A bounded distributed connectivity preserving aggregation strategy with collision avoidance property

This paper presents a bounded connectivity preserving control strategy for the aggregation of multi-agent systems. The problem is investigated for two cases of single-integrator agents and unicycles. Under the proposed control strategy, if two agents are in the connectivity range at some point in time, they will stay connected thereafter. The agents finally aggregate while avoiding collision in such a way that the average of the distances between every pair of neighboring agents is bounded by a pre-specified positive real number, which can be chosen arbitrarily small. The results are developed based on some important characteristics of the positive limit set of the closed-loop system under the proposed control strategy and a fundamental property of convex real functions. The theoretical results are verified by simulation.