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

The affine formation maneuver control problem of a leader-follower type multi-agent systems with the directed interaction graphs is studied in this paper. This paper firstly gives and proves a sufficient and necessary condition of achieving the affine localizability. Then, under the $(d+1)$ -reachable condition of the given d-dimensional nominal formation with $d+1$ leaders, a formation of agents can be reshaped in arbitrary dimension by only controlling these leaders. In the sequel, a novel distributed control method for the followers with single-integrator dynamics is proposed to achieve the desired time-varying maneuvers, and the global stability is also proved. Corresponding simulations are carried out to verify the theoretical results, which show that these followers are tracking the time-varying references accurately and continuously.