The authors consider the problem of control of the mobile robots' motion in a leader-follower formation. They use a method, in which the follower position is defined only in the follower-fixed coordinate system and the only information involved is the relative mutual positions of the leader and the follower. Such an approach is more relevant from the viewpoint of applications. For a mobile robot in the formation, the only available information is usually the data from the sensors concerning its relative position with respect to the other robots in the formation. One of the basic methods used for synthesizing of the laws for control of the objects' motion in the formations is the feedback linearization method, although application of this method is limited due to high complexity of the kinematic model and also rather low robustness of this method with respect to the external disturbances. Many researchers dealing with the control of robots in a leader-follower formation use the theory of systems with a variable structure for development of the control laws invariant to the external disturbances. A significant drawback of such control laws is emergence of high-frequency switching in the control signals. Recently specialists have shown an increased interest to the methods of the spatial (functional or program-coordinate) control mainly aimed at a direct solution of the problem of stabilization of the motion over a manifold. A typical feature of the method of the structural synthesis (functional control), also revealed in this work, is the extension of the definition of the relative motion by using an implicit model. Because of the drawbacks of the existing analytical and experimental investigations done by the method of the structural synthesis and also due to certain functional bottlenecks of the existing approaches, the further development of the structural synthesis of the closed control laws on the basis of organizing of a system of motion along a prescribed trajectory in the space of states, is an important task. In this work, the authors use the method of organization of the forced motion along the desired trajectory in the space of states of an object within the problem of control of the motion of a homogeneous formation of the mobile robots with a differential drive. By keeping the required distance between the robots in case of a limited range of interaction of objects in a group by the method of potential functions, it is possible to avoid collisions and obstacles. Numerical experiments confirm the workability of the control system in the presence of the measurement noise and external disturbances.