Local Topology Inference of Mobile Robotic Networks Under Formation Control

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 a limited observation range can maneuver 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 offline and the interaction range online. 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.