Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Visibility in polygonal environments with holes:
finding best spots for hiding and surveillance
N. Banzal, J. Cortés, S. Martínez
SIAM Journal on Control and Optimization, submitted
Abstract
Visibility plays an important role for decision
making in cluttered, uncertain environments. This
paper considers the problem of identifying optimal
hiding spots for an agent against line-of-sight
detection by an adversary whose location is unknown.
We consider environments modeled as polygons with
holes. We develop a set of mathematical tools for
reasoning about visibility as a function of position
and rely on non-smooth analysis to formally
characterize the regularity properties of various
visibility-based metrics. These metrics are
non-smooth and non-convex, so off-the-shelf
algorithms for optimization can only guarantee
convergence to Clarke critical points. To address
this, the proposed Normalized Descent algorithm
leverages the structure of non-smooth points in
visibility problems and introduces randonmess to
escape saddle points. Our technical analysis allows
for the non-monotonic decrease of the visibility
metric and strengthens the algorithm guarantees to
ensure convergence to local minima with high
probability. Simulations on two hide-and-seek
scenarios showcase the effectiveness of the proposed
approach.
pdf
Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo