The Poincaré representation of equations of motion provides a global characterization of the dynamics of a rigid body subjected to external torques. We use this representation to obtain the global dynamics of a spherical robot with three independent internal rotors rolling on a plane. The robot is subjected to nonholonomic constraints arising out of pure rolling motion. The dynamics of the system is obtained by projecting the kinematic vector fields on the constrained distribution using the nonholonomic affine connection. The rotor torques are incorporated into the dynamics by way of the total angular momentum of the robot about the point of contact. © 2018 IEEE.