Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptive approximation-based feedback linearization control (so-called adaptive computed torque control) combined with an anti-windup compensator is designed to track the desired COM produced by the high-level command. Along the length of the support sole, the ZMP with physical restrictions serves as the control input signal. The viability of the suggested controller is established using Lyapunov’s theory. The low-level control tracks the intended joint movements for a bipedal mechanism with flexible joints. We use two control strategies: position-based adaptive approximation control and cascaded position-torque adaptive approximation control (cascaded PTAAC). The interesting point is that the cascaded PTAAC can be extended to deal with variable impedance robotic joints by using the required velocity concept, including the desired velocity and terms related to control errors such as position, force, torque, or impedance errors if needed. A 6-link bipedal robot is used in simulation and validation experiments to demonstrate the viability of the suggested control structure.