This paper considers a method for local positioning of a group of mobile robots equipped with ultrasonic beacons. The described alternate movement algorithm allows a group of four wheeled robots to move on a flat surface with centimeter accuracy. While one robot is moving, the others act as fiducial beacons for it. The positioning problem is solved based on trilateration and numerical optimization. The overall trajectory is obtained by integrating the steps of each mobile robot. The leader communicates with all participants, receives the necessary data from them and organizes the grouping movement. The proposed approach can be used for autonomous cooperative navigation in the absence of other positioning systems.