Globally convergent leaderless formation control for unicycle‐type mobile robots

Abstract

This study investigates the leaderless formation control problem for unicycle-type mobile robots and designs a formation controller for a two-robot system. The proposed control law is globally effective, namely making mobile robots converge to the formation from all kinds of initial conditions. The kinematic model of mobile robots is directly established on the special Euclidean group, and the mobile robot is merely required to obtain the relative configuration (i.e. position and orientation) in its own body-fixed frame. The approach for the formation problem is to design a virtual system for each mobile robot, which contains the desired formation pattern, so that the formation problem for mobile robots is converted into the consensus problem for virtual systems. Furthermore, the non-holonomic constraint for the virtual systems is derived for the first time, which is explained from the viewpoint of geometric control. In addition, the authors clarify the physical meaning of the multiple control gains, which can guarantee excellent robot behaviour by appropriate selection.