Jerk

The rate of change of acceleration over time — the third time-derivative of position — measured in m/s³.

Jerk, j, is the time derivative of acceleration a: j = da/dt = d³x/dt³ (x is position), measured in m/s³, and it captures how abruptly acceleration itself is changing. A sudden change in acceleration means large jerk, which feels jarring to a person, and also excites mechanical vibration and accelerates wear. That's why robot trajectory planning commonly bounds jerk: cubic polynomial time-scaling has acceleration jump discontinuously at the start and end, which is equivalent to infinite jerk; an S-curve velocity profile splits motion into seven segments to keep jerk bounded throughout; and a minimum-jerk trajectory minimizes the integral of squared jerk over the whole motion. Tamar Flash and Neville Hogan found in 1985 that natural human arm movements approximately follow this minimum-jerk principle. Reinforcement-learning locomotion controllers use a similar idea, commonly penalizing the difference between consecutive actions in the reward function to keep motion smooth.

ExampleIf an elevator's acceleration jumped instantly from 0 to its set value at startup, passengers would feel a hard jolt; real elevators ramp acceleration up gradually over time, which is exactly bounding jerk.

Also called

Jolt

Related

Minimum-Jerk Trajectory · S-Curve Velocity Profile · Quintic Polynomial Interpolation · Trajectory Planning · Action Smoothing · Trapezoidal Velocity Profile

Sources

Jerk (physics) - Wikipedia
Modern Robotics (Lynch & Park) preprint PDF, Ch. 9 Trajectory Generation