Math & Kinematics

Interpolation

Interpolation is the computation of intermediate values between known points, used throughout robotics to turn sparse waypoints or low-rate commands into smooth, dense trajectories. Common schemes include linear and cubic spline interpolation for joint positions, minimum-jerk profiles for smoothness, and spherical linear interpolation (slerp) for rotations, which respects the geometry of orientation space.

Why it matters for physical AI

Learned policies typically emit actions far below servo rates, so interpolation quality directly affects motion smoothness, tracking fidelity, and hardware wear when executing action chunks on real robots.