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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 291372, 6 pages
Research Article

2D Dubins Path in Environments with Obstacle

1Department of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China
2School of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 3 June 2013; Revised 14 October 2013; Accepted 15 October 2013

Academic Editor: John Gunnar Carlsson

Copyright © 2013 Dongxiao Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We recapitulate the achievement about the Dubins path as well as some precise proofs which are important but omitted by Dubins. Then we prove that the shortest path ( -geodesic) in environments with an obstacle consists of no more than five segments, each of which is either an arc or a straight line. To obtain such -geodesic, an effective algorithm is presented followed by a numerical simulation as verification.