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This paper proposes an optimal control method for a 10 degree of freedom (DOF) biped robot with stable walking gait. The biped robot is modeled as a 3D inverted pendulum. From dynamic model of the 3D inverted pendulum and under the assumption that center of mass (COM) of the biped robot moves on a horizontal constraint plane, zero moment point (ZMP) equations of the biped robot depending on the coordinate of the center of the pelvis link obtained from the dynamic model of the biped robot are given based on the DdasiaAlembertpsilas principle. A walking pattern is generated based on ZMP tracking control systems that are constructed to track the ZMP of the biped robot to zigzag ZMP reference trajectory decided by the footprint of the biped robot. An optimal tracking controller is designed to control the ZMP tracking control system. From the trajectory of the COM of the biped robot and an arc reference input of the swinging leg, the inverse kinematics solved by the solid geometry method is used to compute the angles of each joint of the biped robot. The simulation and experimental results show the effectiveness of this proposed control method.