Control

Flatness

Flatness, or differential flatness, is a property of a dynamical system whereby all states and inputs can be expressed algebraically in terms of a set of flat outputs and finitely many of their time derivatives. Flat systems admit straightforward trajectory generation: one plans a smooth curve in flat output space and recovers the full state and input trajectories analytically. The quadrotor with its position and yaw as flat outputs is the canonical robotics example.

Why it matters for physical AI

Flatness turns aggressive trajectory planning into curve fitting, enabling agile drone flight and feedforward-rich control; it exemplifies how exploiting structure yields guarantees that purely learned planners still struggle to match.