Central Pattern Generator (CPG) plays a significant role in the generation of diverse and stable gaits patterns for animals as well as controlling their locomotion. The main contributions of this paper are the ability to develop the Cartesian motor skills and coordinating legs of the quadruped robot for gait adaption and its nominal characteristics with CPG approach. Primary, a predefined relationship between an excitation signal and essential parameters of the CPG design is programmed. Next, the coordinated oscillator's rhythmic patterns by CPG and accordingly output gait diagrams for each foot of the robot are attained. Then, these desirable features such as predictive modulation and programming the gait event sequences including leg-lifting sequences and step length, duration of the time of each footstep within a gait, coordination of swing and stance phases of all legs are calculated in terms of different spatio_temporal vectors. Furthermore, a novel Cartesian footstep basis function is designed based on the robot characteristics and consequently, the associated spatio-temporal vectors can be inserted to it, which caused to spanning the space of possible gait timing in Cartesian space. Next, Cartesian footstep planner can be computed the swing foot trajectories in workspace along movement axes and then according to these footholds and feet placement, ZMP (Zero Moment Point) reference trajectory will be calculated and obtained. Therefore, COG (Center of Gravity) trajectory can be computed by designing a preview controller on the basis of the desired ZMP trajectory. Finally, to demonstrate the effectiveness of the proposed algorithm, it is implemented on a quadruped robot on both simulation or experimental implementations and the results are compared and discussed with other references.