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This paper presents a decentralized algorithm for coverage with mobile robots on a graph. Coverage is an important capability of multi-robot systems engaged in a number of different applications, including placement for environmental modeling, deployment for maximal quality surveillance, and even coordinated construction.We use distributed vertex substitution for locational optimization, and the controllers minimize the corresponding cost function. We prove that the proposed controller with two-hop communication guarantees convergence to the locally optimal configuration. We evaluate the algorithms in simulations and compare them to the coverage algorithm in a continuous domain.

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