Quadruped robots have increasingly been used in complex terrains where barriers and gaps exist. In this paper, a four-legged robot with intelligent controllers is designed and simulated. The designed architecture comprises 12 servo motors, three per leg, to provide considerable flexibility in movement and turning. Proportional Integral Derivative (PID) controllers and Fuzzy controllers are proposed to control and stabilize the motion of the quadruped robot. An ant colony optimization algorithm has been utilized to tune the parameters of the PID controller and the Fuzzy controller. After obtaining the optimal values of both controllers, the entire architecture is implemented using the Multibody Simscape package in MATLAB which models multidomain physical systems. The simulation results are conducted in a 3-dimensional environment and they are demonstrated in three case studies; firstly, when the system is simulated without using a controller which leads to a collapse of the quadruped robot. Secondly, when the PID controller is combined with the system, better movement is obtained. However, the quadruped is unable to complete its path and collapses after a few meters. Thirdly, when the Fuzzy controller is integrated into the designed architecture, a significant improvement is observed in terms of minimizing elapsed time and improving the overall performance of the motion. The stability of the Fuzzy controller has been examined using Lyapunov criteria to validate its overall performance. Comparisons are conducted based on control efforts and travelled distances to demonstrate the suitability and effectiveness of Fuzzy controllers over PID controllers.