Mathematical equation of motion of a differential two-wheeled Sumo robot

[dis]

TL;DR

The Sumo robot is designed with two wheels (motors), each of which can be adjusted separately (giving each its own speed). By combining several facts, it is possible to mathematically describe the movements and obtain a mathematical model.

Greetings readers! I am writing this post because I have a problem and I cannot proceed further. My task is to develop a mathematical model designed to plan the movement of a sumo robot, or x=AX + BX, where all are matrices and AX are the matrices of new coordinates, while BX are the control matrices.

In this image, I have schematically drawn the schematic diagram of the entire robot and part of the ICC theory.
So the equations I have written would be like this. (Unfortunately I can't find how to insert latex into this page)

So the final mathematical model should be like this. However, after testing, it doesn't get the correct next values, and I don't know why. Maybe someone can help?

Thanks for any help!

 

[renormalize]

(Unfortunately I can't find how to insert latex into this page)

Take a look at the handy "LaTeX Guide" at the bottom left of this post.