Affine Formation Maneuver Control of Linear Multi-Agent Systems with Undirected Interaction Graphs

The affine formation maneuver control problem of leader-follower linear multi-agent systems with undirected interaction graphs is studied in this paper. First, this paper provides and proves the sufficient and necessary conditions for affine localizability. If given a d-dimensional nominal formation with no fewer than d+ 1 leaders and generic universal rigidity, then any formation shape satisfying affine transformation can be obtained in arbitrary dimension only by these leaders. In the sequel, a novel distributed control method for the followers with linear dynamic models is designed to achieve the desired time-varying maneuvers, and the stability is proved. Simulations are carried out to verify the theoretical results, which show that these followers can track the time-varying references continuously and accurately.

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