Abstract: Objective To address the challenge of simultaneously achieving formation keeping and flexible obstacle avoidance for multi-Unmanned Underwater Vehicle (multi-UUV) formations in complex underwater environments, this paper proposes a global path planning method that enables adaptive formation transformation.Method The proposed method is grounded in an affine transformation framework, which maps the cooperative path planning problem of the multi-UUV system into a two-dimensional affine parameter space for resolution. First, a front-end path search is conducted using an improved Rapidly-exploring Random Tree* (RRT*) algorithm. By integrating fast exploration and iterative optimization phases, a weighted k-dimensional (KD) tree, a hybrid sampling mechanism, and adaptive adjustment of sampling parameters, this algorithm efficiently generates an initial sequence of affine states. Subsequently, a B-spline-based back-end optimizer employs the gradient descent method to minimize a comprehensive objective function. This function considers trajectory smoothness, UUV kinematic feasibility, environmental collision safety, and the cost of adaptive formation scaling. The optimization yields a continuous and smooth trajectory of affine parameters that satisfies multiple constraints.Results Results from lake experiments demonstrate that the proposed planning method can generate safe and feasible formation paths. It successfully guided the multi-UUV formation through a simulated narrow obstacle area, and the actual velocities and accelerations of the UUVs remained within the predefined feasibility constraints.Conclusion The proposed global planning method, based on affine transformation, effectively provides safe and feasible paths for multi-UUV formations navigating through complex obstacle scenarios by enabling adaptive formation changes. This method significantly enhances the autonomy and environmental adaptability of marine unmanned vehicles, holding positive significance for advancing the development and practical application of marine unmanned systems technology.