Control

Zero Dynamics

Zero dynamics are the internal dynamics that remain in a nonlinear system when its outputs are held identically at zero by feedback, revealing behavior that output control cannot see; systems with unstable zero dynamics are nonminimum-phase and fundamentally harder to control. In legged robotics, the hybrid zero dynamics (HZD) framework of Westervelt and Grizzle designs walking gaits as stable periodic orbits of this reduced dynamics.

Why it matters for physical AI

Underactuated machines like bipeds cannot command every degree of freedom, so what happens in the unactuated remainder decides stability, informing both formal gait design and why some learned locomotion behaviors are fragile.