videogrammetric determination of aircraft position and ... · one camera at left vertical tail ....
TRANSCRIPT
Videogrammetric Determination
of Aircraft Position and Attitude
for Vision-Based Autonomous Landing
Tianshu Liu
Department of Mechanical and Aeronautical Engineering
Western Michigan University, Kalamazoo, MI 49008
Objectives
• To study videogrammetric methods for vision-based
landing based on natural ground features
• To develop algorithms for virtual reality simulation
and real flight control system
• To evaluate the accuracy of videogrammetric methods
Generic Vision System for Landing
• Pattern/target Recognition
• Position, attitude and velocity determination
NASA LaRC OV-10:
Two cameras at wing tips;
One camera at left vertical
tail
Natural Features on Ground:
High contrast, parallel runway edges
Photogrammetry (I)
Perspective projection transformation
3D Object Space 2D Image Plane
)ZZ(m)YY(m)XX(m
)ZZ(m)YY(m)XX(mcydyy
)ZZ(m)YY(m)XX(m
)ZZ(m)YY(m)XX(mcxdxx
c33c32c31
c23c22c21p
c33c32c31
c13c12c11p
Photogrammetry (II)
Collinearity Equations
)Z,Y,Xκ,φ,ω,( ccc
)S/S ,P,P,K,K,y,x(c, vh2121pp
Exterior Orientation
Parameters:
Interior Orientation
Parameters:
Photogrammetry (III)
Camera Orientation
)Z,Y,Xκ,φ,ω,( ccc
)S/S ,P,P,K,K,y,x(c, vh2121pp
To determine exterior orientation
parameters
To determine interior orientation
parameters:
Camera Calibration
• Direct Linear Transformation (DLT)
• Closed-Form Resection Solution
• Optimization Method
Analytical Techniques:
The Point Correspondence Problem
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)
Photogrammetry (IV)
3D Target Field for Camera Orientation
Photogrammetry (V)
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
Wing Deformation Effects (Case #2)
Position Errors Attitude Errors
Lens Distortion Effects (Case #2)
Position Errors Attitude Errors
Camera Parameters: )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 #3
50)20,(4014,)Z,Y,X(acacac gOgOgO
Random Noise Effects (Case #3)
Position Errors Attitude Errors
Wing Deformation Effects (Case #3)
Position Errors Attitude Errors
Lens Distortion Effects (Case #3)
Position Errors Attitude Errors
Determining Aircraft Position and Attitude
Single-Camera Method
)ZZ(r)YY(r)XX(r
)ZZ(r)YY(r)XX(r
X
Z
c
y
)ZZ(r)YY(r)XX(r
)ZZ(r)YY(r)XX(r
X
Y
c
x
acacac
acacac
acacac
acacac
gOg31gOg21gOg11
gOg33gOg23gOg13
ac
ac
gOg31gOg21gOg11
gOg32gOg22gOg12
ac
ac
Special collinearity equations:
Image coordinate system is aligned with aircraft
body coordinate system
Vanishing Point and Horizon
At the vanishing point,
1112vp r/rx
1113vp r/ry
At the horizon,
tankoh
Simulation Cases
(Single-camera method)
Random Noise Effects (Case #2)
(Single camera method)
Position Errors Attitude Errors
Horizontal Line Effects (Case #2)
(Single camera method)
Position Errors Attitude Errors
Two-Camera Method
Single-Camera Method
• Requirements: Camera Calibration/Orientation, Runway Edges
• Requirements: Horizontal line, Runway Edges
• Estimated Errors:
Pitch, Yaw (0.01-0.1 deg) & Roll Angles (0.1-1 deg)
Altitude, Lateral (0.1-3 ft) & Longitudinal Coord. (20-40 ft)
• Estimated Errors:
Pitch, Yaw (0.01-0.1 deg) & Roll Angles (0.03-0.14 deg)
Altitude & Lateral Coord. (0.03-5 ft)
Conclusions
Future Development:
Lunar and Planetary Landing
Four-Camera Vision for Landing