# Path Planning of Obstacle-Crossing Robot Based on Golden Sine Grey Wolf Optimizer
## 6 Conclusions and Future Work  
In order to solve the problems of a single initial population, slow convergence speed in the later stage and the ease with which it falls into the local optimum when the GWO is used in the path planning of an obstacle-surmounting robot, an improved GWO with the golden sine strategy is proposed. The piecewise chaotic sequence, nonlinear convergence factor and golden sine strategy are introduced to improve the performance of the GWO, and the path-planning problem of the obstacle-crossing robot is adapted by improving the working environment, path generation mode and fitness function. According to the results of the simulation experiment, the comparison diagram shown in Figure 9 can be calculated. It can be seen that compared with the GWO, the path length planned by the GSGWO in \(20\times 20\), \(30\times 30\) and \(40\times 40\) maps is optimized by 3.45%, 11.2% and 15.6%, respectively, the number of inflection points is optimized by 28.57%, 22.22% and 57.14%, respectively, and the path cost is optimized by 32.5%, 40.32% and 54.69%, respectively. Although the randomness of the map environment has a certain influence on judging the change rule of the data, the overall optimization rate increases with the increase in the complexity of the map. At the same time, the rotation angle of the path planned by the GSGWO and the stability of the algorithm are also optimized to a certain extent. The feasibility of the path-planning field of the GSGWO obstacle-crossing robot is proved. According to the content described above, some characteristics of the algorithm can be summarized: (1) The GSGWO is improved on the basis of the GWO and can be used to solve single-objective optimization problems. (2) Because the GSGWO adopts the golden sine strategy for secondary convergence, it has a larger amount of calculation and higher requirements for equipment than the GWO when the parameters are the same. (3) The appropriate interval of the weight coefficients \(\lambda\) and \(\mu\) in Equation (15) will change due to the different performance of the map and the obstacle-surmounting robot, so the GSGWO is suitable for robots that often perform tasks within a fixed range. For the subsequent improvement and application expansion of the GSGWO, the following ideas are proposed: (1) Adaptive adjustment of \(\lambda\) and \(\mu\). The preliminary idea is to extract map features such as map size, number of obstacles, average obstacle size and starting and ending positions. The mathematical relationship between these features and \(\lambda\) and \(\mu\) is \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Map Size** & **Performance** & **GWO** & **TGWO** & **IGWO** & **GSGWO** \\ \hline \multirow{3}{*}{\(20\times 20\)} & average & 34.77 & 33.06 & 31.21 & 31.21 \\  & standard deviation & 3.10 & 2.31 & 0.27 & 0.13 \\  & average & 84.94 & 58.34 & 51.87 & 49.77 \\  & standard deviation & 14.94 & 5.49 & 1.01 & 1.05 \\  & average & 154.28 & 82.18 & 67.65 & 61.74 \\  & standard deviation & 25.51 & 9.71 & 3.23 & 2.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Stability test results. Figure 8: Stability change trend: (**a**) change trend of average; (**b**) change trend of standard deviation. analyzed through experiments. Finally, the values of \(\lambda\) and \(\mu\) are calculated by establishing a mathematical equation between the features and \(\lambda\) and \(\mu\). If the adaptive adjustment of \(\lambda\) and \(\mu\) can be achieved, the GSGWO will be able to process new maps through a small map processing program, and robots equipped with the GSGWO will be able to perform tasks in areas that have never been explored. (2) Enrich the types of obstacle-surmountable passage areas. In the actual scene, there are many kinds of obstacle-crossing robots that can cross obstacles, and the ways and costs of obstacle-crossing are not the same.