# Comparison Study of the PSO and SBPSO on Universal Robot Trajectory Planning
## 2 Materials and Methods
### Serendipity-Based Particle Swarm Optimization
For the Rosenbrock function, the stagnation delay was at least 30% of the number of iterations compared to the traditional PSO. To the Griewank function, the SBPSO slowed the stagnation by less 20% when compared to the traditional PSO. For the Rastrigin function, stagnation was delayed at least 34% compared to the traditional PSO. In the HappyCat function, when the SBPSO was compared to the traditional PSO, there was a delay at less than 20% of the maximum iterations number. Finally, in the Ackley function, the SBPSO delayed the stagnation at least 20%, in relation to the traditional PSO algorithm. In these experiments, the SBPSO algorithm gave a better convergence behavior, overcoming some variations in relation to the quality of the solution, such as ability to find the global optimum, the stability of solutions and the ability to restart the swarm movement in stagnation case. In general, the results proved to solve the optimization problem of universal robot UR5 trajectory planning and find the optimal path. In future work, we will apply the SBPSO algorithm to solve more real-world optimization problems, such as vehicle localization, wireless sensor networks, and velocity estimation. Formal analysis, I.J.K. ; investigation, I.J.K. ; methodology, I.J.K. ; supervision Y.T. and R.L. ; writing--original draft, I.J.K., Y.T., and R.L. ; writing--review, I.J.K. All authors have read and agreed to the published version of the manuscript. This work was supported by the Open Research Foundation of Advanced Innovation Center for Intelligent Robotics and Systems under Grant Number 2019 IRS18, and the Fundamental Research Funds for the Central Universities of China under Grant Number 2021 IVA019. Thanks to my mother, my husband ([PERSON]), my family, prof. [PERSON], [PERSON]. Almustafa university college and the reviewers and proof reader for this paper. The authors declare no conflict of interest. ## References

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