Gait planning and stability optimization for three-dimensional walking of biped robots

To address the challenges of complex gait planning, heavy computational load, and insufficient real-time performance during stable three-dimensional (3D) walking of biped robots, this paper proposes a 3D gait planning framework that integrates torso center-of-mass (CoM) trajectory planning with stability optimization. First, cubic spline interpolation is adopted to plan the trajectories of the ankle joints and torso CoM, and the forward and inverse kinematics models of the biped robot are established to derive joint motion parameters during locomotion. On this basis, a zero-moment point (ZMP) solving model is constructed to derive the analytical ZMP trajectory. In the stability optimization, taking the lateral offset of the hip joint as the optimization variable, a stability objective function is established based on the distance from the ZMP to the centroid of the support polygon, and the particle swarm optimization (PSO) algorithm is utilized to obtain the optimal lateral gait parameters. After optimization, the ZMP trajectory of the robot remains entirely within the support polygon throughout the walking cycle. The average stability margin increases from 0.0557 to 0.0672 m, and the minimum stability margin increases from −0.1086 to 0.0181 m, successfully achieving full-cycle stable walking. Furthermore, the computational efficiency of the proposed method is compared with that of the conventional trajectory planning method based on the 3D linear inverted pendulum model (3D-LIPM). The results demonstrate that the computation time of the proposed method is only 0.362 s, which is reduced by more than 90% compared with that of the 3D-LIPM-based method. Finally, the virtual prototype simulations with ADAMS and physical prototype experiments are carried out. The experimental results show that the robot can achieve continuous and stable 3D walking, the measured ZMP trajectory stays within the support boundary at all times, and the trajectory tracking errors of key components are maintained within a small range, thereby verifying the effectiveness of the proposed method.