In geometry, the term Dubins path typically refers to the shortest curve that connects two points in the two-dimensional Euclidean plane (i.e. x-y plane) with a constraint on the curvature of the path and with prescribed initial and terminal tangents to the path, and an assumption that the vehicle traveling the path can only travel forward. If the vehicle can also travel in reverse, then the path follows the Reeds–Shepp curve.[1]
Lester Eli Dubins (1920–2010)[2] proved using tools from analysis[3] that any such path will consist of maximum curvature and/or straight line segments. In other words, the shortest path will be made by joining circular arcs of maximum curvature and straight lines.
^Reeds, J. A.; Shepp, L. A. (1990). "Optimal paths for a car that goes both forwards and backwards". Pacific Journal of Mathematics. 145 (2): 367–393. doi:10.2140/pjm.1990.145.367.
^"IN MEMORIAM Lester Eli Dubins Professor of Mathematics and Statistics, Emeritus UC Berkeley 1920–2010". University of California. Archived from the original on 15 September 2011. Retrieved 26 May 2012.
^Dubins, L. E. (July 1957). "On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents". American Journal of Mathematics. 79 (3): 497–516. doi:10.2307/2372560. JSTOR 2372560.
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