This paper tackles the problem of formation reconstruction for a team of vehicles based on the knowledge of the range between agents of a subset of the participants. One main peculiarity of the proposed approach is that the relative velocity between agents, which is a fundamental data to solve the problem, is not assumed to be known in advance neither directly communicated. For the purpose of estimating this quantity, a collaborative control protocol is designed in order to mount the velocity data in the motion of each vehicle as a parameter through a dedicated control protocol, so that it can be inferred from the motion of the neighbor agents. Moreover, some suitable geometrical constraints related to the agents' relative positions are built and explicitly taken into account in the estimation framework providing a more accurate estimate. The issue of the presence of delays in the transmitted signals is also studied and two possible solutions are provided explaining how it is possible to get a reasonable range data exchange to get the solution both in a centralized fashion and in a decentralized one. Numerical examples are presented corroborating the validity of the proposed approach.
Keywords: active estimation; autonomous underwater vehicles; multi-agent system; range-based navigation; relative localization.
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