Lageman, ChristianHelmke, UweAnderson, Brian2021-03-160005-1098http://hdl.handle.net/1885/227199In this paper we study a second order, distributed control system for a finite number of point agents on the unit circle that achieves simultaneously velocity consensus and distance based formation shape control. Based on tools from Riemannian geometry, we propose a system of second order differential equations on the N-dimensional torus that achieves these two goals. We prove convergence of the trajectories to single closed geodesics on a torus and investigate the stability properties of the distributed algorithm.This work was supported by the DAAD with funds of the German Federal Ministry of Education and Research (BMBF). Further, U. Helmke was supported by DFG Grant HE 1858/13-1. B.D.O. Anderson was supported by Data61-CSIRO (formerly NICTA) and by the Australian Research Council under grants DP110100538, DP130103610 and DP160104500.application/pdfen-AU© 2018 Elsevier Ltd.https://creativecommons.org/licenses/by-nc-nd/4.0/Decentralized controlFormation controlVelocity consensusRiemannian geometrySecond-order systems2018-0410.1016/j.automatica.2017.12.0602020-11-23Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)