Sliding Mode Control for Stable Bipedal Locomotion: Reference Trajectory Design and Stable Analysis

Maintaining stable bipedal locomotion under complex ground vibrations presents a significant challenge in robotics and biomechanics. This study investigates the stability of a three-dimensional bipedal pedestrian model under such conditions and utilizes a sliding mode control (SMC) strategy for stability regulation. The model simplifies the pedestrian to a point mass hip connected by massless, spring-damper legs. Dynamic equations are derived using the Lagrangian formulation. A hierarchical controller is designed to track predefined reference trajectories in the sagittal, lateral, and vertical directions, generated based on gait parameters and ground reaction force characteristics. Numerical simulations demonstrate that the utilized SMC effectively achieves stable walking with accurate trajectory tracking under normal conditions. However, under multi-directional ground vibrations, stability exhibits strong directional dependence. Lateral stability is the most vulnerable, showing significant sensitivity and amplitude amplification, while vertical stability remains robust due to inherent structural support. Crucially, the fixed-parameter SMC fails to maintain stability under sustained and complex 3D vibrations, leading to gait instability after prolonged exposure. The results underscore the limitations of fixed-parameter controllers and highlight the critical need for future control frameworks to incorporate real-time parameter adaptation mechanisms to enhance robustness in dynamically changing environments.