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Videogrammetric Technique for
Aerospace Applications: From Model Attitude and Deformation to
Surface Geometry
Tianshu Liu
Department of Mechanical and Aerospace Engineering
Western Michigan University, Kalamazoo, MI 28004
A. W. Burner, T. W. Jones, D. A. Barrows
NASA Langley Research Center
Hampton, VA 23681
Objectives
• Mapping surface quantities onto surface
• Measurement of static and dynamic aeroelastic
deformation and extracting vibration modes
• Measurement of attitudes and positions of models
and control surface
• Reconstruction of 3D velocity fields
Outline
• Application Examples:
Static and Dynamic Wing Deformation
Model Position and Attitudes
Vision-Based Autonomous Landing
Surface Geometry
• Videogrammetric Attitude and Deformation
Measurement (VMD) Technique:
Hardware (Cameras & Lighting)
Software (Calibration & Intersection)
• Conclusions
• Videogrammetric deformation technique has been
developed for wind tunnel testing at NASA Langley
(Burner 1996, 1997, Liu et al. 2000, Burner & Liu
2001, Liu et al. 2012)
• Viedogrammetry has been used in large-scale space
structures at NASA Langley (Pappa 2002, Jones
2005)
The Working Principle:
Non-Topographic Photogrammetry
Camera Calibration/Orientation
Objective: to determine camera exterior and interior orientation
parameters in the collinearity relation between object space
and image plane.
The Collinearity Equations
Tnnnn )Z,Y,(X=P
Tnnn )y,(x=p
)Z,Y,X,,,( ccc
)/SS,P,P,K,K,y,xc,( vh2121pp
Parameters:
Object point coordinates:
Image point coordinates:
Exterior orientation:
Interior orientation and lens distortion:
n = 1, 2, 3 ...
.coscosm,cossinm,sinm
,cossinsinsincosm
,coscossinsinsinm
,sincosm,sinsincossincosm
,sincoscossinsinm,coscosm
333231
23
22
2113
1211
Rotational Matrix
& Euler Angles:
)ZZ(m)YY(m)XX(m
)ZZ(m)YY(m)XX(mcyyy
)ZZ(m)YY(m)XX(m
)ZZ(m)YY(m)XX(mcxxx
c33c32c31
c23c22c21
p
c33c32c31
c13c12c11
p
Lens Distortion Model
dr xxx
dr yyy
,
4
p2
2
p1r r)x'x(Kr)x'x(Kx
4
p2
2
p1r r)y'y(Kr)y'y(Ky
)y'y)(x'x(P2])x'x(2r[Px pp2
2
p
2
1d
)y'y)(x'x(P2])y'y(2r[Py pp1
2
p
2
2d
2p
2p
2 )y'y()x'x(r
,
,
,
.
where
K1 > 0
K1 < 0
Camera Calibration/Orientation
Object point coordinates: Tnnnn )Z,Y,(X=P n = 1, 2, 3 ...
Image point coordinates: T
nnn )y,(x=p
Given Data:
Unknowns:
Exterior orientation: )Z,Y,X,,,( ccc
Interior orientation &
lens distortion: )/SS,P,P,K,K,y,xc,( vh2121pp
Photogrammetric Intersection
Object point coordinates: Tnnnn )Z,Y,(X=P n = 1, 2, 3 ...
Unknowns:
Given Data:
Tnnn )y,(x=p )Z,Y,X,,,( ccc )/SS,P,P,K,K,y,xc,( vh2121pp
Alternative Forms of Collinearity Equations
3
222p
2
3
111p
1
X
X
)(
)(
c
xxx
X
X
)(
)(
c
xxx
c3
c2
c3
c1
XXm
XXm
XXm
XXm
T321)X,X,X(X
( 1m , 2m , 3m ) Projection form in the frame
are coordinates on ( 1m , 2m , 3m )
0)( c1 XXW
0)( c2 XXW
Projection form least-squares estimation
Typical Methods for Camera Calibration
Iterative Least-Squares Method (The Bundle Method):
Determination of a full set of the parameters
Matrix singularity, Multiple camera stations and roll angles,
Initial guess, Expertise to operate.
Direct Linear Transformation (DLT):
Simplicity and no initial guess when lens distortion is neglected.
Loss of simplicity and large errors when lens distortion exists.
Methods in Comupter Vision (Tsai’s Two-Step Method):
Fast and nearly-automatic calibration.
Not solving the collinearity equations,
Limitations of radial alignment constraint.
