Biped robot locomotion has been studied intensively for many decades, and one of the most challenging topics of study is the dynamic motion of the biped robot. This thesis will utilize the zero-moment point (ZMP) along with a simplified dynamics model, the linear inverted pendulum model (LIPM), to design a dynamically stable trajectory for the biped robot, based on given gaits. Two different approaches will be used for the trajectory generation: boundedness constraint and linear-quadratic-regulator method. Both of these methods compute the center of mass (CoM) trajectory for the biped robot. A stabilizer is also designed, and the CoM trajectories are tested using Reem-c robot under the Gazebo simulation environment. Finally, a comprehensive comparison between the two methods will be given.