臺灣博碩士論文加值系統

自從第一顆人造衛星被發射上軌道並在之後的幾年提出全球定位系統(GPS)理論不過短短三四十年，至今GPS已發展非常成熟，無人機(UAV)的導航便是其應用之一。現今的無人機可以比以往更便宜的價格、更低的汙染以及更高的靈活性來使用，例如多軸無人機幾乎能在各種環境起降，但是GPS輔助仍有些限制條件像是在室內時，GPS的電磁波訊號會大量衰減，在這樣的狀況下操作無人機會有一定的困難及危險性存在。因此此論文便討論一種使用電腦視覺方法來輔助慣性導航系統，其電腦視覺理論稱為homography 演算法。

在本篇論文中，我們運用卡爾曼濾波器(Kalman filter)來估測速度偏差以及角速度偏差，利用這兩項估測值來補償慣性導航系統。

Currently, the Global Positioning System (GPS) products have been matured and have applied in multiple ways. One of the application is Unmanned Aircraft Vehicle (UAV). The feature points of the UAV are the lower pollution and price, highly freedom to change instrument for the mission, and highly maneuverability in the fly field. Therefore, it will make the easy navigation but there are still some limitations of the GPS aiding, for example, the GPS signal is not efficient indoor because of the attenuation of electromagnetic waves. Therefore, we discuss a vision approach to aid low-cost inertial navigation system (INS) where the vision approach is called homography algorithm.
In this thesis, by using the Kalman filter, we estimate the velocity errors and angular velocity errors from the images to compensate the low-cost INS.

TABLE OF CONTENTS
致謝辭. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii
ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iii
TABLE OF CONTENTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv
LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii
LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi

CHAPTER

PART I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.2.1Navigation Review . . . . . . . . . . . . . . . . . . . . .4
1.2.2Computer Vision Review . . . . . . . . . . . . . . . . . .8
1.2.3Homography Matrix . . . . . . . . . . . . . . . . . . . . .10
1.2.4Kalman Filter Review . . . . . . . . . . . . . . . . . . . .12
1.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
PART II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
2. Mechanisation Equations of Inertial Navigation Systems. . . . . .17
2.1 Problem Description: Inertial Navigation System . . . . . . . . . .17
2.2 Euler Angular: Description of Rotation . . . . . . . . . . . . . . .18
2.2.1Yaw Axis Rotation . . . . . . . . . . . . . . . . . . . . .19
2.2.2Pitch Axis Rotation . . . . . . . . . . . . . . . . . . . . .20
2.2.3Roll Axis Rotation . . . . . . . . . . . . . . . . . . . . .21
2.2.43-2-1 Rotation Matrix . . . . . . . . . . . . . . . . . . . .22
2.2.5Angular Velocities . . . . . . . . . . . . . . . . . . . . . .25
2.3 INS Mechanisation Equations . . . . . . . . . . . . . . . . . . . . .26
2.4 GPS Error Equations . . . . . . . . . . . . . . . . . . . . . . . . .28
3. 2D Homography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
3.1.12D Projective Transformation . . . . . . . . . . . . . . .30
3.1.2The Direct Linear Transformation (DLT) Algorithm . . .32
3.2 2D Projective Coordinates . . . . . . . . . . . . . . . . . . . . . . .32
3.2.1Downward-Looking Projective Coordinates . . . . . . . .32
3.2.2Side-Looking Projective Coordinates . . . . . . . . . . . .34
3.3 Homography between Two Images of a 2D Scene . . . . . . . . . .35
3.4 Computation of the Homography Matrix . . . . . . . . . . . . . . .37
3.4.1Feature Extraction and Matching . . . . . . . . . . . . .38
3.4.2The Normalized Direct Linear Transform (DLT) Algorithm 44
4. Homography-Based Vision-Aided Inertia Navigation Model. . .46
4.1 Navigation-Error Process Model . . . . . . . . . . . . . . . . . . .46
4.2 Homography-Based Measure Model . . . . . . . . . . . . . . . . . .49
4.3 Extended Kalman Filter (EKF) Based Estimation of NavigationError . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
PART III. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
5. Implementation on UAV. . . . . . . . . . . . . . . . . . . . . . . . . .54
5.1 Inertial Measurement Sensor Bios Correction . . . . . . . . . . . .54
5.2 Camera Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .56
5.2.1Calibration Step . . . . . . . . . . . . . . . . . . . . . . .56
5.2.2Calibration Result . . . . . . . . . . . . . . . . . . . . . .58
5.3 MAVLink Communication . . . . . . . . . . . . . . . . . . . . . . .64
5.3.1Communication between Groundstation and RaspberryPi 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
5.3.2Communication between Pixhawk and Raspberry Pi 3 . .68
5.4 Automatic Controlled by Sending MAVLink Messages . . . . . . .69
5.5 Flight Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . .72
5.5.1Image Time Problem Lead Data Confusing . . . . . . . .72
5.5.2Timing Implementation of Homography-Based Vision-AidedINS Using Extended Kalman Filter . . . . . . . . . . . .73
5.5.3INS Mechanisation with Compensation . . . . . . . . . .77
6. Flight Experiment Result. . . . . . . . . . . . . . . . . . . . . . . . .88
6.1 Experiment Result . . . . . . . . . . . . . . . . . . . . . . . . . . .91
6.1.1INS Mechanisation with No Aiding . . . . . . . . . . . .91
6.1.2INS Mechanisation with Homography Estimation and Compensation ofδZKFandδψKF. . . . . . . . . . . . . . . .98
6.1.3INS Mechanisation with Estimation and Compensation ofδVKF,δωKF,δZKF, andδψKF. . . . . . . . . . . . . . . 107
6.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
PART IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
7. Conclusion and Future Work. . . . . . . . . . . . . . . . . . . . . . . 121
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123
APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

