The Euler-Poincaré equations for a spherical robot actuated by a pendulum

Mechanical systems with rolling constraints form a class of nonholonomic systems. In this paper we derive the dynamic model of a spherical robot, which has been designed and realized in our laboratory, using Lagrangian reduction theory defined on symmetry groups. The reduction is achieved by applying Hamilton's variation principle on a reduced Lagrangian and then imposing the nonholonomic constraints. The equations of motion are in the Euler-Poincaré form and are equivalent to those obtained using Lagrange-d'Alembert's principle.