# Path Planning for Yarn Changing Robots Based on NRBO and Dynamic Obstacle Avoidance Strategy
## 5 Conclusions  
To address the limitations of the NRBO algorithm in local dynamic obstacle avoidance, this paper presents a novel fusion algorithm known as NRBO-DWA. This approach leverages key nodes in the global path as local target points for the DWA algorithm. A path correction strategy has been implemented to mitigate potential detours. Simulations using standard test functions demonstrate that the NRBO-DWA algorithm outperforms three other comparative algorithms in terms of faster convergence and fewer iterations. Additionally, the NRBO-DWA algorithm is applied to path planning for a yarn-winding robot operating in a three-dimensional dynamic environment. In this context, the costs associated with path length and planning time are given greater weight in the objective function, while height restrictions are assigned less weight. Experimental results indicate that, in comparison to other widely used bio-inspired algorithms, the proposed algorithm successfully completes the path planning task in the shortest possible time while exhibiting strong dynamic obstacle avoidance capabilities.  
Conceptualization, W.S.; methodology, Q.L.; software, Q.L.; validation, Q.L.; formal analysis, Q.L.; investigation, Q.L.; resources, W.S.; writing--original draft, Q.L.; writing--review and editing, L.S.; supervision, L.S.; project administration, W.S.; funding acquisition, W.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China, grant number 2017 YFB1304000.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **Average Path Length (mm)** & **Average Planning Time (s)** & **Optimal Function Value** & **Worst Function Value** & **Average Function Value** \\ \hline GA-DWA & 11,539.26 & 194.91 & 11.72 & 11.78 & 11.75 \\ PSO-DWA & 13,972.75 & 203.03 & 11.66 & 12.38 & 12.03 \\ SSA-DWA & 11,483.74 & 174.83 & 11.28 & 12.18 & 11.63 \\ NRBO-DWA & 9762.12 & 149.15 & 10.71 & 11.61 & 11.22 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental results comparison of different algorithms.  
Figure 10: Comparison of planning times for different algorithms.  
**Data Availability Statement:** The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.  
**Nomenclature**  
\begin{tabular}{l l l l} \(x_{0}\) & Initial point & \(T\) & Current iteration \\ \(\varepsilon_{n}\) & Solution location & \(MaxT\) & Maximum number of iterations \\ \(x_{n+1}\) & Next approximation & \(r_{1}\), \(r_{2}\) and \(r_{3}\) & Random numbers \\ \(lb\) and \(ub\) & Lower and upper bounds & \(\rho\) & Adaptive coefficient for improving exploitation \\ \(dim\) & Problem dimension & \(L_{n}^{T}\) & Current vector position \\ \(L_{j}\) & Decision vector & \(L1_{n}^{T}\) & New vector position by updating \(L_{n}^{T}\) \\ \(N_{p}\) & Population size & \(L2_{n}^{T}\) & New vector position by updating \\ \(L_{n}\) & Population matrix & \(L3_{n}^{T}\) & New vector position by updating \\ \(L_{w}\) and \(L_{b}\) & Worst and best population position & \(\beta\) & Binary number, either 1 or 0 \\ \(\delta\) & Adaptive coefficient for balancing exploration & \(\theta_{1}\) and \(\theta_{2}\) & Uniform random numbers between (\(-\)1,1) and (\(-\)0.5,0.5) \\  & and exploitation & & \\ \end{tabular}