## 6 Discussion  
This study further supports our approach to real-time detection and elimination of the slave robot's position errors during catheterization. We demonstrated that the control approach has the potential to create steady master-slave motion and contribute to procedural safety during R-PCI procedures. In addition, a comparative analysis of existing control approaches for master-slave position tracking shows that the neural-based controllers have a much lower maximum error compared with MLP-PID, ADRC, and FSMC for in-RCS experiments, as indicated in Table 3. Although, RL-PID has the best performance, the control method was only verified with simulation experiments. Overall, we have presented a data-driven control approach for master-slave position tracking, which leverages on neural network capability for robust features learning and representation from training examples, thus yielding a higher precision, accuracy, and lower percentage error. Although single-board computers facilitate easy mobility of the robotic device, we experienced hardware limitations deploying RNN models within Raspberry PI for real-time error predictions. This study suggests the need for more powerful single-board computers. The recent launch of Jetson AGX Orin seems timely; however, large-scale validation is still needed. In addition, machine-learning methods using int  
Figure 16: The master-slave position trajectory for a distance of 120 mm under varying input commands with the GRU model prediction and error compensation within the slave robot. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Authors** & **Control Method** & **Experiment Type** & **Max. Error (mm)** \\ \hline [PERSON] et al. [24] & MLP-PID & Simulation/in-RCS & 1.50 \\ [PERSON] et al. [10] & RL-PID & Simulation & 0.003 \\ [PERSON] et al. [40] & ADRC & RCS & 0.87 \\ [PERSON] et al. [28] & FSMC & Simulation & 0.65 \\ This study & LSTM/GRU & Simulation/in-RCS & 0.04 \\ \hline \hline \end{tabular} Note MLP-PID—multi-layer perceptron-based PID controller; RL-PID—reinforcement learning-based PID controller; ADRC—active disturbance rejection control; FSMC—fuzzy sliding mode controller.  
\end{table} 
Table 3: Performance evaluation of the proposed method with existing studies. reinforcement learning would be operable within the RCS for state-based navigation or task-specific autonomous control. Furthermore, adding reliable proximal and distal force navigation data would enable learning the master-slave robot kinematics as well as tool dynamics within the vasculature, which could lead to the development of a robust model with the potential realization of closed-loop control during R-PCI. At present, acquiring operator-based motion data is time-consuming and laborious. This is because fewer displacement steps are covered within a full stroke under varying motion (Figure 7A-C) compared with uniform translational motion (Figure 9a-c). However, such data contain a higher degree of nonlinearities, thus are closer to real-world characterization of the slave robot's position error. While intraluminal navigation safety is at the top of patients' safety concerns during minimally invasive procedures, recent investigations show potential for task-specific autonomy for tool navigation during R-PCIs. In this study, we described the development of a custom-built master-slave RCS to navigate endovascular tools. We further analyzed the causative factors for position errors at the slave side of the robotic system using the displacement values at both master and slave sides, their velocity, and backlash gaps. Thus, we proposed and validated using learning-based control models for online error compensation in the RCS. The RNN models were trained with master-slave forward motion profiles recorded from the RCS. Furthermore, this study focused on the characterization and control of translational motion in the RCS. However, a hybrid of translational and rotary motion is essential for semi-autonomous navigation. To achieve this, high-resolution rotary encoders would be essential.