Affine formation maneuver control of high-order multi-agent systems over directed networks

To drive a group of agents to maneuver continuously with the desired collective forms, this paper addresses a distributed formation maneuver control problem of directed networked high-order multi-agent systems in arbitrary dimensions. Unlike the conventional methods where the target formation is time invariant, we propose an affine formation method based on the properties of affine transformation, in which the target formation can be time-varying and affinely transformed from the given nominal formation. This paper provides and proves a sufficient and necessary condition of achieving the directed graphical affine localizability, and it only needs that the leaders have a generic configuration and the followers are accessible to the subset of leaders. To achieve the whole formation maneuvers, assume that the leaders decide the whole formation's maneuver actions, then the control algorithms of the arbitrary-order integrator followers are proposed to track the time-varying target formation and the global convergence of tracking errors is also proved. Furthermore, this paper studies the practical problems of formation maneuvers when existing non-uniform time delays. Finally, both two-dimensional and three-dimensional simulation examples are given to demonstrate the effectiveness of theoretical results.