Objective To address the challenge of simultaneously maintaining formation integrity and enabling flexible obstacle avoidance for multi-unmanned underwater vehicle (multi-UUV) formations in complex underwater environments, this paper proposes a global path planning method that supports adaptive formation reshaping.

Method The proposed method is built upon an affine transformation framework that maps the cooperative path planning problem of the multi-UUV system into a two-dimensional affine parameter space. 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 tuning of sampling parameters, this algorithm efficiently generates an initial sequence of affine states. Subsequently, a B-spline-based back-end optimizer employs a gradient descent method to minimize a comprehensive objective function that accounts for trajectory smoothness, UUV kinematic feasibility, environmental collision safety, and the cost associated with adaptive formation scaling. The optimization process yields a continuous and smooth trajectory of affine parameters that satisfies multiple constraints.

Results 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 region, while 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 generates safe and feasible paths for multi-UUV formations navigating complex obstacle environments by enabling adaptive formation reshaping. This method significantly enhances the autonomy and environmental adaptability of marine unmanned vehicles, and holds great value for advancing the development and practical application of marine unmanned systems technology.