### Jorge Cortés

#### Professor

Hedonic coalition formation for optimal deployment

M. Ouimet, J. Cortés

Automatica 49 (11) (2013), 3234-3245

### Abstract

This paper presents a distributed algorithmic
solution, termed "coalition formation and deployment
algorithm", to achieve network configurations where
agents cluster into coincident groups that are
distributed optimally over the environment. The
motivation for this problem comes from spatial
estimation tasks executed with unreliable sensors.
We propose a probabilistic strategy that combines a
repeated game governing the formation of coalitions
with a spatial motion component governing their
location. For a class of probabilistic coalition
switching laws, we establish the convergence of the
agents to coincident groups of a desired size in
finite time and the asymptotic convergence of the
overall network to the optimal deployment, both with
probability 1. We also upper bound the expected
completion time of algorithm executions that use the
"proportional-to-number-of-unmatched-agents" switching
law, that depends on the number of unmatched agents,
under arbitrary and complete communication
topologies. The proposed algorithm is robust to
agent addition and subtraction. From a coalitional
game perspective, the algorithm is novel in that the
players' information is limited to neighboring
clusters. From a motion coordination perspective,
the algorithm is novel because it brings together
the basic tasks of rendezvous (individual agents
into clusters) and deployment (clusters in the
environment). Several simulations illustrate the
correctness, robustness, and time complexity
results.

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Mechanical and Aerospace Engineering,
University of California, San Diego

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