On the Solvability of the Mutual Localization Problem with Anonymous Position Measures

TitleOn the Solvability of the Mutual Localization Problem with Anonymous Position Measures
Publication TypeConference Paper
Year of Publication2010
AuthorsFranchi, A, Oriolo, G, Stegagno, P
Conference Name2010 IEEE Int. Conf. on Robotics and Automation
Pagination3193-3199
Date Published05/2010
Conference LocationAnchorage, AK
KeywordsEstimation, Formation control, Localization, Multi-robot systems
Abstract

This paper formulates and investigates a novel problem called Mutual Localization with Anonymous Position Measures. This is an extension of Mutual Localization with Position Measures, with the additional assumption that the identities of the measured robots are not known. A necessary and sufficient condition for the uniqueness of the solution is presented, which requires O(n^2/\log n) to be verified and is based on the notion of rotational symmetry in R^2. We also derive the relationship between the number of robots and the number of possible solutions, and classify the solutions in a number of equivalence classes which is linear in n. A control law is finally proposed that effectively breaks symmetric formations so as to guarantee unique solvability of the problem is also proposed; its performance is illustrated through simulations.

Citation Key2010a-FraOriSte
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