Name
Abstract | ||
|---|---|---|
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another arc, or from three circular arcs [Dubins, 1957]. Dubins original proof uses advanced calculus; later, Dubins result was reproved using control theory techniques [Reeds and Shepp, 1990], [Sussmann and Tang, 1991], [Boissonnat, C\'er\'ezo, and Leblond, 1994]. We introduce and study a discrete analogue of curvature-constrained motion. We show that shortest "bounded-curvature" polygonal paths have the same structure as Dubins paths. The properties of Dubins paths follow from our results as a limiting case---this gives a new, "discrete" proof of Dubins result. |
Year | Venue | Field |
|---|---|---|
2012 | CoRR | Dubins path,Motion planning,Discrete mathematics,Polygon,Combinatorics,Shortest path problem,Limiting,Mathematics,Bounded curvature |
DocType | Volume | Citations |
Journal | abs/1211.2365 | 0 |
PageRank | References | Authors |
0.34 | 13 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvester David Eriksson-Bique | 1 | 10 | 0.90 |
| David G. Kirkpatrick | 2 | 2394 | 541.05 |
| Valentin Polishchuk | 3 | 252 | 34.51 |