch attitude vs. time (KP? = 32,KP? = 62,KP? = 30)
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
( " ( $ ? " ? $ & "
) * + , - . / , 0 1
23*-
.4561
Figure 6.31: Roll attitude vs. time (KP? = 32,KP? = 62,KP? = 30)
97
CHAPTER 6. RESULTS AND DISCUSSION
! "
# $
# "
% $
% "
" $
" "
& $
& "
? $ ? " ! $ ! " # $
( ) * + , - . + / 0
1234)567)389,
:;/9)/,
-<,
.5)/=,
>834+0
: 2 3 5 > 2 9 9 + > , ? 6 5 @ 6 5
A ) 9 2 5 , B 3 @ 6 5
Figure 6.32: Longitudinal cyclic vs. time (KP? = 32,KP? = 62,KP? = 30)
! "
! #
$ "
$ #
# "
# #
% "
% #
& "
& #
? "
(" (# )" )# !"
*+,-. /0-1 2
345-647.8917:1./;.05:1<.64=>-2
8?=56?77-6. @A5BA5
C : 7 ? 5 . + = B A 5
Figure 6.33: Lateral cyclic vs. time (KP? = 32,KP? = 62,KP? = 30)
98
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! "
! % # $
! %
! & # $
&
& # $
% & % $ " & " $ ? &
()* +, - . +/ 0
1.),
-2340
Figure 6.34: Yaw attitude vs. time (KP? = 32,KP? = 62,KP? = 30)
! "
# "
$ "
% "
" "
& "
? "
( "
) "
! * ! " # * # " $ *
+,-./01.23
456.1/07/18,29/:56;.3
< = 6 8 : = > > . : /? @ 8 A @ 8
B , > = 8 /C 6 A @ 8
Figure 6.35: Vane command vs. time (KP? = 32,KP? = 62,KP? = 30)
99
CHAPTER 6. RESULTS AND DISCUSSION
Axis Kcr Pcr
Pitch 32 1.4 sec (from fig. 6.30)
Roll 124 1.2 sec (from fig. 6.23)
Table 6.2: Critical gain and period for pitch and roll
Type of Controller Kp Ki Kd
P 16 ? 0
PI 14.4 12.3 0
PID 19.2 27.4 3.36
Table 6.3: Ziegler-Nichols Gains (Pitch)
From table 6.1, data in table 6.2 and relations given in equations 6.4 and 6.5, we get
tables 6.3 and 6.4 for pitch and roll axes, respectively.
Proportional Controller
We nowuse gains calculated infirst rows (correspondingto proportional control) oftables
6.3 and 6.4 to implement a proportional controller. The longitudinal and lateral attitude
Type of Controller Kp Ki Kd
P 62 ? 0
PI 55.8 55.8 0
PID 74.4 124 11.16
Table 6.4: Ziegler-Nichols Gains (Roll)
100
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
& " & $ % " % $
) * + , - . / , 0 1
)2,34-
.5461
Figure 6.36: Pitch attitude vs. time (KP? = 16,KP? = 62,KP? = 30)
results for this flight test are shown in figures 6.36 and 6.37, respectively. The corre-
sponding commands given by the controller are shown in figures 6.38 and 6.39. The
performance of the controller is satisfactory but it is found to slowly diverge, i.e., the
vehicle is seen to fly in slowly growing horizontal circles.
With some manual tweaking the performance of the controller is found to improve.
This setting corresponds to a gain of 20% stick range per radian in pitch and 55% stick
range per radian in roll. The longitudinal attitude and the controller inputs are shown in
figures 6.40 and 6.41, respectively. Figures 6.42 and 6.43 show the lateral cyclic com-
mands and the lateral attitude of the vehicle.
101
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
& " & $ % " % $
) * + , - . / , 0 1
23*-.4561
Figure 6.37: Roll attitude vs. time (KP? = 16,KP? = 62,KP? = 30)
! "
# $
# "
% $
% "
" $
" "
& $
& "
# $ # ! # % # & # ? % $ % ! % %
( ) * + , - . + / 0
1234)567)389,
:;/9)/,
-<,
.5)/=,
>834+0
: 2 3 5 > 2 9 9 + > ,? 6 5 @ 6 5
A ) 9 2 5 ,B 3 @ 6 5
Figure 6.38: Longitudinal cyclic vs. time (KP? = 16,KP? = 62,KP? = 30)
102
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
# "
# #
$ "
$ #
% "
% #
& "
& #
?" ?# !" !#
()*+, -.+/0
123+425,
67/58/,
-9,
.38/:,
42;<+0
6 = ; 3 4 = 5 5 + 4 , > ? 3 @ ? 3
A 8 5 = 3 , ) ; @ ? 3
Figure 6.39: Lateral cyclic vs. time (KP? = 16,KP? = 62,KP? = 30)
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
? $ & " & $ % " % $ $ " $ $
) * + , - . / , 0 1
)2,34-
.5461
Figure 6.40: Pitch attitude vs. time (KP? = 20,KP? = 55,KP? = 30)
103
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
! $
! %
! !
! &
! ?
! (
! )
! *
& "
$ & % " % & ! " ! & & " & &
+,-./01.23
4567,89:,6;</=>2<,2/0?/18,2@/A;67.3 = 5 6 8 A 5 < < . A / B 9 8 C 9 8
D , < 5 8 / E 6 C 9 8
Figure 6.41: Longitudinal cyclic vs. time (KP? = 20,KP? = 55,KP? = 30)
! "
! #
# "
# #
$ "
$ #
% "
& # ? " ? # ! " ! # # " # #
( ) * + , - . + / 0
123+425,67/58/,-9,.38/:,42;<+0
6=;34=55+4, >?3@?3
A 8 5 = 3 , ) ; @ ? 3
Figure 6.42: Lateral cyclic vs. time (KP? = 20,KP? = 55,KP? = 30)
104
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
? $ & " & $ % " % $ $ " $ $
) * + , - . / , 0 1
23*-.4561
Figure 6.43: Roll attitude vs. time (KP? = 20,KP? = 55,KP? = 30)
Proportional-Integral Controller
Using the gains in the second rows (corresponding to PI control) of tables 6.3 and 6.4, we
implement the proportional-integral controller. The longitudinal and lateral attitudes are
shown in figures 6.44 and 6.45, respectively. The corresponding controller commands are
shown in figures 6.46 and 6.47. It is found to give a satisfactory performance.
Proportional-Integral-Derivative Controller
Next, we use the gains in the third rows (corresponding to PID control) of tables 6.3 and
6.4. The longitudinal attitude and the controller commands are shown in figures 6.48,
6.49, respectively. Figures 6.50 and 6.51 show the lateral attitude and the corresponding
controller commands, respectively.
As can be seen from these figures, the controller needs to be tweaked in order to
105
CHAPTER 6. RESULTS AND DISCUSSION
!"#$
!"#%
!"#&
!"#?
!"#(
"
"#(
"#?
"#&
"#%
"#$
( " ? " & " % " $ " ) " * "
+,-./ 01.23
+4.56/
07683
Figure 6.44: Pitch attitude vs. time (KP? = 14.4,KI? = 12.3,KP? = 55.8,KI? =
55.8,KP? = 30)
improve its performance. Starting with the gains given by Ziegler-Nichols tuning method,
the gains are manually tweaked and the gains in table 6.5 are found to give satisfactory
performance. The longitudinal attitude and the controller commands are shown in figure
6.52 and 6.53, respectively. Figures 6.54 and 6.55 show the lateral attitude and PID
controller commands, respectively.
