A universal stability criterion of the foot contact of legged robots - adios ZMP

TLDR

The stability of legged robots is traditionally assessed by checking whether the zero‑moment point lies within the support polygon of the feet on a horizontal plane with sufficient friction. This paper introduces a universal stability criterion for foot contact in legged robots. The criterion evaluates whether the combined gravity and inertia wrench at the robot’s center of mass lies inside the polyhedral convex cone defined by the contact wrenches of the feet and environment, enabling assessment of strong stability on arbitrary terrain and under sufficient friction, as well as weak stability when friction follows a physical law. The proposed criterion can determine the admissible ZMP region and is applicable to a broader range of scenarios than traditional methods.

Abstract

This paper proposes a universal stability criterion of the foot contact of legged robots. The proposed method checks if the sum of the gravity and the inertia wrench applied to the COG of the robot, which is proposed to be the stability criterion, is inside the polyhedral convex cone of the contact wrench between the feet of a robot and its environment. The criterion can be used to determine the strong stability of the foot contact when a robot walks on an arbitrary terrain and/or when the hands of the robot are in contact with it under the sufficient friction assumption. The determination is equivalent to check if the ZMP is inside the support polygon of the feet when the robot walks on a horizontal plane with sufficient friction. The criterion can also be used to determine if the foot contact is sufficiently weakly stable when the friction follows a physical law. Therefore, the proposed criterion can be used to judge what the ZMP can, and it can be used in more universal cases