Formation-preserving trajectory planning for USV swarms via risk-aware velocity obstacles

Maintaining a rigid geometric formation for unmanned surface vehicles (USVs) in real-world waters is challenging, especially when the swarm executes sharp turns or encounters external disturbances. Existing work either neglects explicit formation constraints or transfers the burden of keeping the shape to high-frequency feedback control, which is hardly affordable for low-cost marine platforms with limited bandwidth and computational resources. To bridge this gap, we propose a formation-damage-risk (FDR) driven trajectory-planning framework that couples a quantified “risk of shape breakage” with an improved velocity-obstacle (VO) method. Three typical shape-disturbing events—lane invasion, over-speed in curves, and member drifting—are mathematically defined and fused into a continuous, differentiable FDR metric via carefully designed logistic smooth functions. MATLAB-based simulations demonstrate that, under single- and double-amplitude stochastic disturbances, the proposed FDR-VO planner reduces the average position deviation. The results indicate that explicitly incorporating formation risk into the planning layer significantly enhances the robustness and smoothness of USV swarm navigation.