Formation Collision Avoidance Control of Underactuated Surface Vessels Under Input Constraints

In this paper, the collision-avoidance formation control problem for underactuated surface vessels (USVs) subject to input constraints is investigated. The input constraints include both input amplitude saturation and input rate saturation. A controller based on barrier Lyapunov functions (BLFs) is developed for the considered system. First, a disturbance observer is designed to compensate for environmental disturbances and model uncertainties that degrade system performance. Second, an auxiliary dynamic system is introduced to handle input amplitude saturation and input rate saturation. To guarantee connectivity preservation and collision avoidance within the formation, the distance errors and angle errors are transformed using BLFs. Based on the transformed errors and the disturbance observer, a BLF-based anti-saturation controller is then constructed. Lyapunov stability analysis proves that all signals in the closed-loop system are bounded. Finally, simulation results demonstrate that the proposed method can achieve collision-free formation control under both input amplitude saturation and input rate saturation, and verify that the control system achieves fast convergence, small tracking errors, and collision avoidance while satisfying the input magnitude and rate constraints.