# Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots

@article{Smith2007CurveSA, title={Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots}, author={Stephen L. Smith and Mireille E. Broucke and Bruce A. Francis}, journal={IEEE Transactions on Automatic Control}, year={2007}, volume={52}, pages={1154-1159} }

If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The…

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