Abstract: A spherical omnidirectional rolling robot with a stable platform is presented, which is driven by two mutually
perpendicular servo motors placed within the spherical shell that induce the ball to roll in all directions at all times on a
flat surface. A stable platform exists inside the spherical robot to carry sensing devices or actuators, but it does not
rotate and keeps a stable stance when the spherical shell is rolling in any direction. The mechanical construction of the
spherical robot is introduced. Then the kinematic differential equations are derived from the nonholonomic constraints on its
motion using the generalized Euler angles, and a mathematical model of the robot’s motion is established. Finally, the
kinematic analysis and simulation of the spherical robot are developed using numerical examples.

Key words: spherical robot, omnidirectional rolling, stable platform, nonholonomic constraints, kinematic analysis and simulation