Axis Kp Ki Kd
Pitch 24 30 2
Roll 60 70 3
Table 6.5: PID Controller Gains
106
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
( " ? " & " % " $ " ) " * "
+,-./01.23
4
5
,
/0
6
7
8
3
Figure6.45: Rollattitudevs. time(KP? =14.4,KI? =12.3,KP? =55.8,KI? =55.8,KP? =
30)
!"
!#
!!
!$
!%
&"
&#
&!
&$
?" #" (" !" &" $" )"
* + , - . / 0 - 1 2
3456+789+5:;.<=1;+1./>.07+1?.@:56-2
< 4 5 7 @ 4 ; ; - @ .A 8 7 B 8 7
C + ; 4 7 .D 5 B 8 7
Figure 6.46: Longitudinal cyclic vs. time (KP? = 14.4,KI? = 12.3,KP? = 55.8,KI? =
55.8,KP? = 30)
107
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
# "
# #
$ "
$ #
% "
& " ? " ( " ! " # " $ " % "
) * + , - . / , 0 1
2
3
4
,
5
3
6
-
7
8
0
6
9
0
-
.
:
-
/
4
9
0
;
-
5
3
<
=
,
1
7><45>66,5- ?@4A@4
B 9 6 > 4 - * < A @ 4
Figure 6.47: Lateral cyclic vs. time (KP? = 14.4,KI? = 12.3,KP? = 55.8,KI? =
55.8,KP? = 30)
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
" $ ( " ( $ ? "
) * + , - . / , 0 1
)2,34-
.5461
Figure 6.48: Pitch attitude vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
108
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
$ "
$ #
# "
# #
% "
% #
" # & " & # ? "
()*+, -.+/0
1234)567)389,
:;/9)/,
-<,
.5)/=,
>834+0
: 2 3 5 > 2 9 9 + > , ? 6 5 @ 6 5
A)925, B3@ 6 5
Figure 6.49: Longitudinal cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
6.3.2 Perturbation Response
In order to test the robustness of the proportional controller (with 25% stick range per
radian gain), we perturb the system in pitch and study its response. A large pilot input is
applied at about 36 seconds into the experiment as shown in figure 6.56. The variation
of the pitch attitude for this input is shown in figure 6.57. From figure 6.56, we see that
the controller applies a corrective action as soon as the attitude tries to diverge as a result
of the perturbation. The controller is successful in stabilizing the attitude to within 0.1
radian in 3 seconds (fig. 6.57).
109
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
" $ ( " ( $ ? "
) * + , - . / , 0 1
23*-.4561
Figure6.50: Rollattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30)
110
CHAPTER 6. RESULTS AND DISCUSSION
!
" !
# !
$ !
% !
! !
& !
? !
( !
) !
" * !
* ! "* "! #*
+ , - . / 0 1 . 2 3
456.758/9:28;2/0</16;2=/75>?.3
9 @ > 6 7 @ 8 8 . 7 / A B 6 C B 6
D;8@6/ ,> CB 6
Figure 6.51: Lateral cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
!"#$
!"#%
!"#&
!"#?
!"#(
"
"#(
"#?
"#&
"#%
"#$
" $ ( " ( $ ? "
)*+,- ./,01
)2,34-
.5461
Figure 6.52: Pitch attitude vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
111
CHAPTER 6. RESULTS AND DISCUSSION
! "
! #
! $
% &
% !
% "
% #
% $
" &
" !
" "
? " &? &" (?
) * + , -. / , 0 1
2345*678*49:-;<0:*0-.=-/6*0>-?945,1 ; 3 4 6 ? 3 : : , ? - @ 7 6 A 7 6
B * : 3 6 - C 4 A 7 6
Figure 6.53: Longitudinal cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
6.4 Discussion
From the results presented in this chapter, we see that three independent SISO PID loops
can be used to stabilize attitude of the Giant. We get a good estimate of proportional gains
bycomputingthegainsusedbyahumanpilotduringamanualtest-flight. Ziegler-Nichols
method is used to tune the roll and pitch controller gains. Since roll and pitch axes of the
system are coupled, an iteration-based approach has been used in order to determine their
respective critical gains and periods. One axis is stabilized at a time with the best known
gain setting and the gain on the other axis is changed in order to determine its critical
parameters. The value of these critical parameters is used to update the best known gain
setting for one axis at a time. The process is repeated till same critical gain and period
112
CHAPTER 6. RESULTS AND DISCUSSION
! " # $
! " # %
! " # &
! " # ?
! " # (
"
" # (
" # ?
" # &
" # %
" # $
" $ ( " ( $ ? "
)*+,-./,01
2
3
*-.45
6
1
Figure6.54: Rollattitudevs. time(KP? =19.2,KI? =27.4,KD? =3.36,KP? =74.4,KI? =
124,KD? = 11.16,KP? = 30)
! "
# $
# "
" $
" "
% $
% "
& $
& "
? $
? "
$ " ($ (" )$
* + , - . / 0 - 1 2
345-647.8917:1./;.05:1<.64=>-2
8 ? = 5 6 ? 7 7 - 6 . @ A 5 B A 5
C : 7 ? 5 . + = B A 5
Figure 6.55: Lateral cyclic vs. time (KP? = 19.2,KI? = 27.4,KD? = 3.36,KP? =
74.4,KI? = 124,KD? = 11.16,KP? = 30)
113
CHAPTER 6. RESULTS AND DISCUSSION
0
10
20
30
40
50
60
70
25 30 35 40
Time (sec)
L
o
n
g
i
t
u
d
i
n
a
l
 
C
y
c
l
i
 
(
%
 
s
t
i
c
k
 
r
a
n
g
e
)
Controler Output
Pilot Input
Figure 6.56: Longitudinal cyclic with perturbation at 36 sec
Pitch Attitude
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
25 30 35 40
Time (sec)
Theta (rad)
Accelerometer
Gyroscope
Complementary
Figure 6.57: Pitch attitude response to longitudinal perturbation
114
CHAPTER 6. RESULTS AND DISCUSSION
values are obtained for both the axes from two successive iterations.
Having obtained the critical parameters for both axes, the gains for P, PI and PID
controllers are computed following the Ziegler-Nichols method. Some adjustments are
required to get good performance for each case. The final performance of the system is
found to be very similar in all the three cases. Proportional controllers in pitch and roll
are therefore found to be sufficient for implementing attitude stabilization on the Giant.
This is able to maintain the attitude of the Giant within?0.1 radian in both pitch and roll.
It was observed that this corresponds to the vehicle hovering over ground within a radius
of about 2 meters during the one minute duration of test-flight.
115
Chapter 7
Conclusions and Future Work
7.1 Summary
The preliminary experiments conducted to validate the control setup were restricted to a
single degree-of-freedom motion, namely, yaw (Section 3.1). The same yaw stabilization
was then implemented on the Giant in free flight with the development of the onboard
stabilization system (Section 3.2). It was soon realized that a number of features were
desired to enable faster and efficient development of autonomous control (Section 3.2.4).
A new ground-based control setup is then developed incorporating those features (Section
5.2).
