I am trying to simulate and implement the controller in the paper Geometric Tracking Control of a Quadrotor UAV on SE(3). I have the dynamics implemented, however I am stuck at one part in the controller which is the calculation of the following equation:
$$e_\Omega=\Omega-R^TR_d\Omega_{d\cdot}$$
I have all the variables in equation (11) calculated except for $\Omega_d$ which is the desired angular velocity.
From equation (4) of the paper we know the relation:
$$\dot{R}_d=R_d\hat{\Omega}_d$$
However, I don't know how to calculate $\dot{R}_d$. Can someone give the exact equation for getting $\dot{R}_d$ so I can calculate $\Omega_d$ to get the error $e_\Omega$?
My code is available on github.