Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Generalized multicircumcenter
trajectories for optimal design under near-independance
R. Graham, J. Cortés
Proceedings of the IEEE Conference on
Decision and Control, Atlanta, Georgia, USA, 2010, pp. 5499-5504
Abstract
This work deals with trajectory optimization for a network of
autonomous robotic sensors sampling a spatio-temporal random field.
We examine the problem of minimizing over the space of network
trajectories the maximum predictive variance of the estimator. This is
a high-dimensional, multi-modal, nonsmooth optimization problem, known
to be NP-hard even for static fields and discrete design spaces.
Under an asymptotic regime of near-independence between distinct
sample locations, we show that the solutions to a novel generalized
disk-covering problem are solutions to the optimal sampling problem.
This result effectively transforms the search for the optimal
trajectories into a geometric optimization problem. Constrained
versions of the latter are also of interest as they can accommodate
trajectories that satisfy a maximum velocity restriction on the
robots. We characterize the solution for the unconstrained and
constrained versions of the geometric optimization problem as
generalized multicircumcenter trajectories, and provide algorithms
which enable the network to find them in a distributed fashion
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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
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