Local equilibrium controllability of a spherical robot actuated by a pendulum

In this paper, we present local equilibrium configuration controllability analysis of a spherical robot. The robot is actuated by the principle of displacing the center of gravity of the system using an internal mechanism. The system is defined on a trivial principal fiber bundle, characterized by base body motion and the shape dynamics, and the equations of motion are in the form of the nonholonomic Euler-Poincaré equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented.