Stability Analysis of a Simple Active Biped Robot with a Torso on Level Ground Based on Passive Walking Mechanisms

This study focuses on the passive dynamic walking to enable a biped robot on level ground to walk efficiently with simple mechanisms. To build an efficient bipedal robot, utilizing the dynamical property of the robot system is a useful approach. McGeer studied passivedynamic walking, and showed a biped robot without actuators and controllers can walk stably down a shallow slope in simulations and experiments (McGeer, 1990). The simplest passive walker, which has only two mass-less links with hip mass, still can walk (Garcia et al., 1998). Collins et al. built the three-dimensional passive-dynamic walker which has knees and arms (Collins et al., 2001). Passive-dynamic walking is useful to study efficient level-ground walking robots, (e.g. Collins et al. 2005), but passive walking has some limitations. The walking motion of the passive walker depends on the slope angle. The walking speed decreases with the slope angle. On the other hand, increasing the slope angle brings about a period doubling bifurcation leading to chaotic gaits and there are only unstable gaits in high speed region (Garcia et al., 1998). Biped robots based on the passive walking mechanisms were proposed (e.g. Goswami et al., 1997; Asano at al., 2004; Asano at al., 2005; Spong & Bullo, 2005), but the robots are mainly controlled by ankle torque, which has drawback from the viewpoints of Zero Moment Point (ZMP) condition, discussed in (Asano et al., 2005). The limitations of the passive-dynamic walkers and the ankle-torque controlled walkers should be addressed. We propose the level-ground walking by using a torso and swing-leg control. Although using a torso for energy supply replacing potential energy, used in the case of the passivedynamic walking, was proposed by McGeer (McGeer, 1988), there are few studies to use a torso explicitly for energy supply. Wisse et al. showed that the swing-leg motion is important to avoid falling forward (Wisse et al. 2005). From this viewpoint, we introduce a swing-leg control depending on the stance-leg motion. To modify the pendulum motion of the swing-leg by using the swing-leg control, the impact condition between the swing-leg and the ground will be satisfied before falling down. In this paper, we study a knee-less biped robot with a torso on level ground. This paper presents a stability analysis of the biped robot to demonstrate the effectiveness of the swingleg control. We use a Poincaré map to analyze walking motions which is a common tool in the study of the passive walking (McGeer, 1990; Goswami et al., 1996; Garcia et al., 1998;