A Google search (forces inverted pedulum angular rate) produced this online view into a Mathematica Notebook addressing the challenge of robot control.
Note the much greater complexity than the solution that Barello describes in his version of the GyroBot. Perhaps we can derive insight from this demonstration to see how to implement an easier solution. Also note that Mathematica even provides a free viewer tool that allows an intermediate level of access to the model.
Mathematica model contributed by: Stephen Wilkerson (Towson University) and Nathan Slegers (University of Alabama, Huntsville) with contributions by Franz Brandhuber