A bounded connectivity preserving aggregation strategy with collision avoidance property for single-integrator agents

This paper presents a potential-based bounded distributed connectivity preserving control strategy for aggregation of a set of single-integrator agents. Under the proposed control strategy, if two agents are in the connectivity range at some point in time, they will stay connected thereafter. Under the proposed controller, 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 sufficiently 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.