Determination of Spatial Configuration of an Underwater Swarm with Minimum Data

This paper is the extension of work presented at the IARPConference "Bio inspired robotics" held in Frascati (Italy),14 May 2014.The subject is the localization problem of an underwaterswarm of autonomous underwater robots (AUV), in theframe of the HARNESS project; by localization, we mean therelative swarm configuration, i.e., the geometrical shape ofthe group. The result is achieved by using the signals thatthe robots exchange. The swarm is organized by rules andconceived to perform tasks, ranging from environmentalmonitoring to terrorism-attack surveillance.Two methods of determining the shape of the swarm, bothbased on trilateration calculation, are proposed. The firstmethod focuses on the robot's speed. In this case, we useour knowledge of the speeds and distances between themachines, while the second method considers only distancesand the orientation angles of the robots. Unlike atrilateration problem, we do not know the position of thebeacons and this renders the problem a difficult one.Moreover, we have very few data. More than one step ofmotion is needed to resolve the multiple solutions found,owing to the symmetries of the system and optimizationprocess of one or more objective functions leading to the final configuration. We subsequently checked our algorithmusing a simulator taking into account random errorsaffecting the measurements.