Curve Shortening and the Rendezvous Problem for Mobile Autonomous Robots

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dc.creatorSmith, Stephen L.
dc.creatorBroucke, Mireille E.
dc.creatorFrancis, Bruce A.
dc.date2006-05-16
dc.date.accessioned2026-07-07T07:09:32Z
dc.date.available2026-07-07T07:09:32Z
dc.descriptionIf 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 polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing.
dc.description15 pages, 18 figures
dc.identifierhttps://arxiv.org/abs/cs/0605070
dc.identifierhttp://arxiv.org/abs/cs/0605070
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111098
dc.subjectRobotics
dc.subjectMultiagent Systems
dc.subjectI.2.9
dc.titleCurve Shortening and the Rendezvous Problem for Mobile Autonomous Robots
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