Control

Trapezoidal Velocity Profile

A trapezoidal velocity profile is a point-to-point motion trajectory in which velocity ramps up at constant acceleration, holds at a cruise value, and ramps down symmetrically, tracing a trapezoid in the velocity-time plane. It is the default move profile in industrial motion controllers because it is time-optimal under acceleration and velocity limits, though its discontinuous acceleration excites vibration, motivating S-curve profiles with bounded jerk for smoother motion.

Why it matters for physical AI

Simple parametric profiles still execute the vast majority of commanded robot moves in industry, and understanding their limits clarifies when learned or optimized trajectories offer genuine value over classical motion generation.