Direct Linear Transformation (DLT)
Linear Treatment of a Nonlinear Problem
0)1ZLYLXL)(ydy(LZLYLXL
0)1ZLYLXL)(xdx(LZLYLXL
111098765
111094321
The DLT equations (Abdel-Aziz & Karara 1971):
111 L,L The DLT parameters: )Z,Y,X,,,( ccc
)y,x(c, pp
The over-determined system:
T111 )L,L( L
TMM11 )y,x,y,x( Cwhere
B is the 2M11 configuration matrix
CLB
The least-squares solution:
CBB)(B=L T1T
Optimization Method for Camera Calibration (Liu et al. AIAA J. 2000)
Two separated, but interacting procedures:
(1) Resection for the exterior orientation parameters;
(2) Optimization for the interior orientation
and additional parameters, i.e.,
Objective function std(xp) min
(1) A single image, single station method
(2) Automatic calibration when combined with DLT
(3) Determination of a full set of 14 camera parameters
(4) Capability to obtain spatial coordinates for
a multiple-camera system
0
1
2
3
4
5
0
2
4
68
1012
1416
02
46
810
1214
Z (in)
X (in
)
Y (in) x (mm)
-8 -6 -4 -2 0 2
y (
mm
)
-2
0
2
4
6
8
Object space Image plane
imaging
Simulation: Targets on a Step
Topology of the Objective Function std(xp) near
a Minimum-Point in the Parameter Space
Effects of Three-Dimensionality and Noise
on Topology of std(xp)
(a) H = 6 in, (b) H = 2 in. (a) disturbance level of 6 m;
(b) disturbance level of 1 m
3D Effect Noise Effect
Camera Calibration Set-Up
Calibration target-plate
Camera
Parameters c(mm) xp (mm) yp (mm) Sh /Sv K1 (mm-2
) K2 (mm-4
) P1 (mm-1
) P2 (mm-1
)
Optimization 8.133 -0.156 0.2014 0.99238 0.0026 3.310-5
1.810-4
310-5
Optical techniques 8.137 -0.168 0.2010 0.99244 0.0027 4.510-5
1.710-4
710-5
Calibration for a Hitachi CCD camera
with a 8 mm Cosmicar TV lens
c (mm)
10 20 30 40 50 60 70 80 90
xp o
r y
p (
mm
)
-1
0
1
2
Laser illumination technique
Optimization algorithm
xp
yp
c (mm)
10 20 30 40 50 60 70 80 90
K1 (m
m-2
)
-0.0020
-0.0015
-0.0010
-0.0005
0.0000
0.0005
0.0010
Optimization algorithm
Burner (1995)
Calibration for a Hitachi CCD Camera with a Sony Zoom Lens
Zoom setting (mm)
1020304050607080
Principal distance c (mm)
10
20
30
40
50
60
70
80
90
Optimization algorithm
Linear fit
Calibration for a Hitachi CCD Camera
with a Sony Zoom Lens
Effect of Zoom Setting Effect of Step Height
Calculations of Target Coordinates Multiple-Camera Solution
Photogrammetric Intersection:
0)(,0)( c(n)2(n)c(n)1(n) XXWXXW . ( 2,1n )
Generalized Longuet-Higgins Relation:
Image 1 Image 2
Epipolar Line
h(1)x
h(2)x
Epipolar Line
0)xx(Q)x(x )1(hh(1))2(hh(2)
Epipolar Geometry on Point Correspondence:
Geometric illustration of the single-camera solution
Calculations of Target Coordinates Single-Camera Solution
Single-Camera System Two-Camera System
Basic Systems
Single-Camera VMD System in Wind Tunnel
LIMITED EXCLUSIVE RIGHTS NOTICEThese data are subject to Limited Exclusive Rights
under Government contract No. NAS1-20220.
Camera Calibration/Orientation
in Large Wind Tunnels
Video Cameras
Still Cameras
Targets: Retro-Reflecting Targets
Targets: Retro-Reflecting Targets
Targets: Laser-Projecting Targets
(a) Test configuration for proof-of-concept experiment
Camera 1
Camera 2 Laser
Membrane Structure
Diffractive Pattern Generator
(a)
(b) (c) (d)
Flowchart of Software
Key Procedure
Target Tracking and Centroid Calculation
• Real-time target tracking.
• Automatic recovery of lost targets based on
memory of target locations.
• Adjustable intensity level threshold.
• Capability of tracking PSP targets.
target
target in next frame
searching box
Measurement Uncertainty
AOAac
(degree)
-40 -30 -20 -10 0 10 20 30 40
Ran
do
m E
rro
r (d
eg
ree
)
-0.030
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Test 1
Test 2
Test 3 0.01 deg.
