Control

Differential Flatness

Differential Flatness is a system property in which all states and inputs can be expressed algebraically in terms of a set of flat outputs and finitely many of their time derivatives. For flat systems, trajectory planning reduces to designing sufficiently smooth curves in the flat output space, with the required control inputs recovered analytically. The quadrotor is the canonical robotic example, with position and yaw as flat outputs, a result exploited by Mellinger and Kumar's minimum-snap trajectory generation.

Why it matters for physical AI

Flatness turns aggressive trajectory generation into tractable spline optimization, enabling the agile drone flight and smooth mobile-base motion that reactive learned planners are often benchmarked against.