Control

Minimum Jerk Trajectory

A minimum jerk trajectory is a motion profile that minimizes the time integral of squared jerk, the third derivative of position, yielding smooth quintic-polynomial point-to-point movements with bell-shaped velocity profiles. Flash and Hogan showed in 1985 that human reaching movements closely match this profile. In robotics, minimum jerk and related smooth profiles reduce vibration, actuator wear, and tracking error, and make robot motion appear natural and predictable.

Why it matters for physical AI

Smooth, human-like motion is both mechanically gentle and legible to nearby people, and such profiles remain standard for interpolating between waypoints produced by planners or learned policies.