Model predictive controller for path following ships validated by experimental model tests

This paper introduces a practical model predictive controller for surface ships' path following, with validation through experimental tests. Model predictive control (MPC) is a state-of-the-art modern control technique, providing local optimal control action based on prediction and reference. In this approach, a simple predictive model based upon the Nomoto model is employed to forecast the (near) future ship positions, while the SerretFrenet frame and the Spline path function are used to generate a smooth ship speed-based reference. Two optimizers, namely the Spline optimizer and the Cobyla (Constrained Optimization by Linear Approximation) optimizer, are used to retrieve an optimal solution that minimizes the difference between the prediction and the reference. To achieve a real-time control feedback, the optimization variables are reduced significantly to lower calculation time by assuming a constant rudder angle throughout the prediction horizon, which is consistent with a realistic human controlled manoeuvre. In addition, an adaptive prediction horizon strategy is proposed to balance overshoot and accuracy. A series of free running model tests were conducted in the Towing Tank for Manoeuvres in Shallow Water (cooperation Flanders Hydraulics - Ghent University) in Ostend, Belgium, in order to evaluate the effectiveness and performance of the proposed controller, and to explore the impact of its parameter settings. The 20 m wide towing tank provides ample space to design complex paths for the ship to follow, which poses a significant challenge for the controller. Essential parameters in MPC, including weight factor for heading error, parameters of predictive model, prediction horizon, gain of adaptive prediction horizon and optimizer, are described in detail and their effects on the control outcomes are discussed with analysis of experimental results. The results demonstrate excellent control performance of the MPC, i.e. high tracking accuracy, smooth track transition, insensitivity to parameter setting and strong robustness in the presence of inherent model uncertainty, despite the simplifications made for practicality.