Dynamics and Controllability of a Spherical Robot

This paper gives a tutorial on the constraint holonomics and non-linear controllability of physical systems, with application to a spherical robot. By modelling the configuration space as ℝ2× SO(3) parameterized by fixed axis angles, we first derive the uncontrolled equations of motion for a sphere rolling on a planar surface as a solution of the Euler Lagrange equations. We then introd...