Abstract
This paper deals with the general formation control problem for first order multi-agent systems. We investigate the behaviour of an arbitrary number of mobile agents moving on a plane with constrained input velocity when they are required to reach a specific spatial pattern. A general communication graph among agents is considered, relaxing conditions to the only requirement of containing a directed spanning tree. The solution to this problem is provided attending two issues. First, the asymptotic convergence to the desired formation pattern is ensured. Then a non-collision analysis is presented regarding the most general geometrical scenario which can lead to a collision among agents. This later issue is solved by using repulsive vector fields with unstable focus behaviour. Numerical simulations as well as experimental results are provided in order to illustrate the effectiveness of the proposed control law.
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