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

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. 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. Banerjeeet al.