Formation and Flight Control of Affordable Quad-rotor

116 Pages·2009·5.35 MB·English

Formation and Flight Control of Affordable
Quad-rotor Unmanned Air Vehicles
by
Ming Chen
B.A.Sc, Shanghai Jiaotong University, 1998
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
Masters of Applied Science
in
THE FACULTY OF GRADUATE STUDIES
(Department of Electrical and Computer Engineering)
We accept this thesis as conforming
to the required standard
The University of British Columbia
July 2003
© Ming Chen, 2003
In presenting this thesis in partial fulfilment of the requirements for an advanced
degree at the University of British Columbia, I agree that the Library shall make it
freely available for reference and study. I further agree that permission for extensive
copying of this thesis for scholarly purposes may be granted by the head of my
department or by his or her representatives. It is understood that copying or
publication of this thesis for financial gain shall not be allowed without my written
permission.
Department of
The University of British Columbia
Vancouver, Canada
DE-6 (2/88)
Abstract
For several decades, Unmanned Air Vehicles (UAVs) have generated considerable interest
in the control and commercial community due to their advantages over manned systems.
Cutting edge techniques in senors, communications and robust control can now make
affordable commercial missions involving Unmanned Air Vehicles (UAVs) a reality.
The aim of this work was to control an autonomous UAV using HQQ loop shaping and
MPC control laws and further demonstrate formation control with three such identical
UAVs. The UAV used in our project is the four-rotor Dragonflyer III helicopter. To
achieve the project objectives, a nonlinear model of the Dragonflyer III and further a
Quasi-LPV model were developed. An loop shaping control law was designed for
stabilization and speed loops. For the trajectory control, two controllers, an and an
MPC, were designed and compared.
This project then was extended to control 3 quad-rotor UAVs in equilateral triangle
flying formation, objective for which, there layers, Path Planner, Trajectory Generator
and Formation Controller, were introduced and implemented in Matlab and Simulink.,
ready for placing the hardware in the loop. The performance of the proposed methods
was evaluated for several circumstances with satisfactory results.
To validate the low level control laws and demonstrate flying, an experimental sys
tem including a flying mill, a personal computer and DSP dSPACE board, a programmed
microprocessor and a radio transmitter was built for testing.
ii
Ill
Comparing to previous UAV works, a quad-rotor helicopter is first chosen as the UAV
dynamics in our project. The 2 DOF and combined MPC/H^ flight controller are
firstly achieved and animated to control such high nonlinear system. A new implementa
tion of formation flying control is proposed and simulated in MATLAB and SIMULINK. A
self designed experimental setup is also built for identification and control testing purpose.
Acknowledgements
I am sincerely thankful to Dr. Mihai Huzmezan, my supervisor at the University of British
Columbia, for his willingness to guide and discuss my progress, outstanding supervision,
comprehensive knowledge, encouragement and efforts of my career seeking. The opportu
nity of being Dr.Mihai Huzmezan's graduate student has already changed my life to an
aspiring future.
Many thanks also go to mechanical technicians, Leiff Kjolby and Dave Fletcher in Elec
trical and Computer Engineering Department, for their help of designing and building the
flying mill for the Quad-rotor UAVs and their valuable suggestions for the UAV dynamics.
I would also like to thank my good friends and colleagues with whom I shared my
pleasant moments during the study at UBC and life inside and outside Canada.
Ultimately, I truly appreciate my parents and my wife for their unwavering encourage
ment and unconditional support.
iv
Table of Contents
Abstract ii
Acknowledgements iv
Table of Contents v
1 Introduction and Background 1
1.1 UAVs Review 1
1.2 Sensors for Unmanned Air Vehicles 5
1.2.1 Accelerometers 5
1.2.2 Gyroscopes 7
1.2.3 GPS 8
1.2.4 Attitude Estimation for UAVs based on GPS/IMU 11
1.3 High Fidelity Linear Parameter Varying (LPV) Modelling 12
1.3.1 Gain Scheduling and LPV Models 12
1.3.2 Quasi-LPV Models 13
1.4 Jfoo loop shaping design for UAVs 15
1.5 MPC control for UAVs . . 18
2 The Experimental Rig and The Nonlinear UAV Model 21
2.1 The Quad-rotor Helicopter Experimental Setup 21
2.1.1 The Flying Mill .21
2.1.2 Data Flow in the Experimental System 23
2.1.3 The Pulse Modulator 24
2.2 The Nonlinear Four-rotor Helicopter Model 31
