Abstract: Because the inner components of the spherical robot should have omni-directional characteristics with respect to sphere shell, the sensors and the detection equipment applied by the robot cannot work normally without a relative stable platform. A stable platform is provided for the spherical robot by using control techniques. The dynamic model of rolling forward is derived by applying Lagrangian function based on energy dissipation, and then, the proposed function is linearized according to the actual movement situation. The system is transformed into linear and fixed-length state-space form effectively around the new balance points via coordinate transformation. The two importance concepts, balance pendulum angle and balance rolling velocity, are introduced in the process of this transformation, which lay foundation for further analyzing robot motion property. The cyclic coordinates in the dynamic model, as a state variable, are removed in order to assure controllability and observability of the robot system. A state feedback controller, which can realize arbitrarily pole assignment, is designed to get the expected performance index, and corresponding simulation result verifies the effectiveness of the proposed controller.

Key words: Coordinate transformation, Cyclic coordinate, Spherical Robot, State feedback controller