  The subject is the localization problem of an underwater swarm of autonomous
underwater robots (AUV), in the frame of the HARNESS project; by localization,
we mean the relative swarm configuration, i.e., the geometrical shape of the
group. The result is achieved by using the signals that the robots exchange.
The swarm is organized by rules and conceived to perform tasks, ranging from
environmental monitoring to terrorism-attack surveillance. Two methods of
determining the shape of the swarm, both based on trilateration calculation,
are proposed. The first method focuses on the robot's speed. In this case, we
use our knowledge of the speeds and distances between the machines, while the
second method considers only distances and the orientation angles of the
robots. Unlike a trilateration problem, we do not know the position of the
beacons and this renders the problem a difficult one. Moreover, we have very
few data. More than one step of motion is needed to resolve the multiple
solutions found, owing to the symmetries of the system and optimization process
of one or more objective functions leading to the final configuration. We
subsequently checked our algorithm using a simulator taking into account random
errors affecting the measurements