Centroid variation in x direction (pixel)
-0.04-0.03-0.02-0.010.000.010.020.030.04
Population0
20
40
60
80
100
120
Standard deviation = 0.0081 pixels
(a)
Accuracy: 0.01 degrees in angle measurement
0.001 inches in displacement measurement
Wing Twist Calculation
Deformation and Attitude Measurements
Static Deformation of a Semi-Span Model
-3
-2
-1
0
1
0.30.4
0.50.6
0.7
0.8
0.9
1.0
-5
0
5
10
15
20
25
Tw
ist (d
eg
)
Wing Span (%)
AOA (deg)
Spanwise location
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
De
fle
ction
(in
)
0.0
0.5
1.0
1.5
2.0
2.5
AOA = 0 deg
AOA = 5 deg
AOA = 10 deg
AOA = 15 deg
AOA = 20 deg
Static Deformation of a High-Speed Research
Model
Reconstructing Deformed Wing Surface Geometry
The body and local coordinate systems and the wing airfoil
sections along the quarter-chord line
4/c0
4/c0
twtw
twtw
4/c
4/c
ZZ
XX
cossin
sincos
ZZ
XX
Twisted Wing
Sections
Reconstructed Deformed Wing Quarter-chord line
Wing twist
Reconstructed Wing Surface
Rotor Blades in Ames 40-by-80-Ft Wind Tunnel
Rotor Blades in Ames 40-by-80-Ft Wind Tunnel
Thin Wing Vibration Measurements
Biologically-Inspired Concept
Camera Calibration/Orientation in Wind Tunnel
Two-Step Target Plate
for Camera Calibration
Two-Step Target Plate Aligned with
The Tunnel Coordinate System
Orthogonal Eigenfunctions Based on Beam Functions
6
1r
rr )t()y,x(w)t,y,x(w
1st bending 2nd bending
1st torsion
Vibration Control with Flexible Fins
Semispan: 71.5 mm (6.75 in)
Chord: 101.6 mm (4 in)
Thickness: 0.22 mm
Rectangular Flat-Plate Wing:
(Cantilever part: 6 in)
Mylar Fins:
Length: 0.2 chord
Thickness: 0.089 mm
5 segments in semispan
located at 0.1c
Time-Dependent Wing Surface at AoA = 8 deg at 13 m/s
Reconstructed from 6 Eigen Modes
Baseline Wing Wing with Fins
Maximum, Median and Minimum Amplitudes
Amplitude of 1st Torsion Mode at AoA = 8 deg at 13 m/s
Spectra of 1st Torsion Mode at AoA = 8 deg at 13 m/s
Applications in Global Flow Diagnostics
Motion Field on Surface
Image
(Cattafesta et al. 1996)
Skin Friction Topology of Wing-Body Junction Flows
GLOF Images Taken at Five Viewing Angles and Positions
AoA = 6 deg,
U = 27 m/s,
Re based on max
thickness:
151,000,
UV LED Power:
12 W
Long-pass Filter:
550 nm
Reconstructed Intensity Distribution on Surface of
the Wing-Body Junction via Photogrammetry
GLOF Intensity Distribution Surface Mesh
(240,372 grid points)
Reconstructed Skin Friction Field on Surface of
the Wing-Body Junction for AoA = 6 deg
0S#N#
6N#
6S#
• Pattern/target Recognition
• Position, attitude and velocity determination
NASA LaRC OV-10:
Two cameras at wing tips;
One camera at left vertical
tail
Vision-Based Autonomous Landing
(Liu & Fleming 2006)
Vision-Based Autonomous Landing
Natural Features on Ground:
High contrast, parallel
runway edges
3D Target Field for Camera Orientation
Determining Aircraft Position and Attitude
Two-Camera Method
Requirements:
• Two calibrated cameras
• Two parallel runway edges
(Edge detection)
,
3
1i
iaci321312131g3 r|PPPP|/PPPP ee
Aircraft Euler Angles and Position Coordinates
Relation between the ground and aircraft coordinate systems
Triangle
3
iaci12121g1 r|PP|/PP
1i
ee
3
1i
iaci221g321g3g2 r|PP|/PP eeee
3332 r/rtan
31rsin
1121 r/rtan
Roll, Pitch
and Yaw Angles:
Camera Parameters:
118)40,(4477,)Z,Y,X(acacac gOgOgO
)Z,Y,Xκ,φ,ω,( ccc )ft16,0,0,0,88,85( ooo
)ft16,0,0,0,88,85( ooo
feet Position & Attitude: o2 o5
o3
Simulation Case #2
Left-wing camera Right-wing camera
Random Noise Effects (Case #2)
Position Errors Attitude Errors
Surface Geometry of Gossamer Space Structures
1 2
3 4
(McInnes 1999, 2002, West & Derbes 2000,
Spieth & Zubrin 1999, Pappa et al. 2002,
Jones et al. 2006)
The photogrammetric method can be integrated
with other image-based techniques
in wind tunnel testing.
Conclusions
Videogrammetric technique is very useful
as a remote and non-contact measurement
method in wind tunnel testing, ground-based
and flight testing.