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This paper studies the time-varying formation reconfiguration control for multiple underactuated autonomous underwater vehicles (AUVs) with an Euler–Lagrange-like model. The goal is to control a fleet of AUVs to achieve any desired formation shape using a distance-based graph rigidity and affine transformation (GR-AT) algorithm. Firstly, the distance-based graph rigidity with backstepping technology is utilized to solve the formation controlproblem, and we acquire the initial nominal formation. In the sequel, we transform the nominal formation into any desired formation shape using the properties of the affine transformation (including translation, scaling, rotation, shearing, or a combination of them). Even the geometric shapes formed can be constantly changed. The Lyapunov stability theory can ensure the uniform ultimate boundedness of whole distance errors. Finally, several simulation examples with formation reconfiguration are given to validate the efficacy of the designed control methods. Moreover, some experimental results are presented to confirm the validity and applicability of the scheme with four real bionic robot fish. • The underactuated AUVs are considered in this paper. • Graph rigidity and backstepping techniques are employed to achieve formation control. • Affine transformation technique is used to realize formation reconfiguration. • The Lyapunov based stability analysis shows that the proposed controller is stable. • Experimental results demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]