Robust Balancing Control of Biped Robots for External Forces

This paper develops a controller synthesis method for ensuring an admissible bound of external forces on biped robots in a desired level. We first introduce the authors’ preceding results on the norm-based stability criterion for a biped walking constructed on its linear inverted pendulum model (LIPM). More precisely, an induced norm can be taken to formulate the fact that the balance for a biped robot is achieved if its zero moment point (ZMP) always stays in the supporting region at each step. Based on this norm-based criterion, we aim at making the maximum energy of external forces admissible for balancing the biped robot be a pregiven desired bound γ(> 0). To achieve this objective, a robust controller is designed through the linear matrix inequality (LMI)-based approach. More importantly, a necessary and sufficient condition for the existence of a robust controller leading to the desired bound is characterized by some LMI conditions. The effectiveness of the overall arguments is validated through some comparative simulation results of a biped walking robot with external forces.