# Path Planning Based on Obstacle-Dependent Gaussian Model Predictive Control for Autonomous Driving
## 5 Discussion and Conclusions  
This paper proposed an optimal control path plan that enables safe driving and comfort, while ensuring low computational operation for autonomous driving by integrating the ODG and MPC. The ODG algorithm expresses the surrounding environment as a risk-based path using the information on lanes and the obstacle mobile robot. Optimal control is performed using QP to control the desired target direction under the constraints defined through the expressed information and vehicle modeling. The proposed method provides risk information in the form of ODG to the cost function of MPC to quickly respond to obstacle avoidance control by controlling the vehicle in a direction with low obstacle risk. The proposed method has been tested on mobile robots under many overtaking scenarios, such as a static obstacle in front, a low-speed vehicle in front, and a low-speed vehicle in front with an oncoming vehicle from the rear. The proposed method showed superiority when compared with the existing algorithm about safety and comfortability. In the proposed method, the average of the shortest distance to an obstacle is larger than others, and the comfort level, which is directly related to safety, also shows a higher score than others. Experimental results show that the average safety metric is 72.34%, and the average processing time is approximately 14.2 ms/frame, which allows real-time computation. The experiment confirmed that the proposed method operates in the direction of a low-risk path in the space measured by the sensor and path planning is more stable with less computational cost than the comparison algorithms. As a result, the proposed algorithm safely and quickly performs path planning to avoid surrounding mobile robots. The data results using the ISO 2631-1 comfort level indicators confirmed that the proposed algorithm operates more comfortably. Especially in dynamic obstacles, the comfort score had been improved by more than 70% compared to PFMPC. The assumptions in this proposed method are limited to areas where the vehicle's motion model has similar linear and nonlinear results. We also evaluated the algorithms at low speed due to the limitations of the experimental environment, which leads to restrictions in applying the actual vehicle. In future works, we will focus on using reinforcement learning instead of optimal control, which may reduce the amount of computation. Furthermore, we plan to apply the proposed algorithm in an outdoor environment using an actual vehicle. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Distance (cm)** & \multicolumn{3}{c}{**Obstacle 1 (\(S_{1}\))**} & \multicolumn{3}{c}{**Obstacle 2 (\(S_{2}\))**} \\ \hline
**Experiment** & **ODG MPC** & **PF** & **PF MPC** & **ODG MPC** & **PF** & **PF MPC** \\ \hline No. 1 & 4.667 & 4.150 & 4.521 & 5.338 & 4.358 & 4.431 \\ \hline No. 2 & 3.575 & 3.492 & 3.129 & 4.068 & 2.530 & 4.039 \\ \hline No. 3 & 4.719 & 4.468 &  
**Author Contributions:** Conceptualization, D.-S.P. and M.-T.L. ; Data curation, G.-H.K. and D.-S.P. ; Formal analysis, D.-S.P., G.-H.K., and M.-T.L. ; Methodology, D.-S.P., G.-H.K., T.-K.K., and M.-T.L. ; Software, D.-S.P., G.-H.K., and T.-K.K. ; Validation, M.-T.L. and T.-K.K. ; Writing--original draft, D.-S.P. and G.-H.K. ; Writing--review & editing, M.-T.L. and T.-K.K. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Sciences and ICT (Grants No. NRF-2016R1D1A1B01016071 and NRF-2019R1A2C1089742). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest.