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Motion coordination algorithms resulting from classical geometric optimization problems
J. Cortés
Proceedings of the International Workshop on Global Analysis, eds. K. Tas, D. Krupka, D. Baleanu and O. Krupkova, AIP Conference Proceedings, vol. 729, American Institute of Physics, 2004, pp. 54-68

Abstract

This paper introduces various geometric optimization problems and explores their relationship with motion coordination algorithms for networks of mobile agents. For each problem, the objective is the optimization of an appropriate multi-center function encoding the sensing task to be achieved by the mobile network in a dynamic environment. We present five different scenarios: the expected value scenario, the expected value scenario with limited range interactions, the area scenario, the worst-case scenario and the non-interference scenario. We carefully analyze the smoothness properties and gradient information of the multi-center functions. Based on this investigation, we propose distributed motion coordination algorithms specifically tailored for each scenario. The multi-center functions play the role of network aggregate cost functions certifying the validity of the coordination algorithms. Various numerical simulations illustrate the results.

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