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This paper aims to develop a method for the locomotion of a snake-like robot, and proposes a control strategy based on the friction force between robotpsilas body and the ground. Our concept of a control system design is that a control law should be based on the friction force as a real snake is. Both the motion equation of the robot and the friction force are derived by the projection method proposed by W. Blajer. The friction model is evaluated in the cost function of the control system design based on state dependent Riccati equation. As a result a derived control law takes the friction effect into account. We also build an experimental system. The effectiveness of the proposed method is verified by simulations and experiments.