3 research outputs found
Online Searching with an Autonomous Robot
We discuss online strategies for visibility-based searching for an object
hidden behind a corner, using Kurt3D, a real autonomous mobile robot. This task
is closely related to a number of well-studied problems. Our robot uses a
three-dimensional laser scanner in a stop, scan, plan, go fashion for building
a virtual three-dimensional environment. Besides planning trajectories and
avoiding obstacles, Kurt3D is capable of identifying objects like a chair. We
derive a practically useful and asymptotically optimal strategy that guarantees
a competitive ratio of 2, which differs remarkably from the well-studied
scenario without the need of stopping for surveying the environment. Our
strategy is used by Kurt3D, documented in a separate video.Comment: 16 pages, 8 figures, 12 photographs, 1 table, Latex, submitted for
publicatio
A panorama of positivity. I: dimension free
This survey contains a selection of topics unified by the concept of positive semidefiniteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). We put emphasis on entrywise operations which preserve positivity, in a variety of guises. Techniques from harmonic analysis, function theory, operator theory, statistics, combinatorics, and group representations are invoked. Some partially forgotten classical roots in metric geometry and distance transforms are presented with comments and full bibliographical references. Modern applications to high-dimensional covariance estimation and regularization are included