With the objective of implementing attitude feedback control on Giant, an appropri-
ate sensor package, along with a high bandwidth telemetry system is identified (Section
5.3.1). Gyroscopes and accelerometers are the two main sensors that can be used for
sensing attitude. In parallel with the development of hardware, attitude transformation
and estimation algorithms have been investigated (Chapter 4). The attitude information
116
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
from gyroscopes is found to drift with time (low frequency phenomenon) and the attitude
from the accelerometers if found to be corrupted with high frequency noise due to vibra-
tions. Complementary filter is used to fuse information from both these sources to give
a reliable estimate of attitude. It has been experimentally validated and is found to give
much better results instead of using either of accelerometers or gyroscopes alone (Section
4.4).
The hardware and the attitude algorithms have then been used to implement 3 inde-
pendent SISO PID loops, one each in pitch, roll and yaw, for attitude control. In order to
get an estimate of PID gains, a modified Ziegler-Nichols method is adopted. The system
is then tuned in P, PI and PID modes and the results are presented in Chapter 6. The
controller response to perturbation in attitude has also been investigated.
7.2 Conclusions
For efficient testing and validation of control strategies on MAVs, a ground-based system
is better suited over an onboard system for the following reasons:
? Easytodebug: as the controller is programmed in LabVIEW on a PC, the standard
probe and other debug tools are available to monitor its execution. The charts and
graphs in LabVIEW also provides good visibility of different critical parameters of
the system.
? Easy to reprogram: the controller can be modified on a PC in graphical program-
ming environment of LabVIEW. This makes it much more efficient to evaluate
different algorithms, instead of reprogramming an embedded device, as in the case
117
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
of onboard controller implementation.
? Change parameters on the fly: several parameters, like gain settings on differ-
ent channels, can be changed as and when required, even during the flight of the
vehicle.
? Portability of the System and Modular code: Modular design makes it easy to
change transmitter-receiver or upgrade the sensor package. All such differences
are captured in the different interface modules. The core of the controller remains
unaffected by such changes. This makes the system portable between different
vehicles with different configurations (eg., Giant and Micor).
? Selectiveautonomy: usingatwowayinterfacebetweenthetransmitterandthePC,
wecanselectthenumberofchannelsthatneedtobecontrolledbythePCandbythe
human pilot. For example, for autonomous hover, we use manual throttle command
but the other 3 channels (cyclics and vane angle) are autonomously controlled. This
feature is also helpful in implementing maximum channel limits and scale factors
on different channel outputs. For example, it is quite useful to have dual-slope or
exponential-curveonthethrottlechannelinordertoreducethesticksensitivitynear
hover RPM.
? Manual/auto switching: this setup provides a quick way to switch between the
autonomousmodeandthefullmanualmode, byflippingaswitchonthetransmitter,
in case of any problem or malfunction of the controller.
Other main conclusions that follow from this work are listed below:
118
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
? With the availability of advanced wireless transceivers, it is now possible to have
a high bandwidth (57.6 kbps) and a long range (about 200 meters) wireless link,
enabling ground-based implementation of test-bed.
? A complementary filter is able to reject high frequency noise in accelerometer data
and low frequency drift in gyroscope data. It thus gives a very reliable estimate of
attitude for low translational-acceleration flights.
? The algorithms for transformation and filtering of raw data received from the sen-
sors and generating the servo commands, with real time performance, can be im-
plemented much more efficiently on a modern PC (with dual-core processor) using
LabVIEW. A lot more programming effort and tweaking is required with the older
generation PCs (single-core processors) in order to get a reliable real-time perfor-
mance using same algorithms.
? The actuation bandwidth of the system is only limited by the servo bandwidth; i.e.,
the servos are updated at the maximum rate allowed by the standard servo-control
protocol (50 Hz), using the microcontroller.
? Three independent SISO PID loops can be used for control and stabilization of
the Giant for low-speed flight. This enables the use of simple control scheme for
attitude stabilization of the Giant.
? The pitch and roll axes need different gains because of the non-symmetric servo
attachment to the swashplate.
119
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
? Modified Ziegler-Nichols tuning method gives good starting values for PID gains,
but some adjustments are required to get good performance.
? All three, P, PI and PID controllers are found to give comparable performance for
attitude stabilization.
? A suitably tuned PID (or P, or PI) controller can keep the roll and pitch attitude
within ?0.1 radians. From the flight tests it was observed that the vehicle remains
with a radius of about 2 meters for a one minute controlled hover-flight using only
attitude feedback.
? The controller is found to stabilize the vehicle against the perturbations in attitude
issued by the pilot using the transmitter stick inputs. The attitude was found to
reduce from ?0.4 radians to within ?0.1 radians in 3 seconds.
7.3 The Future Roadmap
As mentioned before, the goal of research in this area is to enable autonomous flight and
operation of an MAV. Looking at the bigger picture, the controller for an autonomous
air vehicle can be hierarchically decomposed into three different layers as shown in fig-
ure 7.1 [41]. At the highest level, we have the strategic control layer, which does mis-
sion planning and way-point generation. Tactical layer forms the intermediate layer and
takes care of guidance and trajectory planning. At the lowest level is the reflexive layer
that includes the traditional control functions like stabilization, regulation and command
tracking. Development of reflexive layer needs work in two primary areas, state estima-
120
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
Figure 7.1: Hierarchical decomposition of autonomous control [41]
tion and stabilization or command-tracking controller design. Besides these, a test-bed to
implement, test and evaluate the controller needs to be developed.
During the course of this project a generic test-bed for control implementation had
been developed. It has so far been used to implement an attitude-feedback PID controlled
reflexive layer. Following are the suggestions for future work in this area:
121
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
Translation Feedback Control
As discussed in section 5.1, and shown in figure 5.1, the inner attitude-stabilization loop
forms the core of the controller. Although the vehicle is actuated using lateral and lon-
gitudinal cyclics, which correspond to attitude commands, it is not practical or intuitive
to issue attitude commands to a vehicle in order to navigate it from one point to another.
Thisneedstobeaugmentedwithanoutertranslation-stabilizationloopinordertodirectly
be able to issue translation or position commands instead of attitude commands.
The challenge in implementing the translation feedback control is to identify ap-
propriate sensors that not only give reliable position information, but are also sufficiently
compact, light weight and can operate in closed environments. For initial experiments,
one may use a Global Positioning System (GPS) to demonstrate the basic working of the
system [42]. The GPS is of limited use for MAV applications, as it does not work in
closed environments (e.g., inside a building), i.e., when it is not in line of sight of at least
three GPS satellites.
The other techniques that have evolved over recent years include vision based sys-
tems [43], such as optic flow sensors [44]. The optic flow sensors are based on visual cues
that insects use to navigate. It gives an estimate of a ratio of velocity to distance from a
textures surface as seen by the sensor. So, with the knowledge of distance (using some
other sensor, like pressure transducer or laser ranging system), the velocity of the vehicle
can be estimated, and vice-versa.
122
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
Model Based Control
In the present work, we have implemented PID control in order to achieve some level
of automation. In order to expand the flight envelope and make use of the maneuver-
ing capability of the vehicle, it is important to develop a model based controller [19].
