Movement model & Calibration

Movement model

For localization, the robot will need (relatively) precise movement model.

The model we use is parametrized using five variables: $(b, s_R, s_L, \sigma_R, \sigma_L)$. In this model the robot consists of two perfectly parallel wheels placed at wheel base distance $b$ from each other. $s_R$ and $s_L$ are distance travelled per encoder tick for each wheel. These values are not necessarily equal (because of manufacturing inaccuracies). Distance measurement uncertainty is modelled using a Gaussian random variable for each wheel.

Odometry values come every interval in the form of encoder ticks, counts for left and right wheel are $n_R$ and $n_L$. Distance travelled by a wheel is from a following distributions: $d_{R, L} \sim n_{R, L}s_{R, L}N(0, \sigma_{R, L})$

During a single interval the robot is assumed to travel on a circular arc with length $d = \frac{d_R + d_L}{2}$ and angle $\alpha = \frac{d_R - d_L}{b}$.

Code that handles the calculations mentioned in this section is in the file differential_drive.py

Drive calibration

Because of manufacturing inaccuracies, I don’t know the precise dimensions of the robot. To do this, I wrote a tool that matches replays to known travelled pattern (calibration.py).

WRITE THIS!