Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Nonsmooth coordination and geometric optimization via distributed dynamical systems
J. Cortés, F. Bullo
SIAM Review 51 (1) (2009), 163-189
Abstract
Emerging applications for networked and cooperative
robots motivate the study of motion coordination for
groups of agents. For example, it is envisioned that
groups of agents will perform a variety of useful tasks
including surveillance, exploration, and environmental
monitoring. This paper deals with basic interactions
among mobile agents such as ``move away from the closest
other agent'' or ``move toward the furthest vertex of
your own Voronoi polygon.'' These simple interactions
amount to distributed dynamical systems because their
implementation requires only minimal information about
neighboring agents. We characterize the close
relationship between these distributed dynamical systems
and the disk-covering and sphere-packing cost functions
from geometric optimization. Our main results are: (i)
we characterize the smoothness properties of these
geometric cost functions, (ii) we show that the
interaction laws are variations of the nonsmooth
gradient of the cost functions, and (iii) we establish
various asymptotic convergence properties of the laws.
The technical approach relies on concepts from
computational geometry, nonsmooth analysis, and
nonsmooth stability theory.
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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