A dynamically realizable reconfiguration strategy for steering a spherical rolling with two internal rotors

The paper addresses the problem of reconfiguring a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The problem is stated in dynamic formulation. 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. A working model for solving the motion planning problem is obtained by modifying the contact kinematic equations by the condition of dynamic realizability which constrains the component of the angular velocity of the rolling carrier and depends on the mass distribution. By using a motion planning strategy based on tracing a figure eight on the sphere, an exact and dynamically realizable motion planning algorithm is fabricated and verified under simulation. It is shown that the dynamically realizable contact paths are shorter and essentially different than those resulted from the kinematic model of pure rolling.