Fast Terrain-Adaptive Motion of Humanoid Robots Based on Model Reference One-Step-Ahead Predictive Control

This article presents a model-based control method for achieving bipedal locomotion of a position-controlled humanoid robot on uneven terrain. The method is called model reference one-step-ahead predictive control (MROPC), which considers the tracking error of the next cycle in each control period to improve system responsiveness. To achieve this, it utilizes an inverted pendulum model and a whole-body kinematic model, both of which are set on an equivalent slope, using inertial measurement unit (IMU), encoders, and foot sensors to estimate the local slope of the ground. Through Lyapunov stability analysis, it is proven that MROPC is more robust than the well-known virtual spring damping (VSD) and proportional-derivative (PD) control, effectively suppressing disturbance energy and improving robustness. To verify the theoretical results, tests were first conducted in a simulation environment, and frequency response analysis using Bode plot showed that MROPC performed better at frequencies up to 2 Hz. Then, to check real-world capabilities, the algorithm was deployed on the WALKER-I and tested in several disturbance scenarios such as the unstable plank with a rod placed halfway under it, and applications with active terrain estimation, such as sudden placement of small steps on flat ground under the feet. Ultimately, it achieves an anti-disturbance function on uneven terrain.