# Research on Decision-Making Methods for Autonomous Navigation in Inland Tribitary Waterways
## 3 Methodology
### Collision Risk Model Based on Ship Trajectory Projection
Within this demarcated area, tributary vessels are presumed to complete steering maneuvers before mainstream entry, maintaining a constant _ROT_ throughout the transitional phase. The navigational status of the TS upon mainstream ingress is determined by its kinematic state at the transitional boundary, as shown in Figure 10.  
The collision avoidance model for the TS within the transitional zone (shaded in Figure 10) operates under dual constraints: (1) conflict resolution is achieved solely through course alteration, and (2) steering maneuvers occur at a fixed _ROT_. The _ROT_ is derived computationally through analysis of course variations between successive time intervals \(C_{TS}(t)\) and \(C_{TS}(t+\Delta t)\), as formalized in Equation (15). Subsequent trajectory prediction integrates angular displacement calculations to determine the TS's velocity vector and positional coordinates at future timestamps via Equations (16) and (17). This methodology ensures kinematic continuity between transitional steering maneuvers and post-entry navigation states, enabling accurate collision risk identification while adhering to inland vessel navigation practices. \[ROT(t)=(C_{TS}(t+\Delta t)-C_{TS}(t))/\Delta t \tag{15}\]  
\[ \begin{cases}V\prime_{TS}^{x}(t)=V_{TS}(t)\cdot(\cos{(C_{TS})}+ROT(t)\cdot \Delta t)\\ V\prime_{TS}^{y}(t)=V_{TS}(t)\cdot(\sin{(C_{TS})}+ROT(t)\cdot\Delta t)\end{cases}  \tag{16}\]  
\[P_{TS}(t+\Delta t)=P_{TS}(t)+ \begin{bmatrix}V\prime_{TS}^{x}(t)\\ V\prime_{TS}^{y}(t)\end{bmatrix} \cdot\Delta t \tag{17}\]  
A conflict is characterized as a scenario with a high likelihood of collision, representing a near-collision situation. This conflict can be quantified by assessing whether the projected trajectory of one ship intrudes upon a predefined restricted area surrounding another ship. Figure 10: Derivation of trajectories in inland tributary waterways. Figure 9: Trajectory of a ship pair involved in a conflict. An elliptical ship domain is employed to delineate this restricted area based on the Fujii model. The major axis of the elliptical domain is defined as four times the ship's length, while the minor axis is 1.6 times the ship's length. Consequently, a conflict is identified by evaluating whether a ship, maintaining its current course and speed, is projected to encroach upon the elliptical domain of another ship. The risk of collision is assessed by analyzing the projected trajectories of the OS and TSs. The presence of potential collision risks is indicated if the TSs are predicted to intrude into the OS's ship domain within a future timeframe \(T\). First of all, judge the navigation situation of the OS: when the OS is located outside the channel, such as the OS\({}_{3}\) in Figure 11, the position of OS can be projected according to the MMG model of the OS and the current movement state. If the OS is sailing within the channel, the ship's navigation is constrained by the channel and cannot sail out of the channel, which usually includes two cases. If the OS is sailing along the channel, i.e., when \(|\,C_{OS}-C_{channel}\,|\,\leq\,5^{\circ}\), such as OS\({}_{1}\), under this premise, it can be assumed that the OS will change course to continue along the direction of the next section of the channel after reaching the channel turning point. If the OS's course is at a certain angle to the channel, such as OS\({}_{2}\), it is estimated that the OS will sail out of the channel boundary according to the current course. Therefore, when the projected ship's trajectory is close to the channel boundary, the OS should steer in the same direction as the channel boundary \(C_{channel}\), to ensure that the OS continues to sail along the channel boundary and will not sail out of the channel. Based on navigation practices, a 3-nautical-mile radius surrounding the OS is established as the alert zone.