1. Avneesh Sud Vaibhav Vaish under the guidance of Dr. Subhashis Banerjee
Robot Navigation
Avneesh Sud
Vaibhav Vaish
under the guidance of Dr. Subhashis Banerjee

2. 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)
Camera Calibration
Edge & Corner Detection
Finding Correspondences
3-D Reconstruction
Path Planning
Navigating the Path

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

5. Essential & Fundamental MatricesX
World Point
F = C’-TEC-1
x’TFx = 0
l’ = Fx
E = [T]XR
X’TEX = 0
Right Image plane
Left Image plane x x’ l’ X Y Z C
Left optical center Y’ X’ Z’ C’
Right optical center e
Base Line e’
R,T

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

7. 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)

8. Line Correspondence -Results

9. Line Correspondence -Results

10. Mid-point of shortest distance
Reconstruction
Mid-point of shortest distance

11. 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
TO BE DONE
Identification of ground plane. Current implementation projects onto xz plane of camera co-ordinate system.

12. 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
OUR TARGET
To complete the above by the end of the semester

13. 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.

14. 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.