Addressing parametric uncertainties in autonomous cargo ship heading control

Abstract

The progress of computer technology has had a profound influence on the maritime sector, particularly in relation to ship autonomy. The incorporation of computer-assisted systems for guidance, navigation, and control has emerged as a promising approach to minimize the potential risks associated with human errors during ship maneuvering. These errors have the potential to lead to disastrous consequences such as collisions with obstacles, vessel damage, and endangering the safety of passengers and cargo. Several notable studies have explored ship control systems using different control approaches and conducting simulation-based and real-time implementation tests. These studies include adaptive path following control for accurate target tracking, stabilization of heading angle using cascade control simulations and fuzzy logic-based decision-making mechanisms, integration of sensor information to reduce accidents on common ship routes, collision scenario analysis with fuzzy control-based decision-making aligned with international maritime regulations, design and analysis of planar autonomous position control using two independent propellers, rudder, speed, and position control experiments on a catamaran prototype using a PID approach enhanced by a Kalman Filter, and modeling and real-time control of unmanned surface vehicles with accurate parameter identification. These studies have provided valuable insights and advancements in ship control systems. Extensive research has also been carried out to address the control of ships with uncertain hydrodynamic coefficients, resulting in the exploration of various approaches. One approach involves using a Multi-level Model Predictive Control (MPC) method to regulate ship speed and calculate propulsion energy while considering uncertainties. Another approach is adaptive control, which continuously adjusts control inputs based on real-time measurements of ship behavior. Fuzzy logic-based control is also utilized, incorporating fuzzy rules that account for uncertainty in hydrodynamic coefficients to adapt the ship's control inputs. Machine learning techniques, like reinforcement learning, are employed to adjust control inputs based on available data. Additionally, robust control techniques are developed to ensure stable and predictable ship behavior even when faced with uncertain hydrodynamic coefficients. These studies make valuable contributions to ship motion control by addressing the challenges associated with uncertain hydrodynamic coefficients and proposing effective control strategies. This thesis aims to address two significant aspects in the field of ship control. First, the development of a comprehensive ship motion model for the ship's heading angle. Second, the effective handling of parametric uncertainty in ship hydrodynamics. The research focuses on enhancing the understanding of ship behavior and designing control strategies that can robustly handle uncertainties, ultimately improving the performance, safety, and efficiency of ship operations. The first objective of this thesis is to construct a control-oriented ship motion model that accurately represents the ship's heading angle dynamics. The model incorporates both linear and nonlinear dynamics to account for the complexities of ship motion under various operating conditions. To derive the linear model, certain assumptions are made to simplify the typical six degrees of freedom (6DOF) equation of motion into a three degrees of freedom (3DOF) equation. From a motion perspective, slow-speed displacement vessels exhibit minimal heave, roll, and pitch motions. Therefore, the variables $Z$, $K$, $M$, and their derivatives, along with the angular velocities $w$, $p$, $q$, can be neglected. From a geometric perspective, conventional ships are symmetrical on the $xz$-plane. As a result, it is assumed that the $y$-coordinate of the ship's center of gravity is zero $y_G = 0$. For the nonlinear model, a well-established 3DOF ship model provided by the Manevering Modelling Group (MMG) is utilized. This model extends the previously derived control-oriented ship equation of motion by incorporating the dynamics of the ship's propeller. By integrating the propeller dynamics into the model, a more comprehensive understanding of the ship's behavior and the interaction between its motion and the propeller can be achieved. The derivations and explanations in this subsection aim to provide valuable insights into the nonlinear ship equation of motion with propeller dynamics, serving as a useful tool for ship motion control design and optimization. By establishing a reliable ship motion model, it becomes possible to design effective control strategies for heading angle control. This aspect of the research involves reviewing and analyzing existing studies on ship autopilot design, including control methods such as adaptive path following controllers and cascade control simulations. In order to validate the model's accuracy, a turning circle test was conducted. This validation process done by comparing the model's predictions with experimental data from previous studies. To ensure a reliable validation process, a 1/80 scale model of the DTC Container ship was chosen for physical validation. The study's results convincingly demonstrate the model's ability to accurately approximate the trajectory with a fixed rudder angle of $\delta = 35$ degrees. Both the linear and nonlinear models developed in this study exhibit a high level of agreement with the actual system, comparable to the results obtained from other studies utilizing CFD and system-based approaches. The second objective of this thesis is to address the challenge of parametric uncertainty in ship hydrodynamics, particularly focusing on the uncertainty associated with hydrodynamic coefficients. Hydrodynamic coefficients play a crucial role in understanding the interactions between the ship and the surrounding water. However, these coefficients often exhibit variations due to various factors, such as environmental conditions, vessel modifications, or manufacturing tolerances. The presence of such uncertainty can significantly impact the performance and reliability of ship control systems. To address this issue, optimization techniques such as Particle Swarm Optimization (PSO) and Genetic Algorithms (GA) have been used to determine the optimal coefficients that best match the ship's motion. However, these methods can be slow, particularly if a large number of samples are needed to represent the uncertainties in the hydrodynamic coefficients. To answer this challenge, this thesis designed a fast optimization algorithm to find a robust optimal controller for ship heading angle control with a certain level of error in hydrodynamic coefficients that is difficult to solve deterministically. The proposed optimization algorithm is referred to as "Bisection Optimization via Blind Search". This methodology involves simulating the model for a total of $n$ samples, utilizing $m$ randomly sampled controller parameters $K$. The resulting cost value $\omega$ is recorded for each simulation. Subsequently, the controller parameter $K$ that produces the lowest $\omega$ value is selected. In the second stage, a bisection-based optimization technique is employed to further refine the chosen controller parameter $K$. In this thesis, the uncertainty levels considered in this study are set at $\pm$20$\%$, representing the permissible deviations of parameters from their nominal values. To mitigate the adverse effects of uncertainty, a simulation scenario is created where the controller is tasked with adjusting the yaw angle $\psi$ from 0 degrees to 40 degrees. To evaluate the optimization performance, four different cost functions are employed: Integral Absolute Error (IAE), Integral Squared Error (ISE), Integral Time Absolute Error (ITAE), and Integral Time Squared Error (ITSE). However, the results indicate that the optimal controller parameters obtained using these different cost functions do not exhibit significant differences. Two types of controllers, namely proportional (P) and proportional-derivative (PD) controllers, are investigated in this study. The inclusion of the derivative term in the PD controller aims to mitigate oscillations and overshoot in the system's response, thereby improving stability and settling time. However, the integral term is excluded from consideration due to the inherent stability of the system and its expected slow response. The results demonstrate that the proposed algorithm outperforms existing methods such as Particle Swarm Optimization (PSO) in terms of both execution speed and task performance. By achieving these 2 objectives, this thesis contributes to the field of ship control by providing a comprehensive understanding of ship motion dynamics and offering effective solutions for addressing parametric uncertainty in ship hydrodynamics. The outcomes of this research can significantly impact various maritime applications, including autonomous navigation, collision avoidance, and energy-efficient ship operations. The developed ship motion model and the proposed optimization approaches can be implemented in real-world scenarios, enabling improved control strategies for ship heading angle control and enhancing the overall performance and safety of ship operations. In conclusion, this thesis combines the development of a control-oriented ship motion model with the effective handling of parametric uncertainty in ship hydrodynamics. The research contributes to the advancement of ship control by providing valuable insights, methodologies, and tools that can be utilized in designing robust control strategies for ship heading angle control under uncertain operating conditions. The findings of this thesis have the potential to enhance the efficiency, safety, and sustainability of ship operations, ultimately benefiting the maritime industry as a whole.