Prediction of Postural Balance by Means of Zero Moment Point (ZMP)

Abstract

Abstract Zero moment point (ZMP) is well-known in the robotics literature as an indicator of postural stability and has been successfully used to control anthropomorphic biped robots. In this paper we review the basics of ZMP, explain its behavior by means of planar point-mass models and full 3D extended rigid-body models, and show how it can be applied in the study of postural balance in the human. ZMP is an easily understandable, intuitive, easy-to-use, and physically meaningful criterion for the prediction of balance in dynamic locomotion systems. ZMP may be defined as a point on the ground where the resultant rolling moment on the foot reduces to zero. In order for the foot not to roll, the point should be constrained within the footprint. We relate the foot moment with the dynamics of the body segments and derive the expression of ZMP. We demonstrate that the position of ZMP also indicates the magnitude of rolling moment and the direction of the impending roll. Being a dynamic criterion, ZMP is a function of the position, velocity and the acceleration of the body segments and is shown to be a general concept from which the center of pressure (CP) and the horizontal projection of center of mass (HCM) may be extracted as special cases.