Distributed Control of networked multi-agent systems for formation with freedom of special Euclidean group

In this study, we consider formation control of multi-agent systems with free rotation and translation, without free reflection. The desired formation can be described as a set with the freedom of the special Euclidean group SE(d) = SO(d)×ℝd. Actually, the sets SO(d) and ℝd correspond to the free rotation and translation of the formation, respectively. For a given communication topology, we design a best distributed controller in the sense that the most similar coordination is achievable to the set with the freedom of SE(d). The effectiveness of the proposed controllers is illustrated by simulation results.

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