# Path Planning Based on Artificial Potential Field with an Enhanced Virtual Hill Algorithm
## 6 Conclusions  
The virtual hill technique, which moves along a nearby obstacle when a robot is trapped in an LM, is easy to apply to an unknown variable environment. The virtual hill technique does not require information about space and obstacles, does not create a new the LM even in a complicated environment, and has the advantage of being easy to apply. However, there is a problem in that the mileage can vary greatly depending on which directional obstacle the robot moves along. In this study, the performance of the virtual hill technique is improved by compensating for this shortcoming using _new_\(\mathbf{e}_{b}\) and the dead-end algorithm. The enhanced virtual hill algorithm makes it possible for a robot to reach its goal on a shorter path. Also, when a robot encounters blocked roads, it can come back without entering through the dead-end algorithm.  
In future research, when the robot is trapped in the LM and extra potential is generated, it can be programmed to check in advance whether there is a dead end nearby and exclude that direction. In cases like Figure 20, it is necessary to recognize in advance that if the robot moves in the \((+)\) direction, it will lead to a dead end. In order to recognize dead  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Mileage Using** & **Mileage Using** & \multirow{2}{*}{**Reduction Proportion**} & **Reduction Proportion** \\  & _Previous_\(\mathbf{e}_{b}\) **[m]** & & **_New_\(\mathbf{e}_{b}\) **[m]** & **Dead-End** & **Using** _New_\(\mathbf{e}_{b}\) **[\%]** & **Using Dead-End** \\ \hline Figure 9 & 44.26 & 13.82 & - & 68.78 & - \\ Figure 12 & 16.51 & 11 & - & 33.37 & - \\ Figure 13 & 41.08 & 12.9 & - & 68.60 & - \\ Figure 14 & 36.66 & 12.87 & 14.96 & 64.89 & 40.81 \\ Figure 15 & 35.95 & 15.98 & 14.23 & 55.55 & 39.58 \\ Figure 16 & 25.6 & 17.33 & 6.58 & 32.30 & 25.70 \\ Figure 17 & 33.66 & 19.02 & 14.83 & 43.49 & 44.06 \\ Figure 18 & 32.87 & 20.17 & 3.88 & 38.64 & 11.80 \\ Figure 19 & 26.12 & 16.61 & 6.64 & 36.41 & 25.42 \\ Figure 20 & 29.41 & 30.91 & - & \(-5.10\) & - \\ \hline Average [\%] & - & - & - & 43.69 & 31.23 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Reduction in mileage according to algorithms.  
ends from a long distance, the sensor's obstacle measurement distance must be longer, and more sensor data must be processed for accuracy. It is unnecessary to process this much data in each control cycle. A method is needed to obtain detailed information about distant obstacles only when needed. To verify the proposed algorithm, additional simulations and experiments in diverse and dynamic environments are required. It is also necessary to establish indicators to quantitatively evaluate the stability and flexibility of robot driving. Through these, it is expected that the performance and limitations of the proposed algorithm will be analyzed, and shortcomings can be resolved in various conditions where static/dynamic obstacles exist in combination.  
Conceptualization, H.J.L. and M.C.L.; methodology, H.J.L.; software, H.J.L.; validation, H.J.L., M.-S.K. and M.C.L.; formal analysis, H.J.L.; investigation, H.J.L.; resources, H.J.L.; data curation, M.-S.K.; writing--original draft preparation, H.J.L.; writing--review and editing, M.-S.K. and M.C.L.; visualization, H.J.L.; supervision, M.C.L.; project administration, M.-S.K.; funding acquisition, M.-S.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Development of High-Level Cognitive Prediction Sensor Technology for Autonomous Driving Mobility (RS-2022-00144500, Development of 3D Ultrasonic Sensor Technology for Vehicles based on Meta Structure) funded by the Ministry of Trade Industry & Energy (MOTIE, Republic of Korea).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.  
The authors declare no conflicts of interest.