A Novel Biped Pattern Generator Based on Extended ZMP and Extended Cart-Table Model

Abstract

This paper focuses on planning patterns for biped walking on complex terrains. Two problems are solved: ZMP (zero moment point) cannot be used on uneven terrain, and the conventional cart-table model does not allow vertical CM (centre of mass) motion. For the ZMP definition problem, we propose the extended ZMP (EZMP) concept as an extension of ZMP to uneven terrains. It can be used to judge dynamic balance on universal terrains. We achieve a deeper insight into the connection and difference between ZMP and EZMP by adding different constraints. For the model problem, we extend the cart-table model by using a dynamic constraint instead of constant height constraint, which results in a mathematically symmetric set of three equations. In this way, the vertical motion is enabled and the resultant equations are still linear. Based on the extended ZMP concept and extended cart-table model, a biped pattern generator using triple preview controllers is constructed and implemented simultaneously to three dimensions. Using the proposed pattern generator, the Atlas robot is simulated. The simulation results show the robot can walk stably on rather complex terrains by accurately tracking extended ZMP.