Mollification for efficient curve smoothing with formal guarantees

Resumen

This work presents a new alternative to polynomial splines for trajectory and  path generation.  We present a method that, given a non-differentiable trajectory/path, generates  an infinitely differentiable one in a single step---requiring small computational resources---and can be made as close to the original as desired, both pointwise and on compact subsets of the trajectory's domain. These methods---\textit{mollification} and its improvement, \textit{directional mollification}---possess $O(n)$ numerical complexity, can inherit certain geometric properties from splines (such as confinement to the convex hull of the points defining a curve), and allow for simple analytical curvature bounding for curves described as polygonal chains. We demonstrate the feasibility of these methods through a set of experiments in which the smooth curve adapts to the vehicle's dynamics.