# Research on Decision-Making Methods for Autonomous Navigation in Inland Tribitary Waterways
## 3 Methodology
### Collision Avoidance Decision-Making Model  
In open waters, collision avoidance typically relies on steering maneuvers, and conventional VO methods calculate collision-inducing velocity vectors through relative motion analysis under stable course assumptions. This approach becomes inadequate in confined inland waterways due to the mandatory dynamic heading adjustments required by channel curvature, as the VO framework inherently neglects nonlinear maneuvering dynamics and time-dependent steering processes. To resolve this limitation, a ship motion model integrating a control methodology is developed to simulate inland navigation-compliant collision avoidance strategies. By analytically deriving motion vector evolution under different maneuvering protocols and coupling these with ship domain constraints, the proposed framework enables the quantitative assessment of target vessel intrusion into navigational safety boundaries. This establishes a functional mapping between the maneuvering decision protocols and collision avoidance effectiveness in the inland waterway environment. In Figure 14, the TS is the ship crossing the channel, and the initial course and position of the OS are \(V_{OS}\) and \(P_{OS}\). Considering the nonlinear maneuvering process of the OS, the TS will arrive at \(P_{TS}^{1}\) when the OS turns to starboard to \(V_{OS}^{1}\) and arrives at \(P_{OS}^{1}\), and the TS will arrive at \(P_{TS}^{2}\) when the OS turns to portside to \(V_{OS}^{2}\) and arrives at \(P_{OS}^{2}\). The TS is just outside the ship domain of the OS for safety under the two maneuvering scenarios. Therefore, the maneuvering range [\(V_{OS}^{2}\), \(V_{OS}^{1}\)] is the motion vector that indicates that the OS cannot avoid the TS safely, and the OS can avoid the TS safely when the maneuvering angle \(\theta>V_{OS}^{1}-V_{OS}\) or \(\theta<V_{OS}^{2}-V_{OS}\). In restricted inland waterways, collision avoidance may not be reliably achieved through heading adjustments alone due to operational constraints in narrow channels necessitating coordinated maneuvers that integrate course alterations with deceleration. Define \(f(V)\) to denote the ship motion vector, including course and speed changes. The position \(P_{OS}(t)\) and \(P_{TS}(t)\) of the OS and TS at the moment \(t\) are [\(X_{OS}(t)\), \(Y_{OS}(t)\)] and [\(X_{TS}(t)\) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Flow Direction** & **OS** & **TS** & **Encounter Situation** \\ \hline \multirow{4}{*}{2} & \multirow{4}{*}{2} & 1 & 1 & OS gives way to TS \\ \cline{2-4}  & & 2 & 2 & OS gives way to TS \\ \cline{2-4}  & & 1 & 2 & OS gives way to TS \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{1} & 1 & OS gives way to TS \\ \cline{2-4}  & & 2 & OS gives way to TS \\ \cline{2-4}  & & 2 & OS gives way to TS \\ \cline{2-4}  & & 1 & 2 & TS gives way to OS \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Avoidance relationships in tributary waterways. Figure 13: Classification of encounter situations in tributary waterways. \(Y_{TS}(t)\)], respectively. When the OS's motion vector changes, the OS's position after the moment \(t\) can be projected based on the ship motion model, which is expressed as  
\[P_{OS}(t)=\{f(V)\cdot t\} \tag{18}\]  
_domain_(\(P_{OS}(t)\)) denotes the ship domain space centered on the OS, and the safety space constituted during the OS's movement is expressed by the following equation:  
\[domain=\left\{\sum_{0}^{t}domain(f(V)\cdot t)|t\geq 0\right\} \tag{19}\]  
The trajectory of the TS is represented as  
\[P_{TS}=\left\{\sum_{0}^{t}P_{TS}(t)|t\geq 0\right\} \tag{20}\]  
Therefore, the motion vector of the OS that can safely avoid the TS can be expressed as  
\[f(safe\_V)=\left\{\sum_{t=0}^{T}domain(f(V)\cdot t)\cap\sum_{t=0}^{T}P_{TS}( t)=\emptyset|f(V)\right\} \tag{21}\]  
In multi-ship encounter scenarios, the collision avoidance obligations of the OS become inherently complex due to the necessity of coordinating interactions and decision-making among multiple vessels.