Affine‐Image‐Driven and Finite‐Time Stable Formation Control for Multi‐AUV Systems With Unknown Complex Disturbances: A Geometric Perspective

Formation control of multi‐autonomous underwater vehicle (AUV) systems is essential for collaborative ocean tasks such as environmental monitoring and resource exploration, but it is hindered by challenges like limited flexibility in formation transformation, model uncertainties, and unknown ocean current disturbances. To address these issues, this paper presents a finite‐time flexible formation control strategy based on the affine image framework for second‐order multi‐AUV systems with AUV model uncertainties and external disturbances. The proposed strategy incorporates a finite‐time disturbance observer to accurately estimate composite disturbances (including model uncertainties and ocean currents) and a sliding mode control (SMC) approach to ensure robust finite‐time convergence of the formation. A key innovation is the extension of the affine image framework to second‐order dynamics, enabling flexible transformations between affine and rigid formations while requiring only d + 1 leaders (in d ‐dimensional space) to know the target shape, thus, minimizing global information needs. The proposed method achieves finite‐time stability and strong robustness against uncertainties, providing a unified solution for flexible formation control in uncertain underwater environments. Numerical simulations validate that the strategy effectively guides AUVs to converge to desired formations within finite time.