Iteratively Locating Voronoi Vertices for Dispersion Estimation

— We present a new sampling-based algorithm for iteratively locating Voronoi vertices of a point set in the unit cube Id = [0, 1]d . The algorithm takes an input sample and executes a series of transformations, each of which projects the sample to a new face of the Voronoi cell in which it is located. After d such transformations, the sample has been transformed into a Voronoi vertex. Locating Voronoi vertices has many potential applications for motion planning, such as estimating dispersion for coverage and verification applications, and providing information useful for Voronoi-biased or multiple-tree planning. We prove theoretical results regarding our algorithm, and give experimental results comparing it to naive sampling for the problem of dispersion estimation.

• Type: Conference
• Year: 2005
• Where: ICRA
• Authors: Stephen R. Lindemann, Peng Cheng
• Keywords: ICRA 2005, Robotics, Voronoi, Voronoi Cell, Voronoi Vertices