Comments on Global stabilization of rigid formations in the plane [Automatica 49 (2013) 1436-1441]

Abstract

This paper shows that the modified gradient control law proposed in Tian and Wang (2013) does not globally stabilize rigid formation shapes. Also, further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided.The work of B.D.O. Anderson and Z. Sun was supported by NICTA, which is funded by the Australian Government through the ICT Centre of Excellence program, and by the Australian Research Council under grant DP130103610 and DP160104500. Z. Sun is also supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award from Australian Government. The work of M.H. Trinh and H.-S. Ahn was supported in part by Ministry of Culture, Sports and Tourism (MCST) and Korea Creative Content Agency (KOCCA) in the Culture Technology (CT) Research & Development Program 2014