As the MAVs are small in size and have much lower inertias compared to the manned
aircraft, they have quicker vehicle responses. It is therefore required to have very high
bandwidth models in order to implement model based control on MAVs. A basic struc-
ture of the model of the vehicle first needs to be worked out from the first principles. The
different unknown parameters in this model are then identified using system identifica-
tion techniques [19,45]. Once a sufficiently ?good? model has been developed, different
model-based control techniques [46] can be implemented and evaluated using this test-
bed.
This will complete the development of the reflexive layer and then the research ef-
fort can focus on development of higher layers of autonomy, i.e., the tactical and strategic
layers.
123
Appendix A
Gyroscope Drift
A basic explanation of gyroscope drift is given in Section 4.2. In this appendix, a more
detailed explanation is presented in a form of questions and answers.
? Why does the attitude reading obtained from gyroscope drift?
The fundamental reason is the non-exact determination of bias.
? What is bias?
The gyroscope is an analog angular rate sensor and gives a non-zero voltage for
zero angular rate. This voltage is called the bias. The angular rate is given by:
Rate = (Voltage?Bias)?Calibration constant (A.1)
From this, we see that if bias is not correctly estimated, the ?rate? obtained will be
erroneous. As previously mentioned, the gyroscope only gives us this rate informa-
tion. It needs to be integrated over time to compute the angular position (attitude).
124
APPENDIX A. GYROSCOPE DRIFT
The errors in the determination of rate (due to incorrect bias) lead to diverging error
in attitude estimation (the drift)!
? Why is bias not correctly determined?
There are two reasons for this. The first has to do with the fundamental physical
issues in the operation of gyro itself, and the second has to do with the way they are
interfaced and sampled. Let us first look at the second issue.
Let us assume that we have a perfect gyro (with perfectly steady bias). There is still
a limit to the resolution with which the bias can be determined due to unavailability
of infinite-bit analog-to-digital converters! A 10-bit ADC on a 5-volt scale can only
resolve 5/1024 volts, i.e., about 4 mV. The datasheet for ADXRS150 specifies the
sensitivity as 12.5 mV/deg/s [30]. Therefore we can only resolve a rate of 0.32
deg/sec with this setup. An error of 0.32 deg/sec in the estimation of bias would
lead to a drift of 32 deg in every 100 seconds!
But the gyro is not noise-free. It is in some ways good for us as it introduces a
?dithering? effect which leads to a finer estimation of bias!
? What is dithering?
Suppose the actual output of an analog sensor is 2.6 volts, and it is being sampled
by a device that truncates the fractions and resolves the data only in unit?s place.
This device will show a result of 2 instead of 2.6. Now if we introduce a noise in
the data such that 60% of the time the result of sampling device is 3 and remaining
40% of the time it is 2, the average will turn out to 2.6! This introduction of noise
125
APPENDIX A. GYROSCOPE DRIFT
to improve the estimation of a signal is called dithering.
? Why do we still have problems (after having exploited dithering)?
Firstly, we only have a finite number of samples available at any point in time.
Therefore, going by the above example, there is no guarantee that the data will be
sampled as 3 for 60% of the time; sometimes it might show 3 for much less than
60% of the samples or sometimes more. Even if the bias was correctly determined
by taking a large number of samples, the estimation of rate (and thus angle) for
any subsequent instantaneous gyro reading will still be wrong (although for white
noise, the angle would fluctuate around zero, if bias is perfectly determined).
Secondly, the gyro is not a perfect sensor. That is, the construction of gyro and its
working principle is such that the reading from the gyro is influenced by a num-
ber of factors instead of just angular rate. The MEMS gyro measures the angular
rates by means of Coriolis acceleration, which is measured by estimating the dis-
placement of a resonating mass and its frame (due to the Coriolis effect) through
capacitive sensing elements attached to the resonator [48]. The ADXRS gyro elec-
tronics can resolve capacitance changes as small as 12x1021 farads (12 zeptofarads)
from beam deflections as small as 0.00016 Angstroms (16 femtometers). These sub
atomic displacements are meaningful as the average positions of the surfaces of the
beams, even though the individual atoms on the surface are moving randomly by
much more. There are about 1012 atoms on the surfaces of the capacitors, so the
statistical averaging of their individual motions reduces the uncertainty by a factor
of 106 (dithering effect again!). We cannot do better because of the air molecules
126
APPENDIX A. GYROSCOPE DRIFT
which cause the structure to move. Although these are also averaged, their effect is
far greater. The air is not removed because the device consists of a very fine film
(4 micrograms) and flexures (1.7 micron wide) that are suspended over the silicon
substrate and the air molecules cushion this structure, preventing it from damage
due to shocks.
? How to get better attitude then?
There could be two ways of getting better attitude estimate:
1. Study the nature of bias noise and devise an advanced filter to estimate that
noise much more accurately [49]. This is an involved exercise in itself and
limited success has been achieved to date.
2. An alternate way is to use some sort of external aiding to correct for drift
in the gyro data. This is typically done using an accelerometer [32]. An
accelerometer has no drift as it directly gives the attitude (no integration re-
quired)bymeasuringthegravityvector(assumingthatlinearaccelerationsare
small compared to gravity). Accelerometer and gyroscope have complemen-
tary characteristics. Accelerometer gives a very good low frequency estimate
(no drift) but has high frequency noise due to vibrations. Gyros on the other
hand have a good high frequency performance (higher rates lead to larger ca-
pacitance to be measured, where the air molecule effect is smaller than the
Coriolis effect; also the integration used for angle computation has an effect
of averaging out the signal, so that there are no jerks in the data even at high
frequency) but a poor low frequency performance (drift). Therefore we use a
127
APPENDIX A. GYROSCOPE DRIFT
complementary filter to fuse the data from both these sensors to get the best
estimate.
? What are the other sources of gyro errors?
1. Sensor saturation: If the gyro is subjected to angular rates higher than what
it can measure, it will saturate and in turn miss all the action during that time.
Although the vehicle is not expected to move at rates higher than +- 150
deg/sec (rate limits for ADXRS 150), the vibrations often exceed that limit
and lead to very fast loss of orientation.
2. Temperature: The gyro is known to be sensitive to temperature. In lab ex-
periments no conclusive fixed temperature calibration could be established.
3. ADC warm-up: It has been observed that when the entire system is switched
on, the analog-to-digital converter and other electronics take some time to
stabilize. The bias computed from the first few minutes of data is significantly
worse than that computed a little later.
? How do we take care of these?
The ADC warm up and temperature corrections are taken care of by letting the
system run for a few minutes before starting the experiment. The bias estimation
should be done after this initial period.
Sensor saturation (vibration isolation) is taken care of by appropriate mounting of
the sensor on the vehicle. A packaging is provided to absorb high angular rate
vibrations.
128
APPENDIX A. GYROSCOPE DRIFT
To reiterate, gyro drift occurs because of integration. A MEMS accelerometer does
not have a constant analog bias for all of the same reasons as a gyro. The only difference
is that the accelerometer data does not have to be integrated to measure the angle. If
velocity was measured from integrating the accelerometer, an analogous issue as gyro
drift would occur. It could be called accelerometer drift.
129
Appendix B
Listing of Microcontroller Codes
The microcontroller codes discussed in Sections 3.1.2, 3.1.3, 5.3.2 are listed below. All
these codes are written for the CCS-C cross compiler [26] for PIC microcontrollers.
