Decentralized Formation Control Part I: Geometric Aspects

12 years 11 months ago

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In this paper, we develop new methods for the analysis of decentralized control systems and we apply them to formation control problems. The basic set-up consists of a system with multiple agents represented by the nodes of a directed graph whose edges represent an available communication channel for the agents. We address the question of whether the information ﬂow deﬁned by the graph is suﬃcient for the agents to accomplish a given task. Formation control is concerned with problems in which agents are required to stabilize at a given distance of other agents. In this context, the graph of a formation encodes both the information ﬂow, as described above, and the distance constraints, by ﬁxing the lengths of the edges. A formation is said to be rigid if it cannot be continuously deformed with the distance constraints satisﬁed; a formation is minimally rigid if no distance constraint can be omitted without the formation losing its rigidity. Hence, the graph underlying minim...

Mohamed-Ali Belabbas

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