  We consider the problem of configuration formation in modular robot systems
where a set of modules that are initially in different configurations and
located at different locations are required to assume appropriate positions so
that they can get into a new, user-specified, target configuration. We propose
a novel algorithm based on graph isomorphism, where the modules select
locations or spots in the target configuration using a utility-based framework,
while retaining their original configuration to the greatest extent possible,
to reduce the time and energy required by the modules to assume the target
configuration. We have shown analytically that our proposed algorithm is
complete and guarantees a Pareto-optimal allocation. Experimental simulations
of our algorithm with different number of modules in different initial
configurations and located initially at different locations, show that the
planning time of our algorithm is nominal (order of msec. for 100 modules). We
have also compared our algorithm against a market-based allocation algorithm
and shown that our proposed algorithm performs better in terms of time and
number of messages exchanged.
