Bipedal Walking Control based on the Assumption of the Point-contact: Sagittal Motion Control and Stabilization

In the age of an aging society, the prospective role of robots is turning gradually from just working machines to do monotonous work in a factories to partners who support human life. In recent years, a lot of autonomous humanoid robots have been actually realized (Hirai et al. (1998); Kaneko et al. (2008)). These robots can walk on two legs stably by means of the control based on ZMP (Zero Moment Point). ZMP (Vukobratovic & Borovac (2004)), the indicator of the stability of biped walking, is a point on the floor where the torque generated by both inertial and gravitational forces becomes zero. That is, using ZMP-based control to realize stable walking makes sense, thus a number of researches of ZMP-based control have been presented (Nishiwaki et al. (2002); Takanishi et al. (1985)). However, in terms of the practical use of humanoid robots, these controllers based on ZMP have a problem in terms of the runtime of the battery since ZMP-based method does not take advantage of the robot inherent dynamics. In order to achieve natural and energy efficient biped walking, many control methods based on robot dynamics had been proposed up to this day. As one of such methods, some researchers presented the control methods to take advantage of robot dynamics directly by use of point-contact state between a robot and the ground (Furusho & Sano (1990); Goswami et al. (1997); Grishin et al. (1994); Kuo (1999); Nakanishi et al. (2004); Ono et al. (2004)). Miura et al. produced the point-contact biped robot like stilt and realize dynamic walking by means of stabilizing control to change the configuration at foot-contact (Miura & Shimoyama (1984)). Kajita et al. proposed the control and stabilizing method based on the conserved quantity derived by designing the COG trajectory parallel to the ground (Kajita et al. (1992)). Chevallereau presented the control to converge robot dynamics on optical trajectory by introducing the virtual time (Chevallereau (2003)). Grizzle andWestervelt et al. built the controller by use of the virtual holonomi constraint of joints named virtual constraint realize stable dynamic walking by means of the biped robot with a torso (Grizzle et al. (2001); Westervelt et al. (2004)). As one of point-contact methods, Doi et al. proposed Passive Dynamic Autonomous Control (PDAC) previously (Doi et al. (2004b)). PDAC expresses the robot dynamics as an onedimensional autonomous system based on the two concepts: 1) point-contact 2) virtual con11