3-Cycle-Free Persistence for Cooperative Control of Formations with Acyclic Control Structure

AbstractIn this paper, we analyze the problem of acquiring 3-cycle-free persistent formations of mobile autonomous agents that have acyclic control structure. Nyquist-like criterion for formation stabilization is used in literature for the problem of relative formation stabilization. For this purpose, spectral properties of the Laplacian matrix are used in evaluating desirable structural properties of formations. Establishing measures of near-periodicity are useful in quantifying formation stability margins. In this paper, we analyze constructions to create non-3-periodic persistent formations, i.e., we study the constructions to create 3-cycle-free persistent formations. Central to the development of our analysis will be the use of tools from rigidity theory and graph Laplacians.