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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 …