TheCodeforYawStabilizationExperiment(Section3.1.2)
// Initialization
#include <16f877.h>
#fuses HS,NOLVP,NOWDT,PUT
#use delay(clock=20000000)
#use rs232(baud=9600, xmit=PIN_C6, rcv=PIN_C7)
#include <stdlib.h>
#include <input.c>
#define GREEN_LED PIN_A5
#define YELLOW_LED PIN_B4
#define RED_LED PIN_B5
#define PUSH_BUTTON PIN_A4
char state;
int32 high, cycle = 12500;
// The Interrupt Service Routine
// to generate servo command once every 20ms
#int_ccp1
void isr(){
130
APPENDIX B. LISTING OF MICROCONTROLLER CODES
if (state == 1)
{
output_low(PIN_C2);
CCP_1 += cycle - high;
}
else
{
output_high(PIN_C2);
CCP_1 += high;
}
if (CCP_1 > 65535)
CCP_1 = 65535-CCP_1;
state = 1-state;
}
//The Main Routine
void main()
{
int32 angle,temp1,inc,i,val1,val2,value,temp,base=124;
setup_ccp1(CCP_COMPARE_INT); // Configure CCP1 as input compare
setup_timer_1(T1_INTERNAL | T1_DIV_BY_8);
state = 0;
high = 730;
angle = 10000;
enable_interrupts(INT_CCP1); // Setup interrupt on compare
enable_interrupts(GLOBAL);
CCP_1 = 10; // set interrupt at 10 timer-1 ticks
set_timer1(0); // initialize timer-1
// initialize ADC
setup_port_a(ALL_ANALOG);
setup_adc(adc_clock_internal);
set_adc_channel( 1 );
while(TRUE)
{
value=read_adc(); // sample ADC
if (value < 10)
output_low(RED_LED); // warning for saturation
else
output_high(RED_LED);
131
APPENDIX B. LISTING OF MICROCONTROLLER CODES
if (value > 240)
output_low(YELLOW_LED); // warning for saturation
else
output_high(YELLOW_LED);
inc = value-base; // compute rate
angle += inc; // angle is integral of rate
if (angle<5000)
angle = 5000; // lower limit on angle
if (angle>15000)
angle = 15000; // upper limit on angle
temp = 3730 - (float)angle/4 - value*4; // servo command (PD control)
if (temp<630 || temp>1245) // check for servo saturation
output_low(GREEN_LED);
else
output_high(GREEN_LED);
high = temp; // final servo command
delay_us(50000);
}}
The Code for Yaw Control Experiment (Section 3.1.3)
// Initialization
#include <16f877.h>
#fuses HS,NOLVP,NOWDT,PUT
#use delay(clock=20000000)
#use rs232(baud=9600, xmit=PIN_C6, rcv=PIN_C7)
#include <stdlib.h>
#include <input.c>
#define GREEN_LED PIN_A5
#define YELLOW_LED PIN_B4
#define RED_LED PIN_B5
#define PUSH_BUTTON PIN_A4
char state,state_read;
int32 time, rise, high, cycle = 12500;
// Interrupt Service Routine
132
APPENDIX B. LISTING OF MICROCONTROLLER CODES
// to generate servo command once every 20ms
#int_ccp1
void isr(){
if (state == 1)
{
output_low(PIN_C2);
CCP_1 += cycle - high;
}
else
{
output_high(PIN_C2);
CCP_1 += high;
}
if (CCP_1 > 65535)
CCP_1 = 65535-CCP_1;
state = 1-state;
}
// Interrupt Service Routine
// to read R/C receiver
#int_ccp2
void isr2() {
state_read = 1 - state_read;
if (state_read==0)
{
if (CCP_2>rise)
time = CCP_2-rise;
else
time = 65535 - rise + CCP_2;
setup_ccp2(CCP_CAPTURE_RE);
}
else
{
rise = CCP_2;
setup_ccp2(CCP_CAPTURE_FE);
}
}
// The Main Routine
void main()
{
int32 angle,temp1,inc,i,val1,val2,value,temp,base=124, neutral;
setup_ccp1(CCP_COMPARE_INT); // Configure CCP1 as input compare
133
APPENDIX B. LISTING OF MICROCONTROLLER CODES
setup_ccp2(CCP_CAPTURE_RE);
setup_timer_1(T1_INTERNAL | T1_DIV_BY_8);
state = 0;
state_read = 0;
time = 0;
high = 730; // default servo output
angle = 10000; // Initial value of angle
neutral = 0;
enable_interrupts(INT_CCP1); // Setup interrupt on compare
enable_interrupts(INT_CCP2);
enable_interrupts(GLOBAL);
CCP_1 = 10; // set interrupt for timer-1 = 10
set_timer1(0); // initialize timer-1
// Initialize ADC
setup_port_a(ALL_ANALOG);
setup_adc(adc_clock_internal);
set_adc_channel( 1 );
while(TRUE)
{
value=read_adc(); // Read Gyro data
if (value < 10)
output_low(RED_LED); // warning for sensor saturation
else
output_high(RED_LED);
if (value > 240)
output_low(YELLOW_LED); // warning for sensor saturation
else
output_high(YELLOW_LED);
inc = value-base;
angle += inc;
if (angle<5000)
angle = 5000; // lower limit on angle
if (angle>15000)
angle = 15000; // upper limit on angle
neutral = time-700; // modify input
134
APPENDIX B. LISTING OF MICROCONTROLLER CODES
// compute servo command
temp = 3730 + 833 - (float)angle/3 - value*4 + (float)neutral*2;
if (temp<630 || temp>1245)
output_low(GREEN_LED); // check for servo saturation
else
output_high(GREEN_LED);
high = temp; // set final servo command
delay_us(50000);
}}
The Code for R/C Transmitter Interface (Section 5.3.2)
// Initialization
#include <16F877.h>
#fuses HS,NOLVP,NOWDT,PUT
#use delay(clock=20000000)
#use rs232(baud=57600, xmit=PIN_C6, rcv=PIN_C7)
#include <stdlib.h>
#include <input.c>
char i=1,statew=0;
// set default values for different channels (write to transmitter)
unsigned int16 high[8]={700,696,712,418,690,468,676,7500};
char stater=0, pos = 0;
// set default values for different channels (read from transmitter)
unsigned int16 rise, time[10]={700,700,700,410,700,468,676,700,700,700};
// Interrupt Service Routine
// to read transmitter data
#int_ccp1
void write(){
if (statew == 1)
{
output_low(PIN_E1);
CCP_1 += 250; //400ns low time
}
else
{
135
APPENDIX B. LISTING OF MICROCONTROLLER CODES
output_high(PIN_E1);
CCP_1 += high[i];
i++;
if (i==8)
i=1;
}
if (CCP_1 > 65535)
CCP_1 = 65535-CCP_1;
statew = 1-statew;
}
// Interrupt Service Routine
// to read from the transmitter
#int_ccp2
void read() {
stater = 1 - stater;
if (stater==0)
{
if (CCP_2>rise)
time[pos] = CCP_2-rise;
else
time[pos] = 65535 - rise + CCP_2;
setup_ccp2(CCP_CAPTURE_RE);
if (time[pos] > 1500) // sync pulse
pos = 0;
pos++;
}
else
{
rise = CCP_2;
setup_ccp2(CCP_CAPTURE_FE);
}
}
void main() {
unsigned int16 temp;
unsigned int8 output, j;
setup_ccp1(CCP_COMPARE_INT); // Configure CCP1 as output compare
setup_ccp2(CCP_CAPTURE_RE); // Configure CCP2 as input capture (rising)
setup_timer_1(T1_INTERNAL | T1_DIV_BY_8);
enable_interrupts(INT_CCP1); // Setup interrupt on compare
enable_interrupts(INT_CCP2); // Setup interrupt on input capture
enable_interrupts(GLOBAL);
CCP_1 = 10;
136
APPENDIX B. LISTING OF MICROCONTROLLER CODES
set_timer1(0);
while(TRUE)
{
putc(255);
for(j=1;j<7;j++) // write to PC
{
output = (time[j]-200) >> 2; // adjust data in 1 byte
putc(output);
}
temp = getc(); // read from PC
while (temp!=255)
temp = getc();
temp=getc();
high[1] = (temp<<2) + 200; // expand data to 2 bytes
temp=getc();
high[2] = (temp<<2) + 200;
temp=getc();
high[3] = (temp<<2) + 200;
temp=getc();
high[4] = (temp<<2) + 200;
temp=getc();
high[6] = (temp<<2) + 200;
}
}
137
Appendix C
Implementing Digital Filters
The raw data collected from the sensors is often corrupted by other unwanted signals,
referred to as noise. It is therefore required to filter this noise in order to get meaningful
information from the sensors. In most cases, such filters have to implemented on some or
the other form of digital processor as software. Since the sensors are sampled at a very
high rate (hundreds of readings per second) and the entire system has to react in real time,
the implementation of the filters needs be to very efficient in terms of both processing
time and memory usage.
