I focused on its maths, solving different problems related with the movement of the robot, making a very looking forward model which only implements the maths necessary to run the robot, showing how every equation is related with the real robot and givin a general view of it.
This is not the most robust way of building a model, as in real world robots there are lot of additional maths methods in order to pulish the behaviour of the robot, for example, adding interpolation methods would make the robot performs smoother or building an state stimator + filter (kalman state stimator) would let you do very preccise meassurements on the robot and make its movements even more natural.