## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**DE**} & \multicolumn{8}{c}{**Linear Contour**} & \multicolumn{8}{c}{**Non-Linear Contour**} \\ \cline{2-13}  & **Fitness** & \multirow{2}{*}{**Fitness**} & \multirow{2}{*}{**Function**} & \multirow{2}{*}{**\(\epsilon_{c}\)**} & \multirow{2}{*}{**T\({}_{\text{m1}}\)**} & \multirow{2}{*}{**T\({}_{\text{m2}}\)**} & \multirow{2}{*}{**T\({}_{\text{m3}}\)**} & \multirow{2}{*}{**T\({}_{\text{m4}}\)**} & \multirow{2}{*}{**T\({}_{\text{m5}}\)**} & \multirow{2}{*}{**T\({}_{\text{m6}}\)**} & \multirow{2}{*}{**\(\epsilon_{c}\)**} & \multirow{2}{*}{**T\({}_{\text{m1}}\)**} & \multirow{2}{*}{**T\({}_{\text{m2}}\)**} & \multirow{2}{*}{**T\({}_{\text{m3}}\)**} & \multirow{2}{*}{**T\({}_{\text{m4}}\)**} & \multirow{2}{*}{**T\({}_{\text{m5}}\)**} & \multirow{2}{*}{**T\({}_{\text{m6}}\)**} \\ \hline \multirow{4}{*}{**Algorithm**} & ISE & \(3.72\times 10^{-6}\) & 0.94 & 0.73 & 0.63 & 0.7 & 0.9 & 0.56 & \(2.32\times 10^{6}\) & 5.56 & 1.43 & 0.79 & 1.3 & 5.4 & 0.7 \\  & IAE & \(8.18\times 10^{-6}\) & 0.56 & 0.78 & 0.78 & 0.7 & 0.5 & \(0.7\) & \(3.23\times 10^{-6}\) & 5.53 & 1.74 & 1.33 & 1.6 & 4.5 & 0.9 \\  & MSDAE & \(4.87\times 10^{-6}\) & 9.46 & 0.73 & 0.6 & 0.67 & 0.8 & 0.5 & \(1.29\times 10^{-6}\) & 5.43 & 1.30 & 0.84 & 1.0 & 0.37 & 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean torques and contour errors. Figure 6: Contour performance of linear tracking. Figure 7: Contour performance of non-linear tracking. Finally, the effect of position domain control on Joints 2 and 3 needs to be explored. The reason of choosing these two joints is that they have big variations in joint angle compared to other joints. Tests were conducted using two configurations. The first configuration assumed for joints angles is represented by \([-80,\,-45,\,-55,\,-80,\,260,\,-94]\) and the second configuration is represented by \([35,\,-105,\,-75,\,90,\,-125,\,110]\). Figure 8(a),b shows the step response to the first and second robot configurations for Joint 2 where PID refers to the design controller and dif. refers to the difference in joint angle between the optimum angle and the angle produced using the PID controller. Figure 9(a),b show the step response to the first and second robot configurations for Joint 3. The second section of the result is to improve the APF by DE algorithm to obtain the contour tracking with obstacle avoidance. In the step response of the PDC-PID controller, there was no overshoot in contrast to other types of controllers. This is true only in linear contour tracking, while there was no overshoot observed in both linear and non-linear contour tracking when the DE algorithm is applied to improve the performance of PDC-PID. This result shows the advantage of using DE optimization algorithm in linear and non-linear contour tracking. Figure 8: Mean torques required in linear and non-linear tracking. Figure 9: Step response of the UR5 robot for the two configurations of Joint 2. APF parameters are often adopted empirically which makes the process expensive but with the application of DE algorithms, an improvement in the performance of the APF algorithm is achieved due to the generation of collision-free trajectories. APF-DE simulations were presented for a population of 30 individuals with 50 iterations. The APF algorithm with DE trajectory showed the smoothest trajectory. It was also possible to verify the average position error between the last required position of the path generated by the APF-DE and the final position. In terms of computational cost, the DE algorithm showed shorter execution time for the calculation of the parameters of APF algorithm. Advantages of these simulations can be attributed to the improvement of the APF algorithm, because the parameters are now being generated in optimized way and the precision of the points of the trajectories reached. Figure 11 shows the effect of DE algorithm for 30 individuals and 50 generations where the best individual and the population average are also given.