This paper proposes a novel locomotion robot that slides and rotates on a slippery downhill by utilizing the dynamical effect of an actively-controlled wobbling mass. First, we introduce a 4-DOF seedlike robot model that consists of two identical arc-shaped body frames and a short link, and develop the equation of motion, friction dynamics, and control law for generating a wobbling motion. Second, we numerically show that a stable downward motion can be generated based on the effect of entrainment to the wobbling motion at high frequencies on a slippery downhill. Third, we analyze the fundamental properties of the generated motion, such as moving speed and ground reaction force, through numerical simulations. Throughout this paper, we show that the robot's arc-shaped body frame can maintain kinetic energy or rotation motion without stopping on the high-frictional downhill, and that this property also enables the indirect control of the moving speed by utilizing the wobbling effect.