This paper considers the problem of distributed control of rigid formation shapes in the plane for multi-agent systems. A constructive perturbation method is proposed and combined with the conventional gradient control law. The proposed control law stabilizes the desired rigid formation in a global sense for all initial conditions except the case when a pair of communicating agents happen to have the same initial location. It also avoids collisions between any two communicating agents during the motion. Simulation results are provided to illustrate the effectiveness of the control algorithm. (c) 2013 Elsevier Ltd. All rights reserved.