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In this paper, we propose a spherical mobile robot, which is composed of a sphere-shaped outer shell and and a 2-d.o.f. mass-control device inside it. We assume that there exists rolling contact constraint between the spherical surface of the robot and the floor. Our purpose is to realize locomotion control of the robot by appropriately actuating the internal driving mechanism. First, we derive a mathematical model of the robot as a nonlinear differential-algebraic equation (DAE). There are two differences between the conventional rolling sphere problem and our robot: (1) our robot is allowed to spin around the vertical axis, and therefore (2) we have to consider not only kinematics but also dynamics of the robot, because the angular momentum around the vertical axis plays an essential role its behavior.