Subdivision of point-normal pairs with application to smoothing feasible robot path

TL;DR

This paper introduces a new subdivision scheme for point-normal pairs that ensures the limit normals match the limit curve normals, improving the smoothing of robot paths.

Contribution

It proposes a novel averaging method for point-normal pairs, addressing the mismatch issue in previous schemes, and applies it to robot path smoothing.

Findings

New averaging method ensures limit normals match curve normals

Subdivision scheme effectively smooths robot paths

Enhanced editing capabilities for point-normal data

Abstract

In a previous paper [11] we introduced a weighted binary average of two 2D point-normal pairs, termed circle average, and investigated subdivision schemes based on it. These schemes refine point-normal pairs in 2D, and converge to limit curves and limit normals. Such a scheme has the disadvantage that the limit normals are not the normals of the limit curve. In this paper we solve this problem by proposing a new averaging method, and obtaining a new family of algorithms based on it. We demonstrate their new editing capabilities and apply this subdivision technique to smooth a precomputed feasible polygonal point robot path.