There are many different ways to design filters, but the most common ones have
their roots in simple averaging. Digital filters can be divided into two categories based on
implementation [47]:
1. Finite Impulse Response (FIR), or the filters based on convolution: The output of
these filters is affected by a finite number of samples taken in the past. That is, after
a certain amount of time, the old sensor data will have no influence on the output
138
APPENDIX C. IMPLEMENTING DIGITAL FILTERS
of the filter.
2. Infinite Impulse Response (IIR), or the filters based on recursion: The output of
these filters is affected by all the sensor data samples collected in the past.
We now discuss the implementation of 3 different digital filters that are commonly
used. The first two filters (generic FIR, and moving average) belong to the FIR type of
filters and the last one (exponentially weighted averaging filter) is an IIR kind of digital
filter.
Generic FIR Filter
The most generic way to design a digital filter is to convolve the input signal with the
digital filter?s impulse response. In this method, each sample in the output is calculated by
weighting the samples in the input using the filter kernel (impulse response or convolution
coefficients), and adding them together.
MATLAB?s Filter Design Toolbox [50] provides several useful functions for de-
signing, simulating and analyzing digital filters. ?FDATool? command in this toolbox
provides a graphical interface to design filters. Filter kernels for generic FIR filters, can
also be obtained using the ?fir? MATLAB command. This MATLAB function can be
called directly from a LabVIEW VI during initialization and the kernel obtained can be
repeatedly used over input data to get filtered data.
Although this is a powerful digital filtering technique, it needs a lot of computa-
tion per output sample. This imposes a serious limitation on how fast the sensor can be
sampled and thus on the bandwidth of the control system.
139
APPENDIX C. IMPLEMENTING DIGITAL FILTERS
Moving Average Filter
Moving average filter is one of the simplest and most commonly used filters in digital
signal processing. It is very efficient as it can be implemented in a recursive form.
Suppose that at any instant k, the average of the latest n samples of a data sequence,
xi, is given by:
?xk = 1n
k?
i=k?n+1
xi (C.1)
Similarly, at the previous time instant, k?1, the average of the latest n samples is:
?xk?1 = 1n
k?1?
i=k?n
xi (C.2)
Therefore,
?xk = ?xk?1 + 1n (xk?xk?n) (C.3)
Here, the average at each kth instant is based on the most recent set of n values. Or,
a moving window of n values is used to calculate the average of the data sequence. It can
be seen that this filter only needs one division, one addition and one subtraction operation.
This is always the case, irrespective of the size of the window, n; although, we need to
store the value of xk?n, which may require n storage locations.
Exponentially Weighted Averaging Filter
In the previous filter design (moving average filter), each data point in the window is
given equal importance when calculating the average. In dynamic systems, however, the
140
APPENDIX C. IMPLEMENTING DIGITAL FILTERS
most current values from the sensor reflect better the sate of the plant. We now look at the
implementation of a recursive infinite response filter (that uses all the sensor data from
the past), that places more emphasis on the most recent data.
In the most simple form, the exponentially weighted averaging filter can be repre-
sented by the following equation:
?xk = ??xk?1 +(1??)xk (C.4)
where, 0?? < 1
This implementation requires only one addition, 1 subtraction and two multiplica-
tions. There is no need to store a window of samples as was the case with moving average
filter. The filter constant, ?, dictates the degree of filtering, i.e., how strong the filtering
action will be. When the filtering is strong, i.e., ?? 1, then, ?xk ? ?xk?1, or, the current
measurement does nor affect the output. On the other hand when the filtering is weak,
i.e., ??0, then, ?xk ?xk, or, the measurement if not even modified by the filter.
Exponentially weighted averaging filter places more importance on the more recent
data in an exponential manner. This is be seen by expanding equation C.4:
?xk = ??xk?1 +(1??)xk, (C.5)
and,
?xk?1 = ??xk?2 +(1??)xk?1 (C.6)
therefore,
?xk = ??xk?1 +(1??)xk = ?[??xk?2 +(1??)xk?1]+(1??)xk (C.7)
141
APPENDIX C. IMPLEMENTING DIGITAL FILTERS
Or,
?xk = ?2?xk?2 +?(1??)xk?1 +(1??)xk (C.8)
Expanding further,
?xk = ?3?xk?3 +?2(1??)xk?2 +?(1??)xk?1 +(1??)xk (C.9)
From equation C.9 we see that the contribution of the older values of xi is weighted
by increasing powers of ?. Since ? is less than 1, the contribution of older values of xi
becomes exponentially smaller.
This is in fact a very simple implementation of first-order low-pass filter. The
equivalence of a exponentially weighted averaging filter and a first-order low-pass filter
is shown next.
Consider the Laplace transfer function of a first-order low-pass filter, with time
constant ?f. The following equation relates the filtered signal, ?x(s) to the measurement,
x(s):
?x(s)
x(s) =
1
1+?fs (C.10)
Time equivalent of equation C.10 is:
?f d?x(t)dt + ?x(t) = x(t) (C.11)
Now, we discretise equation C.11 using the following approximation:
d?x(t)
dt ?
?xk? ?xk?1
Ts (C.12)
where, Ts is the interval between each measurement, i.e., the sampling interval. Thus
equation C.11 leads to:
Tf ?xk? ?xk?1T
s
+ ?xk = xk (C.13)
142
APPENDIX C. IMPLEMENTING DIGITAL FILTERS
Simplification and re-arrangement gives:
?xk =
parenleftbigg T
f
Tf +Ts
parenrightbigg
?xk?1 +
parenleftbigg T
s
Tf +Ts
parenrightbigg
xk (C.14)
By letting, ? =
parenleftBig T
f
Tf+Ts
parenrightBig
, we get:
?xk = ??xk?1 +(1??)xk (C.15)
which is same as equation C.4.
