Bipedal Walking Pattern Design by Synchronizing the Motions in the Sagittal and Lateral Planes

Abstract

In these two decades, the technology of bipedal and humanoid robots has been made great progress. Up so far, many bipedal and humanoid robots are successfully developed (Hirai et al., 1998; Takanishi et al., 1985; Ogura et al., 2004; Kaneko et al., 2004; Nakasaka et al., 2004; Loffler et al., 2003; Lohmeier et al., 2004). In these robots, the gait planning and control for bipedal walking are based on ZMP concept (Vukobratovich et al., 1990; Goswami, 1999; Kakami, 2000). There are generally two methods for implementation of the dynamic and stable walking. The first one is based on a multiple rigid body robot model (Takanishi et al., 1985). This model is comparatively precise, but it requires a huge computation cost. The second one is simply based on the assumption that the whole robot mass is concentrated to robot’s CoG (Center of Gravity). The typical approach is using a 3D inverted pendulum model (Kajita & Kobayashi, 1987; Kajita et al., 2002; 2003; Zhu et al., 2003, 2004), in which, the robot locomotion in the sagittal and lateral planes are supposed to be independent. However, up to now, the bipedal walking nature and limitations of walking speed, stride, stride motion time, and so on, have not been completely understood. Partially this is because (1) few attentions are paid on the motion in double support phase and its effect to whole bipedal walking; (2) the investigation is not done intensively even for single support phase; for example, motion in sagittal plane are simply dealt with independent of the motion in lateral plane in most literatures on biped and humanoid robots. As revealed latter, in fact, such an approach is improper since the motions in the two planes are strongly coupled together. (3) ZMP is fixed to a point in robot sole for most of bipedal or humanoid robots. This paper mainly discusses the above first two problems based on ZMP concept and an inverted pendulum model with the assumption that ZMP is fixed at the center of the robot sole in single support phase. To do this, the relation between the motions in the sagittal and lateral planes is investigated first. By dividing a whole bipedal walking cycle into a double support, a deceleration, and an acceleration phases, and synchronizing the motions in the sagittal and lateral planes, we point out that the motions in these two planes are strongly coupled together, in other words, the motion in the lateral plane greatly restricts the motion in the sagittal plane, vice versa. Then, the role of the double support phase in biped walking is discussed. By changing the start and finish points of the double support phases in the lateral plane, the walking parameters such as walking speed, walking period, phase stride