Math & Kinematics

Spline Interpolation

Spline interpolation is the construction of smooth piecewise-polynomial curves passing through or near a sequence of waypoints, widely used to turn sparse via-points into continuous robot trajectories. Cubic splines guarantee continuous velocity and acceleration; quintic splines additionally control jerk, and B-splines offer local control without exact interpolation. Trajectory generators fit splines in joint or Cartesian space and time-parameterize them against velocity and acceleration limits.

Why it matters for physical AI

Discontinuous acceleration excites vibration and tracking error on real arms, so spline smoothing sits between virtually every planner or policy and the servo loops executing its output.