Towards visual localization, mapping and moving objects tracking by a mobile robot: a geometric and probabilistic approach
Author: Joan Solà <3
- Define euclidean vectors
- All frames are defined right handed
- good part on Euler angle and Quaternions
- Rotation matrix used to perform rotation of points, quaternion to store rotation in state vectors (easy for filtering derivation and differentation) and Euler angles for human interface
- Lens are here to enhance the luminosity (awesome figure 2.1)
- Homogeneous matrix = transformation matrix
- defines distortion as an application
$d : \mathbb{R}^2 \rightarrow \mathbb{R}^2 $ - defines image as an application
$I : \mathbb{R}^2 \rightarrow \mathbb{R}_+$ - projection is the combination of the following
$\mathbf{u} = pixellize(distort(project(ToFrame(\mathbf{p}))))$ - back projection: pixel unmapping, undistortion and back projection
- solution to invert distortion model: calibrate both distortion and correction model as polynomials
- compute the correction model from the distortion coefficients by solving a least square on a set of pairs
$r_i, d_{di}$ $\mathbf{p} = backProject(correct(unpixellize(\mathbf{u})))$
- Observability analysis of the pb with bearing only sensor: the observer should move quite randomly, with faster dynamics than those of the target (complicated condition to meet)
- BiCAM slam (with static lmks) + 1 EKF per target
- objects considered punctual defined by their position and linear velocities