zero-moment point
The zero-moment point, almost always shortened to ZMP, is a single spot on the ground that walking robots use as a balance check. Imagine a robot standing on one foot. The ground pushes back up on that foot, but it does not push evenly — it presses harder under the toe or the heel depending on how the robot is leaning. The ZMP is the one place on the sole where all that upward pressure can be thought of as pushing through a single point with no leftover twisting or tipping force around it. If you balanced the whole foot on a single pin stuck in at the ZMP, the foot would not start to rock or tip at that instant.
Why does this matter? A foot can only push, it cannot pull or grab the floor. So as long as the ZMP stays inside the patch of ground actually covered by the foot (or by both feet), the robot is safe — the ground can supply whatever push is needed and the foot stays flat. But the moment the ZMP reaches the very edge of the foot and tries to go past it, there is no more ground out there to push against, the foot peels up at one side, and the robot begins to topple. Walking controllers therefore plan every step so the ZMP stays comfortably inside the support area, and they nudge the arms, hips, or stride to pull it back if it drifts.
The ZMP is the workhorse criterion behind most classic two-legged robots, because it turns the messy question of "will it fall?" into one tidy rule: keep one computed point inside the contact area on the floor. It works beautifully for flat, predictable ground and confident, deliberate walking. It is less suited to running or hopping, where both feet leave the ground and there is momentarily no support patch to stay inside at all.
When a humanoid robot reaches forward to lift a box, its weight shifts toward its toes. The balance controller feels the zero-moment point sliding toward the front edge of the feet and quickly bends the knees and pushes the hips back, sliding the ZMP back to the middle of the soles before the robot can pitch over.
Balance, reduced to keeping one computed point inside the feet.
Keeping the ZMP strictly inside the foot guarantees the sole never tips, but it is a conservative rule — agile robots that are allowed to briefly rock on a foot edge can step and run more naturally than ZMP walking alone permits.