# A Review of Autonomous Tugboat Operations for Efficient and Safe Ship Berthing
## 4 Autonomous Tugboat Element Technologies
### Modeling Technology  
Modeling technology is a fundamental aspect that plays a crucial role in the successful operation of autonomous tugboats, as control technology is directly applied based on the modeling form. Tugboats and motherships are treated as a single swarm, and their multibody dynamics must be modeled by breaking down the hull, joints, forces, and contact elements. To achieve an accurate modeling of the multibody dynamics, factors such as the tension of the topline, tugboat specifications such as length and weight, thrust capacity, and the frictional force between the tugboat and the mothership during ship berthing must be taken into account. This comprehensive modeling of the tugboat swarm dynamics enables a better understanding and control of the system during operation. For autonomous tugboats, high maneuverability and agile maneuvering are crucial; thus, they are commonly equipped with azimuth-type propellers. To investigate their maneuverability and stopping performance, previous studies such as [50; 51] have developed models for ships equipped with azimuth propellers. In the early stage, in studies such as [18; 19; 20; 21; 22], each tugboat was modeled as a three-degree-of-freedom azimuth propeller to simulate a fully autonomous tugboat (Figure 15). In Figure 15, \(f_{i}\) is the unidirectional control force of the tugboat, \((x_{i},y_{i})\) is the position at the contact point, \(\alpha_{i}\) is the clockwise X-axis direction of the tugboat based on the body-fixed coordinate, and \(\theta\) represents a clockwise X-axis angle based on the body-fixed coordinate system. It is assumed that the tugboats is strategically placed close enough. In other words, the tugboats was modeled as thrusters attached to the mothership. Consequently, the geometric configuration matrix for the thrust allocation of the tugboat is continuously cal  
Figure 14: Simulation environment of path planning in the work by [35]. Polygons with white lines represent the obstacles in harbor environment. culated. Subsequently, modeling techniques that incorporate environmental disturbances were developed [24], which differed from previous studies. In the study by [24], the effect of environmental disturbance is decomposed into low-frequency drift motion and wave motion components. The wave frequency component, which describes the vibrational motion of the ship, can be ignored, and the low-frequency components, such as slow wind, tidal current, and waves, are grouped together to form a model of environmental disturbance. To compensate the effect of disturbances, Sliding Mode Control (SMC) was applied, which is a robust control technique commonly used in the presence of uncertainty or disturbance. However, the studies mentioned only modeled tugboats as thruster and assumed that they operated as a single system, which differs from the actual operation of pushing and pulling the mothership. In 2019, there was a study [27] which controlled a ship using a towline between the tugboat and the ship being towed, as shown in Figure 16. When the tugboat tows the ship using a towline, the system is affected by environmental disturbances such as waves and currents. To address this, the system was controlled using three active directional fins attached to the hull and the towline. In Figure 16, \((x_{0},y_{0})\) and \((x,y)\) represent the connecting point at the towing point and the center of the towed vessel, respectively. \(\psi\) and \(\psi_{T}\) are towed vessels, respectively, the heading angle and towed vessel relative heading angle about the rope, representing the center line. Additionally, \(\gamma\) indicates the relative angle made by the target position and the control position, and \(\sigma\) (=1, 2, 3) indicates the rotation angle of each rudder. Finally, \(l_{r},l_{r},l_{y},l_{s},l_{ss}\) mean the length shown in the figure.