The dynamic modeling and tracking controller design were carried out for underactuated non-holonomic six-legged rolling running robot.According to the structural characteristics of the robot，the Lagrangian method was used to establish the dynamic model in the two directions of pitch and roll respectively,and they were converted into standardized dynamic equations;the drive motor torque was used as the control input,the sliding mode robust controller was designed based on the HJI theory in the pitch direction in order to improve the trajectory tracking control accuracy.In the roll direction,in order to improve the robustness of the system,a back-step sliding mode controller was designed,and the stability of the closed-loop system was proved by using the Lyapunov function;simulations experiments were carried out by using MATLAB.The results show that the proposed method is feasible.