Zero moment point

What it means

The zero moment point, or ZMP, describes a resultant force and moment relative to a reference plane. In flat-ground balance analysis, it is the point on that plane where the net contact moment has zero components along the two axes tangent to the plane. This construction requires a nonzero normal component of resultant contact force. Stéphane Caron calls it the zero-tilting moment point because a moment about the plane's normal can remain. [1, 2]

For flat-ground walking, the supporting feet define a region in which an appropriate resultant contact can be supported. MIT's humanoid-control chapter derives the familiar planar ZMP picture and explains why definitions and assumptions matter. It is a mechanics quantity, not the physical location of a dedicated sensor. [1]

How it applies to humanoids

Bipeds make and break contacts as they walk. Caron and colleagues study the conditions for a surface contact to remain stable, including friction, the position of the ZMP in the support area and limits on yaw torque. This connects the familiar balance diagram to the fuller contact-force problem. [3]

Walking controllers can reason about support forces through simplified models. MIT's treatment explains how such models help organize planning and control of articulated robots. The purpose is to make balance reasoning tractable, while retaining awareness of what was simplified. [1]

Terminology and stability traps

ZMP is not simply the vertical projection of the center of mass. MIT's derivation includes acceleration and angular-momentum effects, so a static center-of-mass picture can omit terms that matter during motion. Interpret a ZMP trajectory within its stated model. [1]

The point being inside the support polygon is not a complete test for all forms of contact failure. The surface-contact study also requires friction and yaw-moment conditions. A foot can slip or rotate in ways that a single point-in-polygon check does not capture. [3]

Center of pressure and ZMP are related under suitable contact assumptions, but their definitions start from different descriptions of loading and dynamics. Caron's explanation distinguishes them and states when they coincide. Do not use the terms interchangeably without the conditions of the model. [2]

How to read it on humanoidversus.com

The current robot schema has no ZMP metric or balance score, so this entry has no live table. Joint counts, speed and peak torque provide hardware context but cannot tell you whether a cited controller uses ZMP planning.

No robot is linked solely because it stands on two feet. Attribute a ZMP implementation only when the record cites a relevant technical source. When reading a balance demonstration, look for its contact assumptions, perturbations and failure criteria rather than treating the ZMP label as proof of reliability.

Further reading

MIT provides a derivation within legged-robot control. Caron's explainer clarifies the zero-tilting definition, and the surface-contact paper expands the discussion to friction and yaw constraints. [1–3]