## 7 Results and Future Work  
Table 5 shows the comparison in particle swarm size, number of iterations, convergence time, end effector space degrees of freedom, joint space degrees of freedom and accuracy between our PSO algorithm and those of references [3; 12].  
Several algorithms have been created for the issue of inverse kinematics, and each one has been fine for its particular need. As a result, it is challenging to undertake a qualitative comparison that considers all performance factors. In addition, few cited studies specify the execution time. Table 5 contrasts our technique with other strategies used by researchers to solve inverse kinematics among those who had included execution time. [PERSON] [3] solely concentrates on converging position values, as shown in Table 5, and finds that after 500 iterations with 0.1 mm accuracy, the average execution time varies between 230 and 930 milliseconds depending on the optimization technique. [PERSON] [3] claims that PSO is the second-worst optimization in terms of time for tackling only 3-dimensional objectives (Px, Py, Pz). On the other hand, our method using the POSIX thread with full (Position, Orientation) convergence only requires 18-40 milliseconds with a precision of less than 0.1 mm. The number of iterations is irrelevant because our approach is based on independent particles.  
Figure 11: Particles arriving at solution (close\(-\)up).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Paper** & **Particle/Iteration** & **Time (ms)** & **Algorithm** & **Dimension** & **Accuracy (mm\(\,\)I\(\,\)RD)** \\ \hline [PERSON] [3] & 300/500 & 449.8 & PSO & [Position] & \(67.1\times 10^{-3}\) \\ \hline [PERSON] [3] & 100/500 & 444.1 & ABC & [Position] & \(54.7\times 10^{-4}\) \\ \hline [PERSON] [3] & 50/500 & 920.4 & Firefly & [Position] & \(65.0\times 10^{-5}\) \\ \hline [PERSON] [3] & 150/500 & 231.9 & QPSO & [Position] & \(27.7\times 10^{-17}\) \\ \hline [PERSON] [12] & NA & 22 & HGSA & [Position, Orientation] & 1.00 \\ \hline [PERSON] [12] & NA & 30–600 & PSO & [Position] & 1.00 \\ \hline [PERSON] [12] & NA & 50–500 & GA & [Position] & 1.00 \\ \hline Our Algorithm & 20/NA & 18–40 & PSO & [Position, Orientation] & \textless{}0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of our algorithm with other swarm intelligence methods.  
Nonetheless, it may be possible to calculate the average number of updates made by each particle. Hence, even in the search for 7-dimensional space [Px, Py, Pz, q0, q1, q2, q3], Table 4 and the comparison Table 5 demonstrate that the performance of our algorithm is faster and could establish more calculations in a shorter amount of time. [PERSON] [12] suggests that a heuristic hybridization of GA and PSO can achieve much more efficiency than the individual methods and still be a general and all-encompassing strategy for resolving the inverse kinematics problem. [PERSON] [11] believes his method is practical for various real-time applications. Our POSIX threads implementation demonstrated faster computation times with more accuracy using one technique. The originality of our algorithm, which is moving the particles independently without waiting for the previous particle, increased the algorithm's performance and decreased the computation time.  
Nevertheless, combining [PERSON]'s [11] approach and our method may improve efficiency, robustness and reliability. Since the I9 processor only has 20 cores, testing could only be done with 20 threads. Since our approach applies to a limitless number of threads, theoretically, the speed of convergence for our approach is only limited by the number of available computer processors that can run in parallel. Our future work will be to continue testing our algorithm with better computing equipment that is accessible to us.