Human-like ZMP trajectory reference in sagittal plane for a biped robot

This paper introduces two new important issues to be considered in the design of the zero moment point (ZMP) reference trajectory for the sagittal plane balance control of an autonomous walking biped robot with an human-like gait. ZMP trajectory reference generation is very important in the design and balance control of the walking of a biped robot. ZMP reference generation algorithms based on the Linear Inverted Pendulum Model (LIPM) and moving ZMP references in the swing phase have already been proposed with the ZMP trajectory during the swing phase being designed moving along a symmetric trajectory relative to the center of the foot. It was verified experimentally that in the human gait the ZMP trajectory moves along the foot in a way that it is shifted forward relative to its center. To take this into account a shift parameter is then proposed to move forward the X_ZMP trajectory reference during the swing phase. It was also verified experimentally that in the human gait the ZMP trajectory amplitude depends on the swing time. Its variation law has been determined experimentally and it was verified that this range decreases as the swing time increases, reducing to zero for a static gait. It is then proposed a parameter H to take into account this variation with the swing time of the gait. In order to evaluate and compare the performance of the X_ZMP trajectory references and the natural movement two performance indexes are proposed.