Elliptical Disk-Based Collision Avoidance for Formation Tracking Control of Underactuated Surface Vessels Under Input Saturation

This paper investigates a formation tracking problem for underactuated surface vessels (USVs) subject to collision avoidance and input saturation constraints. Many existing APF-based formation-control approaches formulate collision avoidance using a single reference point or an inter-center distance, which may provide insufficient geometric information during close-range maneuvers. To improve navigation safety, an elliptical disk-based collision avoidance mechanism is developed by introducing safety points at the bow, stern, port, and starboard sides of each USV, such that multiple characteristic-point distance constraints can be simultaneously enforced. To address unknown nonlinearities caused by model uncertainties and external disturbances, a neural network-based observer is designed to estimate unavailable velocity states and lumped disturbances. Distributed control laws are synthesized by integrating artificial potential functions (APFs), the observer, and a backstepping technique. Additional controllers are introduced to address the input saturation and underactuated issues while preserving the collision avoidance capability. Stability of the closed-loop system is rigorously established via Lyapunov theory. Simulation results demonstrate that the proposed approach achieves safer close-range maneuvering performance compared with conventional single-point methods.