In this paper, a general solution to the formation control problem without collisions for first-order multi-agent systems is proposed. The case of an arbitrary number of mobile agents on a plane with saturated input velocity is analysed. Besides, conditions on the communication graph among agents are relaxed to the only requirement of containing a directed spanning tree. This general approach is an extended result from the simpler case of combinations of cyclic pursuit communication graphs. The proposed solution to this problem is designed in two steps. First, the asymptotic convergence in the absence of collisions is ensured. After this, the non-collision problem is faced by analysing the most general possible geometrical scenario which can lead to collision among agents. Discontinuous vector fields with unstable counterclockwise focus behaviour are applied by every agent in order to repel each other. Numerical simulations illustrate the performance of the proposed scheme.
