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A distributed control law that guarantees connectivity maintenance in a network of multiple mobile agents is presented. The control law respects the limited sensing capabilities of the agents by allowing each agent to take into account only agents within its sensing radius in the controller implementation. In contrast to previous approaches to the problem, the proposed control law does not attain infinite values whenever an edge tends to be lost, and is therefore a bounded distributed control law. This is achieved via the use of decentralized navigation functions which are potential fields with guaranteed boundedness and are redefined in this paper in order to take into account the connectivity maintenance objective. We first treat the case of connectivity maintenance in a static initial position based communication graph and extend the results to the case of dynamic edge addition. The results are then applied to a formation control problem.
Dimarogonas et al. (Thu,) studied this question.