LIST OF TABLES
Table
3.1 Comparison of SIFT and SURF. . . . . . . . . . . . . . . . . . . . . . . .38
5.1 MAVLink package frame description. . . . . . . . . . . . . . . . . . . . .65

LIST OF FIGURES
Figure
2.1 3-2-1 Euler Angles transform, display the transformation from Earth tothe body frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
2.2 First step: Rotate the yaw axis with theψangle by following the right-hand rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
2.3 Second step: Rotate the pitch axis with theθangle by following theright-hand rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
2.4 Third step: Rotate the roll axis with theφangle by following the right-hand rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
2.5 Simple model of INS mechanization. . . . . . . . . . . . . . . . . . . . . .28
2.6 A lever arm with a distancelbbetween GPS antenna and IMU frame. . .29
3.1 A cuboid structure in 3D space projects onto 2D photo. . . . . . . . . . .31
3.2 The projective pointspAandpBtaken from 3D space pointPare appliedon aircraft capturing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
3.3 According to the Figure 3.2, the projective frame models are transformedto apply to the ground vehicle. . . . . . . . . . . . . . . . . . . . . . . . .34
3.4 The camera lens mounted on the ground vehicle points toyaxis direc-tion. The axisx′andy′are represented the image axis and they will betransformed tou′andv′to fix with vehicle body frame. . . . . . . . . . .35
3.5 The difference of Gaussian: Each octave in initial image is repeatedlyconvolved with Gaussian to produce scale space image which is shown inright image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40
3.6 The image gradients vector will be accumulated into a histogram, thenthe gradients from histogram will integrate to become new bigger regionshown in right image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
3.7 The matching feature points calculated from the images by SIFT algo-rithm. (a) Two original images captured by front and rear cameras at thesame time. (b) The result of (a) after doing SIFT calculation. The 395matching point was found and the descriptor was stored in the front andrear matrices [128×2621] and [128×1809] separately. . . . . . . . . . .42
3.8 The matching interest points are calculated from images after SURF al-gorithm. The matching points used by SURF are less than SIFT but thecomputing time is much faster than SIFT. . . . . . . . . . . . . . . . . .43
5.1 Accelerometer measurement: the measurements from top to bottom arerepresented x-, y- and z-axis separately with accelerometer biasεaandnoisewa. (Unit:meters/sec2) . . . . . . . . . . . . . . . . . . . . . . . .55
5.2 Gyroscope measurement: the measurements from top to bottom are rep-resented x-, y- and z-axis separately with gyroscope biasεgand noisewg.(Unit:radian/sec) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
5.3 MATLAB Toolbox initial window. . . . . . . . . . . . . . . . . . . . . . .56
5.4 Image names. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
5.5 Image names result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
5.6 Input the designated extract window size. . . . . . . . . . . . . . . . . . .58
5.7 Input the size of one grid measured from real life grid. The measurementsize is 97×94 millimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . .59
5.8 Extract the number of the grid: (a) The four boundary points of gridcircled by the green line. (b) The red symbols “+” are represented thecross points of each grid. . . . . . . . . . . . . . . . . . . . . . . . . . . .59
5.9 Calibration result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60
5.10 The extracted grids from image (a) to image (i) denote the captured po-sitions from left top of image to right bottom of image. Each capturedimage will include 15 different rotation angles and little shifts to increasethe diversity of database. . . . . . . . . . . . . . . . . . . . . . . . . . . .62
5.11 3D camera-centered view presents the result of capturing 135 images fromgrid in MATLAB. The symbolOon the left side denotes camera location.The captured grid is locatied on the right side. . . . . . . . . . . . . . . .63
5.12 3D world-centered view presents the fixed grid is captured by a movablecamera. This image transforms the Figure 5.11 from camera-centered toworld-centered view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63
