The Generation of a Stable Walking Trajectory of a Biped Robot based on the COG based-Gait Pattern and ZMP Constraint

Abstract

The research works contained in this paper are focused on the generation of a stable walking pattern of a biped robot and the study of its dynamic equilibrium while controlling the two following criteria; the centre of gravity COG and the zero-moment point ZMP. The stability was controlled where the biped have to avoid collision with obstacle. The kinematic constraints were also taken into consideration during the walking of the biped robot. In fact, the generation of the walking patterns is composed of several stages. First, we used the Kajita method for the generation of the COG trajectory, based on the linear inverted pendulum LIPM during the simple support phase SSP and linear pendulum model LPM during double support phase DSP. After that, we used two 4thspline function to generate the swing foot trajectory during the SSP and we used exact formulate for the foot trajectory during DSP. Finally, Newton's algorithm was performed (at the level of the inverse geometric model), in order to calculate the different joints according to the desired trajectories of the hip and the feet. Ground reaction forces were also determined from the dynamic model to satisfy the kinematic constraints on both feet of the biped. The generation of walking is done for two different speeds. To study the biped balance, ZMP generation algorithm was performed during the different walking phases and the results obtained for the two cases were compared.