On the generation of a trigonometric interpolating curve in R3

Abstract

The problem of generating smooth trajectories of me-chanical systems is particularly important in robotics. Traditionally, cubic splines are the most used for path-planning of mobile robots moving in a two-dimensional environment. Although these curves are easy to com-pute, in practice they have some disadvantages over other interpolating curves. In this paper we introduce a class of new splines whose segments are composed by convex combination of circular arcs and straight lines. One particular feature of such interpolating curve re-lies on the fact that the calculation of each segment depends only on local data. This is an important ad-vantage from a practical point of view. We also study optimality properties in order to make a comparison with cubic splines. 1