A Real-Time Center of Gravity Trajectory Generation of a Biped Humanoid under Variable Reference ZMP Trajectory

Abstract

This paper describes a method for generating a center of gravity trajectory of a biped humanoid robot under variable reference ZMP trajectory. A simple inverted pendulum model (SIPM) is used to calculate a center of gravity (CoG) trajectory from a reference zero moment point (ZMP) trajectory with an analytic form, which is based on the Fourier series. Fundamentally, we used a time segmentation based approach. For each segment, we defined its duration and boundary conditions, which are the key parameters of ZMP trajectory design. After designing the ZMP trajectory in each segment, we can automatically calculate the CoG trajectory by matching the boundary conditions and by calculating the coefficients between the time segments. The reference ZMP trajectory can be changed by updating the boundary conditions during walking. We successfully verified the proposed method through full-body dynamic simulations with variable step length.