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In this paper, we propose a distributed global connectivity maintenance and control framework of multi-robot networks, which can adapt connectivity online. Based on a series of energy functions, the control framework can make each robot autonomously move along the direction of gradient descent of the energy functions in order to reach the desired global connectivity of the multi-robot networks. This framework has enhanced adaptability and flexibility of multi-robot systems, because adapting connectivity online enables the system to maintain, promote or degrade connectivity at different stages of an integrated mission which require different desired connectivity values. Online connectivity adaptation can also help to change connectivity when the environment becomes more complicated, unknown and dynamic. Theorems are proposed to prove that the framework can not only maintain global connectivity, but can also effectively adapt global connectivity to desired values online, which has rarely been studied. Furthermore, connectivity promotion in the presence of bounded external control terms, such as collision avoidance, is also investigated, which helps to expand the scope of the framework. Finally, simulation and experiment results are presented so as to validate our unified control framework.

Distributed Global Connectivity Maintenance and Control of Multi-Robot Networks