Math & Kinematics

Jerk

Jerk is the third time derivative of position, the rate of change of acceleration, measured in meters per second cubed or the angular equivalent. High jerk excites structural vibration, degrades tracking accuracy, stresses transmissions, and produces motion that humans perceive as abrupt, so trajectory optimization frequently penalizes or bounds jerk, and minimum-jerk profiles characterize smooth human reaching movements.

Why it matters for physical AI

Smoothness is not cosmetic: jerk-aware trajectories reduce wear, protect payloads and sensors, and produce the predictable motion people working near robots implicitly rely on.