A necessary condition for global performance guarantees in most of the motion coordination algorithms is connectivity of the underlying network topology. In proximity networks, connectivity maintenance becomes critical because the neighborhood set of each agent is dynamic and depends on the locations of all the other agents in the network. We present an efficient framework for distributed motion coordination in proximity networks. The proposed framework relies on identifying agents in a so called weakly connected dominating (WCD) set of the underlying network graph. Maintaining only the edges incident to the agents in WCD, which we call as critical edges, preserves the connectivity of the overall network. The proposed framework is presented in the context of rendezvous problem, which is selected because of its canonical importance in distributed systems with mobile agents. We propose a controller that drives all the agents to a common point by preserving the critical edges only. The proposed scheme is robust to failure of edges that are not critical and nodes that do not belong to WCD. Moreover, it performs well in terms of energy consumption and computational complexity.
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