Math & Kinematics

Bezier Curve

A Bezier curve is a parametric polynomial curve defined by a set of control points and blended through Bernstein basis polynomials, beginning at the first control point, ending at the last, and remaining within the control points' convex hull. Popularized by Pierre Bezier for automotive body design, in robotics it parameterizes smooth trajectory segments, swing-foot trajectories in legged locomotion, and lane-change paths in autonomous driving.

Why it matters for physical AI

Low-order Bezier segments give planners a compact way to generate smooth, bounded motions whose derivatives are easy to constrain, keeping commanded trajectories within the dynamic limits real actuators can track.