On the Geometric Phase Approach to Motion Planning for a Spherical Rolling Robot in Dynamic Formulation

The paper deals with the problem of motion planning for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. To solve the problem, we employ the so-called geometric phase approach based on the fact that tracing a closed path in the space of input variables results in a non-closed path in the space of output variables. To set up the governing equations, the contact kinematic equations are modified by the condition of dynamic realizability, which constrains the component of the angular velocity of the rolling carrier and depends on the mass distribution, and parameterized. By using a motion planning strategy based on tracing two circles on the spherical surface, an exact and dynamically realizable motion planning algorithm is fabricated and verified under simulation.