Forces Acting on a Biped Robot. Center of Pressure—Zero Moment Point

TLDR

Recent advances in biped robot research have improved dynamic walking, yet challenges remain for fast, anthropomorphic gaits on uneven terrain. This theoretical study defines CoP and ZMP with respect to ground‑foot contact and gravity‑plus‑inertia forces, proves their coincidence, and introduces a virtual CoP‑ZMP for uneven terrain. The authors provide strict definitions, prove CoP equals ZMP, analyze related control aspects, and define a virtual CoP‑ZMP, with experimental validation presented in a companion paper. CoP and ZMP are shown to coincide and are useful for control of biped robots, especially when extended to uneven terrain.

Abstract

In the area of biped robot research, much progress has been made in the past few years. However, some difficulties remain to be dealt with, particularly about the implementation of fast and dynamic walking gaits, in other words anthropomorphic gaits, especially on uneven terrain. In this perspective, both concepts of center of pressure (CoP) and zero moment point (ZMP) are obviously useful. In this paper, the two concepts are strictly defined, the CoP with respect to ground-feet contact forces, the ZMP with respect to gravity plus inertia forces. Then, the coincidence of CoP and ZMP is proven, and related control aspects are examined. Finally, a virtual CoP-ZMP is defined, allowing us to extend the concept when walking on uneven terrain. This paper is a theoretical study. Experimental results are presented in a companion paper, analyzing the evolution of the ground contact forces obtained from a human walker wearing robot feet as shoes.