  The interaction topology is critical for efficient cooperation of mobile
robotic networks (MRNs). We focus on the local topology inference problem of
MRNs under formation control, where an inference robot with limited observation
range can manoeuvre among the formation robots. This problem faces new
challenges brought by the highly coupled influence of unobservable formation
robots, inaccessible formation inputs, and unknown interaction range. The novel
idea here is to advocate a range-shrink strategy to perfectly avoid the
influence of unobservable robots while filtering the input. To that end, we
develop consecutive algorithms to determine a feasible constant robot subset
from the changing robot set within the observation range, and estimate the
formation input and the interaction range. Then, an ordinary least squares
based local topology estimator is designed with the previously inferred
information. Resorting to the concentration measure, we prove the convergence
rate and accuracy of the proposed estimator, taking the estimation errors of
previous steps into account. Extensions on nonidentical observation slots and
more complicated scenarios are also analyzed. Comprehensive simulation tests
and method comparisons corroborate the theoretical findings.