This is the simplest and most efficient way of implementing a first-order low-pass
filter. It has been used in several places in the VI described in Chapter 5.
143
Appendix D
Setting up the Test-Bed
The procedure to setup the test-bed is given below:
1. Load the appropriate code (ReadWriteTrans.hex) on the microcontroller.
2. Connect the transmitter with the microcontroller and the microcontroller to the PC.
3. Power on the transmitter and the microcontroller.
4. Use ?Device Manager? under ?Control Panel? on the PC to identify the Serial Port
to which the microcontroller is connected.
5. Launch ?LabVIEW? and load the ?ReadWriteTransTrial.vi? in order to test the
transmitter communication.
6. Setup the correct Serial Port parameters in the VI and run it.
7. The transmitter stick positions should be correctly read by the PC/VI. If this does
not work, refer to the troubleshooting section of this appendix.
144
APPENDIX D. SETTING UP THE TEST-BED
8. Close the ?ReadWriteTrans.vi? if the transmitter connection is working fine.
9. Connect the Bluetooth dongle to the PC.
10. Power on the Giant MAV (along with the onboard avionics box).
11. Use the ?IVT BlueSoleil? software on the PC to establish connection to the blue-
tooth transceiver on the Giant.
12. Launch ?GiantClosedLoopControl.vi? in LabVIEW.
13. Setup the correct Serial Port parameters for the transmitter and Bluetooth commu-
nication (Fig. D.1).
14. Select the ?Type of Control? and enter gain settings (Fig. D.2).
15. Select ?Need to Initialize? in order to enable initialization of the Bluetooth link.
16. Run the VI and stop it after 5 seconds.
17. Check if the LED on the avionics box (on Giant) starts to blink. The blinking
indicates successful start of data transmission.
18. If the LED is not blinking refer to the section on troubleshooting.
19. Un-select the ?Need to Initialize? option on the VI and rerun it (Fig. D.1).
20. After about 10 seconds, the data from the sensors should be available on the charts
of the VI.
21. Make sure that data from all channels of the avionics box and transmitter is within
expected limits.
145
APPENDIX D. SETTING UP THE TEST-BED
22. Pull the trainer switch on the transmitter to go into autonomous mode and perform
the experiment.
23. After the experiment, press the ?Stop? button on the VI.
24. The VI will request for the names of the files (one for sensor data and other for
transmitter data) where the on-screen data is to be stored for later analysis, before
terminating.
Troubleshooting
? ReadWriteTransTrial.vi does not respond to transmitter stick movements
This problem is usually due to some minor mistake in the setting up of the system
and is usually resolved by one of the following:
? Make sure the transmitter and the microcontroller are powered on.
? Check the connecting wires between the transmitter and the microcontroller,
and between the microcontroller and the PC. The wires on the microcontroller
should be connected to correct I/O pins.
? Reset the microcontroller.
? Remove the USB cable from the PC and reconnect it (this way it can reinitial-
ize).
? Make sure that the VI is reading from the correct Serial Port (as shown by the
?Device Manager?).
146
APPENDIX D. SETTING UP THE TEST-BED
Figure D.1: Communication settings in LabVIEW
147
APPENDIX D. SETTING UP THE TEST-BED
Figure D.2: Control settings in LabVIEW
148
APPENDIX D. SETTING UP THE TEST-BED
? Check the battery level of the transmitter. Recharge it, if necessary.
? BlueSoleil software fails to connect to the Bluetooth transceiver
This usually happens when the onboard avionics box has already been initialized
(LED is blinking) but the communication link with the PC is required to be re-
established. The solution is to reset the avionics box so that first the link can be set
up before it begins transmission of data.
? LED on the avionics box is not blinking after trying to initialize it
The most common reason for this problem is improper link between the PC and the
onboard avionics box. The solution is to reset the avionics box and re-establish link
using the ?IVT BlueSoleil? software on the PC.
149
References
[1] McMichael, J. M., Francis, M. S., ?Micro Air Vehicles - Towards a New Dimension
in Flight,? DARPA Document, 1997.
[2] Grasmeyer, J. M., and Keennon, M. T., ?Development of the Black Widow Mi-
cro Air Vehicle,? AIAA Paper No. AIAA-2001-0127, Presented at the 39th AIAA
Aerospace Sciences Meeting and Exhibit, Reno, NV, January, 2000.
[3] Anon., Unmanned Air Vehicles Roadmap, 2002-2027, Office of the Secretary of
Defence, 2002.
[4] Anon., Unmanned Air Vehicles Roadmap, 2005-2030, Office of the Secretary of
Defence, 2005.
[5] Sirohi, J., Tishchenko, M., and Chopra, I., ?Design and Testing of A Micro-Aerial
Vehicle with a Single Rotor and Turning Vanes,? American Helicopter Society
61stnd Annual Forum, Grapevine, TX, 1-3 June, 2005.
[6] Bohorquez, F., Samuel, P., Sirohi, J., Pines, D., Rudd, L., and Perel, R., ?Design,
Analysis and Performance of a Rotary Wing MAV,? Journal of the American Heli-
copter Society, Vol. 48, No. 2, pp. 80-90, April, 2003.
150
REFERENCES
[7] Young, L., and Aiken, E., ?New Concepts and Prespectives on Micro-Rotorcraft and
Small Autonomous Rotary-Wing Vehicles,? AIAA-2002-2816, Presented at the 20th
AIAA Applied Aerodynamics Conference, St. Louis, Missouri, June 24-26, 2002.
[8] Bohorquez, F. and Pines, D., ?Rotor and Airfoil Design for Efficient Rotary Wing
Micro Air Vehicles,? 61st Annual American Helicopter Society Forum, Grapevine,
TX, June 2005.
[9] Pereira, J., and Chopra, I., ?An Investigation of the Effects of Shroud Design Vari-
ables on the Hover Performance of a Shrouded-Rotor Micro Air Vehicle,? American
Helicopter Society International Specialists? Meeting on Unmanned Rotorcraft, Jan-
uary, 2005.
[10] Parsons, E., Sirohi, J., and Chopra, I., ?Micro Air Vehicle; Cycloidal Rotor
Concept,? American Helicopter Society International Specialists? Meeting on Un-
manned Rotorcraft, January, 2005.
[11] Singh, B., Ramasamy, M., Chopra, I., and Leishman, J., ?Experimental Studies on
Insect-Based Flapping Wings for Micro Hovering Air Vehicles,? 46th Annual AIAA
uctural Dynamics and Materials Conference, Austin, TX, April 2005.
[12] Newcome,L.R.,UnmannedAviation: ABriefHistoryofUnmannedAerialVehicles,
AIAA, 2004.
[13] Arning, R., and Sassen, S., ?Flight Control of Micro Aerial Vehicles,? AIAA Guid-
ance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island,
Aug. 16-19, 2004.
151
REFERENCES
[14] Amidi, O., Kanade, T., and Miller, J. R., ?Autonomous Helicopter Research at
Carnegie Mellon Robotics In stitute,? Proceedings of the Heli Japan ?98, April,
1998.
