Robot Navigation and Mapping

1. Robot Navigation 2
Robot Navigation 2

2. Problem Description
Problem Description
The aim is to enable a robot to move
around on the ground plane by
visually detecting and avoiding
obstacles.

3. Stages Involved (Existing)
Stages Involved (Existing)
Camera Calibration
Edge & Corner Detection
Finding Correspondences
3-D Reconstruction
Path Planning
Navigating the Path

4. Camera Calibration
Camera Calibration
m = Ai [Ri|ti] M
 A co-ordinate system for each camera
 4+3+3 = 10 unknowns

5. Problem Description
Problem Description
The aim is to enable a robot to move
around on the ground plane by
visually detecting and avoiding
obstacles.

6. Camera Calibration
Camera Calibration
m = Ai [Ri|ti] M
 A co-ordinate system for each camera
 4+3+3 = 10 unknowns

7. Right Image plane
Left Image plane
Essential & Fundamental Matrices
Essential & Fundamental Matrices
e’
e
x
x’
R,T
Y’
X’
Z’
C’
Right optical center
Base Line
X
Y
Z
C
Left optical center
X
World Point
• E = [T]XR
• X’T
EX = 0
• F = C’-T
EC-1
• x’T
Fx = 0
• l’ = Fx
l’

8. Corner Detection
Corner Detection
Toolkit used : horatio
 Edges are
determined
 Line Map is fit on
the edges
 Junctions of the
lines are found

9. Right Image plane
Left Image plane
Essential & Fundamental Matrices
Essential & Fundamental Matrices
e’
e
x
x’
R,T
Y’
X’
Z’
C’
Right optical center
Base Line
X
Y
Z
C
Left optical center
X
World Point
• E = [T]XR
• X’T
EX = 0
• F = C’-T
EC-1
• x’T
Fx = 0
• l’ = Fx
l’

10. Corner Detection
Corner Detection
Toolkit used : horatio
 Edges are
determined
 Line Map is fit on
the edges
 Junctions of the
lines are found

11. Finding Correspondences (Lines)
Finding Correspondences (Lines)
Candidate Lines should have similar
orientation
Images of end-points are got using
the epipolar constraint
An new approach considers
orientation of nearby lines (Amit Garg)

12. Line Correspondence -Results
Line Correspondence -Results

13. Line Correspondence -Results
Line Correspondence -Results

14. Reconstruction
Reconstruction
Mid-point of shortest distance

15. Locating Obstructions
Locating Obstructions
The reconstructed scene is projected on
the ground plane.
Clustering is done, by deleting long
edges in MST
Each cluster is bounded by its convex
hull
Identification of ground plane. Current implementation projects onto xz
plane of camera co-ordinate system.
TO BE DONE

16. Reconstruction
Reconstruction
Mid-point of shortest distance

17. Needed for Navigation
Needed for Navigation
Hand-eye calibration: to locate robot
w.r.t. co-ordinate system
Visual Servoing: using visual
feedback for correction in motion
Path Planning: Simple backtracking
algorithm
To complete the above by the end of the semester
OUR TARGET

18. New Approaches
New Approaches
Avoid Calibration by:
Self-Calibration
this was attempted by Amit Garg & Deepak
Verma, without much success.
Inner Camera Invariants
this will let us handle varying or unknown
internal parameters of the camera.

19. References
References
 Three Dimensional Computer Vision
O. Faugeras
 The Geometry of Multiple Views
Andrew Zissermann
 A Versatile Camera Calibration Technique
Roger Tsai (IEEE J. of Rob. & Aut., 1987)
 Inner Camera Invariants & Applications
S. Banerjee et al.