Proving Asymptotic Stability of Dynamic Walking for a Five-Link Biped Robot with Feet

During the dynamic walking of biped robots, the underactuated rotating DOF emerges between the support foot and the ground. This makes the biped model hybrid and dimension-variant. In this paper, we present the definition of orbit stability for dimension-variant hybrid systems (DVHS). Based on the work of Grizzle et al. (2001), we generalize Poincare theorem to a class of DVHS, and this result is then used to study asymptotically stable dynamic walking for a five-link planar biped robot with flat feet. Time-invariant gait planning and nonlinear control strategy, which is organized around the hybrid zero dynamics of Westervelt et al. (2003), is also introduced to realize dynamic walking with feet. Simulation results indicate that an asymptotically stable limit cycle of dynamic walking is achieved, and the effectiveness of the proposed method is illustrated

I. Introduction

To date, the stability and control of biped robots with flat feet have been based on zero moment point (ZMP) criterion, which states that when the ZMP is contained within the interior of support polygon, the robot is stable, i.e., will not topple [1]. The basic idea of this principle is to avoid the underactuation between the supporting foot and the ground before heel strike by the swing leg. To maintain this condition, the walking of the robot has restrictions such as the maximum walking speed limitation and the variety of biped locomotion. Based on ZMP criterion, the robot can only realize static walking or quasi-dynamic walking, as shown in Fig. 1(a) and (b). During the dynamic walking, the underactuated DOF emerges between the support foot and the ground, as shown in Fig. 1(c) [2]. This induces the biped model not only hybrid but also dimension-variant.