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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