# Robotics Teaching Assistant lectures (Como)

Materials used in the Tutorial part of Robotics course (academic year 2011-2012, Como)

The latex sources and Matlab code are also available on the svn

`svn co https://svn.ws.dei.polimi.it/airlab/Courses/Robotics_como`

## 1st lecture

• Homogeneous coordinates for points in 2D and 3D
• Rotation and translation in 2D and 3D homogeneous coordinate
• Transformation inversion and composition.
• Lines in 2D homogeneous coordinates, duality with points, line intersection and line joining two points
• The line at the infinity (2D)
• Brief introduction to conics
• 2D projective transformation introduction

Slides with animations File:Robotics-ceriani-ese-01-anim.pdf

## 2nd lecture

• Projective 2D transformations (Homographies) of points, lines and conics
• Homography estimation and image rectification
• Hierarchy of transformations (isometries, similarities, affine, homographies)
• Vanishing points
• Parametric lines and Cross Ratio (with exercize)
• Affine reconstruction
• 3D projective geometry: points and planes, quadrics, transformations, vanishing points and lines
• Brief recall to art and usage of vanishing points
• Some videos and images examples
• Image definition, Camera system, Thin lenses approximation, Fresnel law, depth of field
• Pin hole model, Intrinsic camera matrix
• Extra exercises with cross ratio

Slides with animations File:Robotics-ceriani-ese-02-anim.pdf Videos:

To see videos in the presentation you have to download and extract them into a folder named "videos" in the same folder of the slide file Video are visible in the pdf file in Windows using Acrobat Reader, in Linux using Okular

Matlab code File:Robotics-matlab-02.zip

## 3th lecture

• Pin hole model recall
• Projection Matrix
• Interpretation line
• Image of origin and vanishing points
• Angle of view
• Radial and tangential distortion model
• Camera calibration (Matlab Camera Calibration Toolbox [1])
• Epipolar geometry
• Fundamental matrix
• Features in image
• Canny edge detector
• Hough transformation for lines extraction
• Corners
• Template matching: patches and SIFT
• Final Exercize on Camera Geometry

Slides with animations File:Robotics-ceriani-ese-03-anim.pdf

Matlab code File:Robotics-matlab-03.zip

## 4th lecture

• Mobile robot localization
• Taxonomy of localization problems
• Probability recall
• Bayes formula and bayes filter
• Markov Localization

Slides with animations File:Robotics-ceriani-ese-04-anim.pdf

Matlab code File:Robotics-matlab-04.zip

## 5th lecture

• Kalman Filter
• Kalman Filter example: falling body
• Extended Kalman filter
• Extended Kalman filter localization
• Correspondances, data association and Mahalanobis distance
• Qualitative introduction to Monte Carlo Localization and Particle filters

Slides with animations File:Robotics-ceriani-ese-05-anim.pdf

Matlab code File:Robotics-matlab-05.zip

## 6th lecture

• Introduction to SLAM
• EKF-SLAM: motion model, addition, measurement
• Data associaton: Examples with JCBB
• Visual SLAM & Monocular SLAM
• Large scale SLAM issues
• Some videos...
• SLAM with OmniDirectionalCamera
• PTAM, Laser based SLAM

Slides with animations File:Robotics-ceriani-ese-06-anim.pdf Videos:

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Note: Some videos are missed due to limits of upload of this wiki, you can download them directly from youtube, links are on the slides. To see videos in the presentation you have to download and extract them into a folder named "videos" in the same folder of the slide file Video are visible in the pdf file in Windows using Acrobat Reader, in Linux using Okular

Matlab code File:Robotics-matlab-06.zip (this material is from [2])