5.13 MAVLink package frame. . . . . . . . . . . . . . . . . . . . . . . . . . . .64
5.14 Communication map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
5.15 CERIO operating mode. . . . . . . . . . . . . . . . . . . . . . . . . . . .66
5.16 Setting the ID of Repeater AP. For example, the ID is called “RepeaterAP”in the figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
5.17 The system connects successfully. The Pi3 IP is 192.168.2.13 which isgiven by CERIO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
5.18 Raspberry Pi 3 pinout. . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
5.19 Raspberry Pi3 controls the roll, pitch and yaw axis which representx,yandzaxis of UAV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
5.20 Drepresents the ground project of pixel resolution.D=6×10−66×10−3×100 = 0.1 72
5.21 The homography time ∆THis extended to a longer time to remove theeffect of errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73
5.22 UsingδˆHto compensate INS model. . . . . . . . . . . . . . . . . . . . .74
5.23 Homography time ∆THis 0.33 seconds but Kalman filter time ∆TKFis0.01 second. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75
5.24 Simple INS model with Kalman filter. . . . . . . . . . . . . . . . . . . . .77
5.25 δVcompensator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81
5.26 δZcompensator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
5.27 Calculate DCM and Euler angles. . . . . . . . . . . . . . . . . . . . . . .83
5.28 INS mechanisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84
5.29 INS mechanisation with Kalman filter. . . . . . . . . . . . . . . . . . . .85
5.30 Raw angular velocity records from the gyroscope of Pixhawk. . . . . . . .86
5.31 Inertial Accelerometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . .87
6.1 Road test trajectory displayed on Google map. . . . . . . . . . . . . . . .88
6.2 Flight experiment trajectory displays on Mission Planner by using GPS. .90
6.3 The position data imported from Pixhawk displays on MATLAB. . . . .91
6.4 The estimation of Euler angle. . . . . . . . . . . . . . . . . . . . . . . . .94
6.5 Altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
6.6 Velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
6.7 Anguler velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
6.8 Height error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
6.9 ψerror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
6.10 The trajectory of pure INS mechanisation. . . . . . . . . . . . . . . . . .97
6.11 The estimation of Euler angle. . . . . . . . . . . . . . . . . . . . . . . . . 101
6.12 Altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.13 The errors of the homography estimates. . . . . . . . . . . . . . . . . . . 102
6.14 The compensationsδV,δω,δZ, andδψestimated by Kalman filter. . . . 103
6.15 Velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.16 Anguler velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.17 Height error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.18 ψerror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.19 The trajectory of INS with homography estimation and compensation ofδZandδψ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.20 The estimation of Euler angle. . . . . . . . . . . . . . . . . . . . . . . . . 109
6.21 Altitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.22 The errors of the homography estimates. . . . . . . . . . . . . . . . . . . 110
6.23 The compensationsδV,δω,δZ, andδψestimated by Kalman filter. . . . 111
6.24 Velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.25 Anguler velocity error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.26 Height error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.27 ψerror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.28 The trajectory of INS with homography estimation and all compensations:δV,δω,δZ, andδψ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.29 The trajectories of Section 6.1.1, 6.1.2, and 6.1.3 which are performed inblue, green, and red lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.30 Example of images that captured by binocular camera. . . . . . . . . . . 118
6.31 Histogram of match points between reference images and current images. 119
6.32 Histogram of ∆TH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

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