# Homework for MECHANICS – Kinematics Calibration of a Differential drive wheelchair The aim of the homework is to:

1. [Mandatory] estimate from the encoder and the camera data the kinematics parameters wheels radius Rl and Rr and wheelbase b. To pursue this goal you can use the following paper. Suggestion: suppose as simplification at this stage the camera is perfectly located on the vehicle reference point (i.e. the mid point of the wheelbase).
2. [Important] now estimate also the camera position with respect to the vehicle reference point and again the kinematics parameters (that were simplified in the previous point) using an optimization algorithm that try to fit the two trajectories: the camera and the vehicle trajectory estimated by the kinematics equations of the differential drive vehicle.
3. [Optional] again estimate the camera position with respect to the vehicle reference point and again the kinematics parameters using an optimization algorithm that try to fit the two trajectories: the camera and the vehicle trajectory estimated by the kinematics equations of the differential drive vehicle weighting with the target location uncertainty (provided in the dataset). Suggestion: if an unweighted least squares optimization is something like [Xc-Xv]T * [Xc-Xv], a weighted least squares optimization is something like [Xc-Xv]T * C-1 * [Xc-Xv]. Conventions: X is a column vector; Xc camera trajectory; Xv vehicle reference point trajectory; C covariance of the camera estimated trajectory data points.

Hereafter you can find the dataset1 and dataset2 and the conventions used to collect the data. Here you can find other two datasets collected with the same convention of the previous: dataset3 and dataset4.

The two datasets have been collected steering the vehicle clockwise and counterclockwise.

The encoders are characterized by 16384 ticks per revolution. You have to consider also the transmission ratio of the mechanical reducer that has a value of 25. The “n0” parameter has a value of 16384 * 25.

The data was collected using PVI library that gives us the information when one of the variable under control was changed.
In the file may be two subsequent lines with the same timestamp. This means that at the same time were changed both the encoder ticks and the camera pose/ covariance.
You can notice that in one line is changed the camera information and in the other the odometric ticks. So, at the same timestamp, in the second line both the information are changed. You can take this line to do the exercise.