On the solvability of the mutual localization problem with anonymous position 
measures

Franchi, A; Oriolo, G; Stegagno, P

doi:10.1109/ROBOT.2010.5509511

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On the solvability of the mutual localization problem with anonymous position measures

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Citation

Franchi, A., Oriolo, G., & Stegagno, P. (2010). On the solvability of the mutual localization problem with anonymous position measures. In 2010 IEEE International Conference on Robotics and Automation (ICRA 2010) (pp. 3193-3199). Piscataway, NJ, USA: IEEE.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-C04A-1

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(n2= log n) to be verified and is
based on the notion of rotational symmetry in R2. 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.