Optimization of humanoid robot locomotion behavior using hybrid technique combines between preview control algorithm and discrete algebraic Riccati equation (DARE)

Achieving stable bipedal walking remains a significant challenge, as conventional Zero Moment Point (ZMP) methods often struggle to balance disturbance rejection with real-time performance. Other approaches improve computational efficiency or adaptive stability but still face limitations that hinder practical deployment on embedded platforms. In this study, we propose a hybrid control architecture that combines the Discrete Algebraic Riccati Equation (DARE) with preview control for optimal Center-of- Mass (CoM) trajectory generation. The framework integrates cubic-spline swing-leg trajectory planning and adaptive foot placement using damped numerical inverse kinematics, enabling smooth joint motion and precise foot placement. Simulation experiments were conducted on a 12-DoF humanoid robot in the PyBullet physics engine during forward walking on flat terrain. The proposed controller maintained the ZMP within the support polygon with a mean absolute error of 0.03 m, achieved real-time performance at 240 Hz with only 33% CPU usage, and demonstrated rapid stability recovery from a 10 N disturbance within 0.8 s. Additional performance metrics showed a torque efficiency of 9.96 Nm (simulation) , indicating that the method is suitable for low-power embedded platforms. These results highlight a computationally efficient, low-energy, for real-time bipedal locomotion. The proposed architecture improves the feasibility of cost-effective humanoid robots by enabling stable, adaptive walking without sacrificing performance.