A New Stability Framework for Trajectory Tracking Control of Biped Walking Robots: A Dissemination Version

This paper introduces a novel stability criterion for biped walking systems using the linear inverted pendulum model in which the dynamics between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. The criterion is based on ensuring that the ZMP error, the difference between the reference and real ZMP, remains within a specified area to maintain walking stability. Considering this criterion, we examine the initial CoM conditions necessary for walking balance and define the stability regions based on these conditions. Toward a more practical significance, we address the impact of unknown disturbances on walking balance of biped walking systems. More importantly, the stability region is shown to be computable through a finite number of calculations, ensuring stability over an indefinite period. Finally, simulation results are provided to validate the proposed method.

1. INTRODUCTION

As the applications of biped robots for practical tasks are studied widely in [1] – [5], the stability problem of biped walking has been considered deeply in the literature. More importantly, a biped robot is shown in [6] – [8] to be stable if its zero moment point (ZMP) trajectory is always located inside the supporting regions. In this regard, the maximal output admissible (MOA) set [9], [10] is used in [11] to characterize the initial conditions for the center of mass (CoM), with which the aforementioned ZMP condition holds. This pioneering study proposes a method for designing feedback controllers based on the linear inverted pendulum model (LIPM) of biped robots [12], in which the dynamics between the CoM and the ZMP of the biped robots is described by a linear time-invariant (LTI) system. Subsequently, more sophisticated arguments on the capture point [13] and foot position control have been developed in [14] and [15], respectively, with the MOA set-based treatment of biped walking systems.