I am studying the book "B. Sicilliano -Robotics. Modelling, Planning and Control" chapter 11, Input/output linearization topic. Where does the formula for theta in 11.75 come from?
In the case of the unicycle, consider the following outputs:
$ y_1 = x + b cos θ; $
$ y_2 = y + b sin θ $
with $ b \neq 0 $. They represent the Cartesian coordinates of a point B located along the sagittal axis of the unicycle at a distance |b| from the contact point of the wheel with the ground. How to find the following input-output linearization?
$ \dot{y_1} = u_1; $
$ \dot{y_2} = u_2; $
$ \dot{\theta} = \frac{u_2 \cos\theta − u_1\sin\theta}{b} $
I am not very good at robotics, I would like to get an answer simple to understand.
Thank you for all the help.