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Cooperative localization of underwater robots with unsynchronized clocks

Abstract This paper proposes an interval based approach for localizing a group of underwater robots with unsynchronized clocks. We use sonar communication and consider that the travel time of the sonar waves cannot be neglected, e.g. when the robots are fast and far-spaced. Therefore we cannot suppose that we measure a true distance between robots at the same time, but between robots at di􀉼erent times. Moreover, as the clocks of the robots are unsynchronized, the emitting and receiving times of the sonar waves are uncertain. To solve this problem, we cast the state equations of our robots as a constraint satisfaction problem and consider the sonar measurements as intertemporal constraints on uncertain times. We introduce the notion of interval of function to encompass the robots trajectory and clock with their uncertainty. We then use interval propagation to successively contract these intervals around the true position and clock of the robots. Several test cases are provided, with both simulated and experimental results.