2.2.1 Dynamics of Four-rotor Helicopter 32
2.2.2 The Quasi-LPV model of the Four-rotor Helicopter 35
2.2.3 The SIMULINK Model of the Four-rotor Helicopter 36
3 2 DOF Hoo and Combined MPC/Hoo Flight Controller Design 38
3.1 The Roll And Pitch Angles, Yaw Rate and Vertical Speed Inner Loop Design 39
3.1.1 The Design Procedure 39
3.1.2 Simulation Results 43
3.2 Longitudinal and Lateral Speed, Throttle and Yaw Angle Outer Loop Design 46
CONTENTS vi
3.2.1 Design Procedure 46
3.2.2 Simulation Results 50
3.3 The Trajectory Outer Loop Design 52
3.3.1 Design Procedure 52
3.3.2 Simulation Results 56
3.4 A Combined MPC/tfoo UAV Flight Controller . 60
3.4.1 Motivation 60
3.4.2 Design Procedure And Results 62
4 Formation Control 67
4.1 The Formation Control Path Planner 69
4.1.1 The Dijkstra's Algorithm 69
4.1.2 The Path Planner Design 73
4.2 The Trajectory Generator ,. 75
4.3 Formation Controller 80
5 Conclusion and Future Work 86
A M-file of the Two DOF Loop Shaping Flight Controller Design 89
B M-file of the Combined MBPC/H infinity Controller Design 94
C M-files for Formation Control 96
C.l M-file of Dijkstra's algorithm for Path Planner 96
C.2 M-file of Trajectory Generator 97
C.3 M-file of Formation Controller • 99
Bibliography 101
List of Figures
1.1 2 DOF Hoo Loop Shaping Controller 16
1.2 Prediction Strategy 19
2.1 Photo of The Flying Mill With Dragonfiyer III 22
2.2 The Data Flow In Experimental System 24
2.3 PWM Signal Definition 24
2.4 The Data Flow of The Pulse Modulator System 25
2.5 The Top Level Simulink Model of The Pulse Modulator 27
2.6 The Base Level of The Pulse Modulator Simulink Model 27
2.7 Flow Chart of Pulse Modulator in MASM 29
2.8 Flow Chart of Subprogram For Channel 5 in MASM 30
2.9 The Four-rotor Helicopter Model 31
2.10 Sub Level SIMULINK Model Diagram of Dragonfiyer III 37
3.1 3 loop controller architecture 38
3.2 Inner Loop of The Two DOF Flight Controller 39
3.3 Dragonfiyer III Reduced Model For Inner Loop Design 40
3.4 Open Loop Singular Values of The Unshaped Plant 41
3.5 Open Loop Singular Values of The Shaped Plant 41
3.6 Closed-loop Sensitivity Function of The Inner Loop 43
vii
LIST OF FIGURES viii
3.7 Closed-loop Complementary Sensitivity Function of The Inner Loop . . .. 44
3.8 Step Responses With Controller 44
3.9 Output Step Disturbance Responses 45
3.10 Simulation of The Nonlinear Model 45
3.11 Simulation of The Nonlinear Model With Noise 46
3.12 The First Outer Loop of The Two DOF Flight Controller 47
3.13 Inner Loop And The Nonlinear Dragonfiyer III Model For The First Outer
Loop Design 48
3.14 Open Loop Singular Values of The First Outer Loop Design 49
3.15 Shaped Open Loop Singular Values of The First Outer Loop Design . . .. 49
3.16 Closed-loop Sensitivity Function of The First Outer Loop 50
3.17 Closed-loop Complementary Sensitivity Function of The First Outer Loop . 51
3.18 Step Responses With Controller of The Velocity Outer Loop 52
3.19 Output Step Disturbance Responses of The Velocity Outer Loop 53
3.20 Simulation Of The Nonlinear Model of The Velocity Outer Loop 53
3.21 The Trajectory Loop of The Two DOF Flight Controller 54
3.22 Nonlinear Model For The Trajectory Loop Design 54
3.23 Open Loop Singular Values of The Trajectory Loop Design . . 55
3.24 Closed-loop Sensitivity Function of The Trajectory Loop 56
3.25 Closed-loop Complementary Sensitivity Function of The Trajectory Loop . 57
3.26 Step Responses With Controller of The Second Outer Loop 57
3.27 Output Step Disturbance Responses of The Second Outer Loop 58
3.28 Trajectory Simulation of The Nonlinear Model With 2 DOF Controller 58
3.29 Half Circle Scenario With 2 DOF Controller 59
3.30 Trajectory Scenario With 2 DOF Controller 59
3.31 A State Observer 62
LIST OF FIGURES ix
3.32 MPC In Longitudinal and Lateral Channel 63
3.33 Longitudinal and Lateral Channel Step Responses in The Combined MPC
And Hoo Controller 65
3.34 Sensitivity Function Of The Combined MPC/Foo Controller (The Uncon
strained Case) 65
3.35 Complementary Sensitivity Of The. Combined MPC/i^oo Controller (The
Unconstrained Case) 66
4.1 Formation Control Scheme For Multiple UAVs 68
4.2 Dijkstra's Algorithm Example 69
4.3 Voronoi Diagram for Threat Locations 73
4.4 Initial Path from The Path Planner 74
4.5 Path Formed by The Trajectory Generator 75
4.6 Trajectory Generator and Quod Rotor UAV Architecture 76
4.7 Simulation Results ff Trajectory Generator and Closed Loop UAV 78
4.8 Trajectory Simulation Results 79
4.9 3 UAV Equilateral Triangle Formation in Inertial Frame 80
4.10 The Overall Formation Control Architecture 82
4.11 Animation of Equilateral Triangle Formation Flying 83
4.12 Formation Flying Results of Follower B UAV 84
4.13 Formation Flying Results of Follower C UAV 85