## 4 Discussion  
The optimization of a 3-DOF parallel robotic system for laparoscopic pancreatic surgery, using an integrated genetic algorithm and fuzzy logic approach, has demonstrated significant potential in addressing critical challenges inherent in surgical robotics. This study illustrates the distinct advantages of leveraging fuzzy logic to optimize the design parameters of a robotic system, effectively handling uncertainties and complexities associated with minimally invasive surgical procedures. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optimization Target** & **Evaluated Parameter** & **Before Optimization** & **After Optimization** & **Result** \\ \hline \multirow{2}{*}{RCM} & Reachability & 5241/6951 points & 6906/6951 points & +23.96\% \\  & Workspace & 9,366,060.48 mm\({}^{3}\) & 12,226,455.35 mm\({}^{3}\) & +30.54\% \\ \hline \multirow{2}{*}{Links} & Reachability & 6142/6951 points & 6899/6951 points & +10.89\% \\  & Workspace & 8,224,547.69 mm\({}^{3}\) & 9,240,279.33 mm\({}^{3}\) & +12.35\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of optimized and unoptimized parameters. Initially, the robotic design optimization started from an unoptimized Remote Center of Motion (RCM) point located at coordinates [100, 0, 300]. Using the genetic algorithm coupled with fuzzy logic evaluation, the system determined an optimized position for the RCM at coordinates [119.003337, \(-\)146.610801, 269.07376]. This new location was identified to ensure superior workspace coverage and enhanced manoeuvrability of the surgical instrument, addressing recorded points obtained from manual manipulation of the surgical instrument during preliminary tests. Fuzzy logic's incorporation into the optimization framework provided a notable advantage over traditional deterministic methods. By employing fuzzy membership functions, the approach successfully captured the inherent uncertainties of surgical environments, converting these uncertainties into quantifiable measures to guide optimization. This flexibility enabled the optimization framework to incorporate linguistic and heuristic knowledge, significantly enhancing the robot's performance concerning critical surgical factors such as workspace accessibility, instrument manoeuvrability, and surgeon ergonomics. The optimized design demonstrated substantial improvements in key performance metrics, particularly in robot workspace accessibility and instrument insertion precision. The genetic algorithm determined optimal lengths for critical robotic links: specifically, 213.5455 mm for link a\({}_{1}\), 248.48918 mm for link a\({}_{3}\), and 48.5886 mm for link a\({}_{2}\)min. These values were practically adjusted to 215 mm, 250 mm, and 50 mm, respectively, to facilitate mechanical implementation. By converting geometric parameters into fuzzy membership functions and aggregating them into a coherent suitability score, the robot's configurations were optimized to maximize operational effectiveness. Simulation results underscored that the optimized robotic system exhibited superior capabilities in navigating narrow anatomical pathways critical for pancreatic surgery. This was evidenced by the improved reachability ratio and increased convex hull volume, both of which directly translate to enhanced manoeuvrability and surgical precision. While this study uses a genetic algorithm based on fuzzy logic exclusively for offline preoperative optimization of the design parameters of the robot, future clinical implementation requires that the robotic system meet real-time performance standards during the surgery. In order to achieve this requirement, several strategic improvements can be systematically integrated into the robotic control architecture. Development of a fuzzy inference system for the control logic of the robot constitutes an effective approach.