A Metropolis-Hastings Algorithm for Task Allocation

Doha Hamza, Sarah Asad Toonsi, Jeff S Shamma

Abstract:

We consider a robot-location assignment
problem. The problem is confounded by a location network
that restricts robots’ motion to neighboring locations. The
problem can be optimally solved using a centralized Hun-
garian algorithm. We propose a distributed game-theoretic
algorithm, based on the Metropolis-Hastings mechanism,
to eliminate the need for a central coordinator. Agents
are activated at random. Agents compare their action,
location, against a neighboring one based on the location
network. If the new location represents an improvement in
agent’s utility, they move with probability one, otherwise,
they move with a probability proportional to the difference
in the two locations’ utilities. Our algorithm converges to
the optimal assignment of robots to locations. We provide
extensive simulations, compare with previous work, and
demonstrate the versatility of the proposed algorithm to
various task allocation scenarios.