Locomotion

Zero Moment Point (ZMP)

The zero moment point (ZMP) is the point on the ground where the horizontal moment of the ground reaction forces vanishes; keeping it strictly inside the support polygon ensures a walking robot's feet do not tip. Formalized by Vukobratovic in the late 1960s, ZMP-based pattern generation, often via preview control of a linear inverted pendulum model, underpinned classic humanoids such as Honda's ASIMO and the HRP series.

Why it matters for physical AI

ZMP remains the baseline notion of dynamic balance against which capture-point, MPC, and reinforcement-learned humanoid controllers are understood, and it still governs conservative walking modes in deployed bipeds.