NOTE ON THE ARTICLE "ZERO-MOMENT POINT — THIRTY FIVE YEARS OF ITS LIFE"

Abstract

In Vol. 1, No. 1 of Int. J. Humanoid Rubotics, we gave a review of the Zero-Moment Point (ZMP) concept, on the occasion of thirty five years of its use in modeling dynamics of the biped gait. At the time of writing this article, we thought that thirty five years was a long enough period in which all confusions, if they existed, could be cleared up. However, we were not quite right, and we will indicate here some of the most important points concerning the concept. A survey of the literature that appeared in the last several years related to the widely accepted ZMP method reveals a diversity of terms used to describe the state in which the biped system performs “regular” gait, safe from overturning. The terms in use are: stability (stable gait), dynamic balance, and dynamic equilibrium. Stability is a customary term in the theory of automatic control, and in this domain it has its well-defined meaning and usage, so that it is not appropriate to use it in some other instances, straying from its basic meaning. The term dynamic equilibrium is also unsuitable because it is used in the D’Alambert principle to transform dynamic equations into a static form, with a zero on the right-hand side — hence the term equilibrium. Therefore, dynamic balance remains the most appropriate term, as it fully reflects the nature of the related notion, and is not in use in other areas. We ourselves did not make clear this terminological distinction in the aforementioned article, which would have been prudent. Another issue we want to address is the situation illustrated in Fig. 4 in the paper — to make it easier to follow the explanation we repeat it here — concerning the notions of ZMP and fictitious ZMP (FZMP). As is well known, the crucial characteristic of a dynamically balanced gait is that the point at which the conditions ΣMx = 0, ΣMy = 0 are fulfilled is within the support polygon (Fig. 4), whereby