[15] Spraque, K., et. al., ?Design and Applications of an Avionics System for a Minia-
ture Acrobatic Helicopter,? The 20th Digital Avionics Systems Conference, Daytona
Beach, FL, Oct. 14-18, 2001
[16] Johnson, E., Schrage, D., ?The Georgia Tech Unmanned Aerial Research Vehi-
cle: GTMax,? AIAA Guidance, Navigation, and Control Conference and Exhibit,
Austin, Texas, Aug. 11-14, 2003.
[17] Koo, T., Hoffmann, F., Shim, H., Sinopoli, B., and Sastry, S., ?Hybrid Control of
an Autonomous Helicopter,? IFAC Workshop on Motion Control, Grenoble, France,
Sep. 21-23, 1998.
[18] Garcia-Pardo, P. J., Sukhatme, G. S., and Montgomery, J. F., ?Towards vision-based
safe landing for an autonomous helicopter,? Robotics and Autonomous Systems,
Vol. 38, Issue 1, January, 2002, pp. 19-29.
[19] Mettler, B., Indentification Modeling and Characteristics of Miniature Rotorcraft,
Springer, 1st edition, USA, Sep. 30, 2002.
[20] Britting, K., Inertial Navigation Systems Analysis, Wiley Interscience, New York,
1971.
[21] Broxmeyer, C., Inertial Navigation Systems, McGraw-Hill, New York, 1964.
152
REFERENCES
[22] King, A. D., ?Inertial Navigation - Forty Years of Evolution,? GEC Review, Vol. 13,
No. 3, 1998, pp. 140-149.
[23] Anon., ?E-flite Blade CP,? http://en.wikipedia.org/wiki/E-flite Blade CP, accessed
Oct. 30, 2006.
[24] Anon., ?Triaxial angular rate (gyro), acceleration and magnetic field Inertial Sen-
sor,? http://www.memsense.com/products/mag3.asp, accessed Oct. 30, 2006.
[25] Anon., ?PIC16F877A,? http://www.microchip.com/stellent/idcplg?IdcService=
SS GET PAGE&nodeId=1335&dDocName=en010242, accessed Oct. 30, 2006.
[26] Anon., ?CCS, Inc. - PIC16F877A Development Kit,? http://www.ccsinfo.com/ prod-
uct info.php?products id=16F877Akit, accessed Oct. 30, 2006.
[27] Conroy, J. K., Samuel, P. D., and Pines, D. J., ?Development of an MAV Control
and Navigation System,? AIAA-2005-7065, Infotech@Aerospace, Arlington, VA,
Sep. 26-29, 2005.
[28] Pamadi, B. N., Performance, Stability, Dynamics, and Control of Airplanes, 2nd
edition, AIAA, Dec. 2003.
[29] Barbour, N., Schmidt, G., ?Inertial Sensor Technology Trends,? IEEE Sensors Jour-
nal, Vol. 1, No. 4, December, 2001, pp 332-339.
[30] Anon., ?Analog Devices ADXRS150 - Angular Rate Sensor ADXRS150,?
http://www.analog.com/en/prod/0,2877,ADXRS150,00.html, accessed Oct. 30,
2006.
153
REFERENCES
[31] Anon., ?QP-2HC Datasheet,? http://www.midoriamerica.com/pdf/QP-2HC.pdf, ac-
cessed Oct. 30, 2006.
[32] Baerveldt, Albert-Jan and Klang, R., ?A Low-cost and Low-weight Attitude Esti-
mation System for an Autonomous Helicopter,? IEEE International Conference on
Intelligent Engineering Systems, 1997, pp. 391-395.
[33] Lu, Y., Brown, A., ?Performance Test Results of an Integrated GPS/MEMS Inertial
Navigation Package,? Proceedings of the ION GNSS 2004, Long Beach, California,
Sep. 2004.
[34] Jun, M., Roumeliotis, S. I., Sukhatme, G. S., ?State Estimation of an Autonomous
Helicopter Using Kalman Filtering,? Proceedings of the 1999 IEEE/RSJ Interna-
tional Conference on Intelligent Robots and Systems, Vol. 3, 1999, pp. 1346-1353.
[35] Anon., ?Spark Fun Electronics,? http://www.sparkfun.com/commerce/product info
.php?products id=411, accessed Oct. 30, 2006.
[36] Anon., ?MMA7260Q Product Summary Page,? http://www.freescale.com/webapp/
sps/site/prod summary.jsp?code=MMA7260Q&nodeId=01126911184209, ac-
cessed Oct. 30, 2006.
[37] Anon., ?BlueSMiRF v1 Datasheet,? http://www.sparkfun.com/datasheets/RF/
BlueSMiRF v1.pdf, accessed Oct. 30, 2006.
[38] Anon., ?IMU 6-DOF v2 Datasheet,? http://www.sparkfun.com/datasheets/Sensors/
IMU 6DOF-v21.pdf, accessed Oct. 30, 2006.
154
REFERENCES
[39] Anon., ?LabVIEW - The Software That Powers Virtual Instrumentation,?
http://www.ni.com/labview/, accessed Oct. 30, 2006.
[40] Ogata, K., Modern Control Engineering, Prentice-Hall Inc., New Jersey, 2002.
[41] Stengel, R. F., ?Toward Intelligent Flight Control,? IEEE Transactions on Systems,
Man and Cybernetics, vol. 23, no. 6, 1993, pp. 1699-1717.
[42] Ananda, M. P., Bernstein, H., Cunningham, K. E., Feess, W. A., and Stroud, E. G.,
?Global Positioning System (GPS) Autonomous Navigation,? IEEE Position Loca-
tion and Navigation Symposium, Las Vegas, NV, Mar. 20-23, 1990.
[43] Amidi, O., Kanade, T., and Miller, R., ?Vision-based Autonomous Helicopter Re-
search at Carnegie Mellon Robotics Insitute 1991-1997,? American Helicopter So-
ciety International Conference, Japan, April, 1998.
[44] Barrows, G. L., Chahl, J. S., and Srinivasan, M. V., ?Biomimetic Visual Sensing and
Flight Control,? The Aeronautical Journal, Vol. 107, No. 1069, pp. 159-168, 2003.
[45] Wu, H., Sun, D., Zhou, Z., ?Model Identification of a Micro Air Vehicle in Loitering
Flight Based on Attitude Performance Evaluation,? IEEE Transactions on Robotics,
Vol. 20, No. 4, pp. 702-712, Aug. 2004.
[46] Shim, D. H., Koo, T. J., Hoffmann, F., and Sastry, S., ?A Comprehensive Study of
Control Design for an Autonomous Helicopter,? 37th IEEE Conference on Decision
and Control, 1998.
155
REFERENCES
[47] Smith, S. W., The Scientist and Engineer?s Guide to Digital Signal Processing, Cal-
ifornia Technical Pub., 1st edition, 1997.
[48] Geen, J, Krakauer, D., ?New iMEMS Angular Rate-Sensing Gyro-
scope,? Analog Dialogue, Vol. 37, No. 3, 2003 (available online:
http://www.analog.com/library/analogdialogue/archives/37-03/gyro.pdf).
[49] Xiyuan, C., ?Modeling Random Gyro Drift by Time Series Neural Networks and by
Traditional Method,? IEEE Int. Conf. on Neural Networks and Signal Processing,
Nanjing, China, Dec. 14-17, 2003.
[50] Anon., ?The MathWorks - Filter Design toolbox,?
http://www.mathworks.com/products/filterdesign/, accessed Oct. 30, 2006.
156