Trajectory fitting with smoothing splines using velocity information

We present a derivation for a spline smoother which takes into account local velocity information. This smoother is well suited for finding a best-fit trajectory from multiple example trajectories and is thus useful in applications such as programming by demonstration and online gesture recognition for teleoperation. Currently available smoothers are designed to consider only position information and not local velocity information, and are thus less suited for smoothing trajectories over time of dynamic systems.