(The) upper bound of bounded curvature path

Abstract

Since Dubins introduced the problem, the shortest bounded curvature path problem is becoming more interesting not only in the field of robotics, but also in geometry and theoretical computer science. Consider two configurations $S$ and $F$ in a plane, where a configuration is a point with a direction of travel. We call a path from $S$ to $F$ whose curvature is everywhere at most one a \emph{bounded curvature path}. In this thesis, we show that given any two configurations there always exists a bounded curvature path whose length does not exceed $d+2\pi$, where $d$ is the Euclidean distance between the two points and is at least 2.0.