3-cycle-free rigidity for multi-agent control systems

This paper is concerned with rigid formations of mobile autonomous agents. For the problem of relative formation stabilization, Nyquist-like criterion for formation stabilization is used in literature, where spectral properties of the Laplacian matrix play a role in evaluating desirable structural properties of formations. Establishing measures of near-periodicity would be useful in quantifying formation stability margins. In this paper, we analyze constructions to create non-3-periodic rigid formations, i.e., we study the constructions to create 3-cycle-free rigid formations. Central to the development of our analysis was the used of tools from rigidity theory and graph Laplacians.