Three-Dimensional Dynamic Positioning Using a Novel Lyapunov-Based Model Predictive Control for Small Autonomous Surface/Underwater Vehicles

Small Autonomous Surface/Underwater Vehicles (S-ASUVs) are gradually attracting attention from related fields due to their small size, low energy consumption, and flexible motion. Existing dynamic positioning (DP) control approaches suffer from chronic restrictions that hinder adaptability to varying practical conditions, rendering performance poor. A new three-dimensional (3D) dynamic positioning control method for S-ASUVs is proposed to tackle this issue. Firstly, a dynamic model for the DP control problem considering thrust allocation was established deriving from dynamic models of S-ASUVs. A novel Lyapunov-based model predictive control (LBMPC) method was then designed. Unlike the conventional Lyapunov-based model predictive control (LMPC), this study used multi-variable proportional-integral-derivative (PID) control as the secondary control law, improving the accuracy and rapidity of the control performance significantly. Both the feasibility and stability were rigorously proved. A series of digital experiments using the S-ASUV model under diverse conditions demonstrate the proposed method's advantages over existing controllers, affirming satisfactory performances for 3D dynamic positioning in complex environments.