# Research on Decision-Making Methods for Autonomous Navigation in Inland Tribitary Waterways
## 3 Methodology
### Collision Risk Model Based on Ship Trajectory Projection  
In inland navigation scenarios where a ship's course aligns with the designated channel traffic flow, the ship is typically classified as a channel-following ship. Such vessels maintain their course along the channel axis until reaching predefined turning points,  
Figure 6: Deconstruction of inland waterway data. Figure 7: Digitization of inland tributary waterway environments. where directional adjustments are executed to align with subsequent channel segments. Conversely, TSs exhibiting substantial angular deviation from the channel direction or sailing outside channel boundaries may be categorized as non-channel-following vessels. For these special cases, TS position estimation can be performed through velocity vector projection analysis based on real-time kinematic data. According to the captain's experience, the maximum angle difference between the navigating ship and the channel in the inland waterway is about 5\({}^{\circ}\). This study accordingly adopts a threshold angular deviation of \(\theta=5^{\circ}\) as the criterion for channel-following status determination. The methodology employs continuous monitoring of the angular differential between a ship's course and the channel direction to classify TS navigation patterns, as formalized in Equation (12). \[orientation=\left\{ \begin{array}{ll}1,&C_{TS}-C_{channel}\leq\theta\\ -1,&\text{otherwise}\end{array} \right. \tag{12}\]  
where \(C_{TS}\) = the course of TS; \(C_{channel}\) = the direction of the channel where the TS is located. As shown in Figure 8, TS\({}_{1}\) is the ship sailing along the channel when TS\({}_{2}\) and TS\({}_{3}\) are both not. The corresponding trajectory projection method for the TS is shown in Equations (13) and (14). \[ \begin{bmatrix}x_{TS}(t)\\ y_{TS}(t)\end{bmatrix} = \begin{bmatrix}x_{TS}(0)\\ y_{TS}(0)\end{bmatrix} +v_{TS}\cdot \begin{bmatrix}\cos(C_{TS})\\ \sin(C_{TS})\end{bmatrix} \cdot t\ \ t\in(0,n)\ \ \text{if }orientation=-1\end{bmatrix} \tag{13}\]  
\[ \begin{cases}\begin{bmatrix}x_{TS}(t)\\ y_{TS}(t)\end{bmatrix}=\begin{bmatrix}x_{TS}(0)\\ y_{TS}(0)\end{bmatrix}+v_{TS}\cdot\begin{bmatrix}\cos(C_{TS})\\ \sin(C_{TS})\end{bmatrix}\cdot t\ \ t\in(0,T)\\ \begin{bmatrix}x_{TS}(t)\\ y_{TS}(t)\end{bmatrix}=\begin{bmatrix}x_{TS}(T)\\ y_{TS}(T)\end{bmatrix}+v_{TS}\cdot\begin{bmatrix}\cos(C_{channel})\\ \sin(C_{channel})\end{bmatrix}\cdot(t-T)\ \ t\in(T,n)\end{cases}  \tag{14}\]  
Current methodologies for modeling tributary egress maneuvers typically oversimplify TS kinematics through constant-velocity linear motion assumptions, as exemplified by the dead reckoning formulation in Equation (13). This conventional approach calculates projected position \(P_{TS}(t_{2}\,|\,t_{1})\) at time \(t_{2}\) using initial parameters \(P_{TS}(t_{1})\), \(C_{TS}\), \(v_{TS}\), but fundamentally misrepresents the curvilinear trajectory characteristics inherent to channel transition maneuvers. Such linear extrapolation proves particularly inadequate when modeling vessels transitioning from tributary to mainstream channels, where hydrodynamic constraints and navigational protocols necessitate deliberate course alterations. A paradigm shift emerges through the anticipatory integration of TS's channel transition intent, enabled by rate of turn (_ROT_) analysis. By monitoring angular displacement between sequential course measurements \(C_{TS}(t)\) and \(C_{TS}(t+\Delta t)\), this _ROT_-driven predictive framework reconstructs nonlinear motion patterns during tributary egress. The methodology not only enhances trajectory forecasting precision but also enables strategic differentiation between essential collision avoidance actions and superfluous maneuvers. To prevent overestimation of vessel steering angles (as exemplified by the projected position \(P^{\prime}_{TS}(t_{3})\) at time \(t_{3}\) in Figure 9), this study establishes a transitional zone at the  
Figure 8: Schematic diagram of the ship’s navigation posture. confluence of tributary and mainstream channels.