Abstract: To address the stable walking issue of biped robots in three-dimensional space, this paper first employed the cubic spline interpolation method to plan the hip and ankle joint trajectories required for the three-dimensional walking of the robot. Subsequently, forward and inverse position analysis models were proposed, and their parameters were solved. Based on this, an accurate numerical calculation of the foot zero moment point (ZMP) trajectory during the three-dimensional walking process of the robot was achieved. To ensure the stability of the robot’s three-dimensional walking, this paper proposed a particle swarm optimization (PSO) algorithm for optimizing the lateral offset of the robot’s hip joint and obtained the optimal lateral trajectory of the hip joint that guarantees the robot’s stable walking. The results of the subsequent virtual simulation experiments show that the approach proposed in this paper, first planning the hip and ankle joint trajectories, then solving the position model parameters and ZMP trajectory, and finally optimizing the lateral trajectory of the hip joint, is not only reasonable, feasible, and easy to calculate but also reliably ensures the stable three-dimensional walking of the robot. The research methods and conclusions of this paper are expected to lay a necessary foundation for the motion planning and control of humanoid robots.

Key words: 3D walking, gait planning, zero moment point (ZMP) trajectory, particle swarm optimization (PSO), lateral offset