A Walking Pattern Generation Method for Humanoid Robots using Least Square Method and Quartic Polynomial

Humanoid robot has been developed for human’s convenience in the human environment. Humanoid robots like ASIMO, HRP, WABIAN and Johnnie were successively developed (Hirai et al., 1998; Yamaguchi et al., 1999; Kajita et al., 2003; Löffler et al, 2003). Researches on humanoid have been done about balancing, walking pattern generation, motion generation, whole body cooperation and so on. In particular, many walking pattern generation methods have been developed to prevent a robot from tipping over. There are generally two groups for the walking pattern generation (Kajita et al., 2003; Hirukawa, 2006). The first group uses forward dynamics with multiple rigid-body (Hirai et al., 1998; Yamaguchi et al., 1999). This group demands precise information of the robot such as mass, inertia, and center of mass(CoM) of each link, and so on. In this group, the footprints of biped robot are changed for keeping the planned configuration of the robot (Hirukawa, 2006). On the other hand, the second group (Huang et al., 2001; Kajita et al., 2003; Löffler et al., 2003; Harada et al., 2004; Zhu et al., 2004; Oh et al., 2006) utilizes limited knowledge such as the total center of mass and total angular momentum. And this group makes use of the inverted pendulum model for the walking pattern generation and changes the configuration of the robot for keeping the planned footprints (Hirukawa, 2006). Our walking pattern method belongs to the second group. The inverted pendulum model is transferred the complex dynamic equation of humanoid robot into second order differential equation with some assumptions. Most researches on walking pattern generation dealt with periodic walking. However it is difficult to implement various gaits by periodic walking generator. Harada et al. introduced the analytical walking pattern method on real-time generation for coping with change of gait. Kajita et al. proposed the omni-direction walking pattern generation method using the preview control. Zhu et al. proposed walking pattern generation method with fixed ZMP and variable ZMP in order to make the biped walking pattern more human-like and more agile. This paper describes the omni-directional walking pattern method for the humanoid robots using the least square method with the quartic polynomials. And we design that the ZMP trajectory has the slope in single support phase. The CoM trajectory becomes effective in regard of velocity compared to the ZMP trajectory