## 6 Performance Evaluation on Simulator
### Performance of Path Planning  
#### 6.3.1 Path Accuracy Performance Measure  
The MGPF-Hybrid A* algorithm is evaluated compared with A* in an environment of straight roads, straight roads with obstacles, and curved roads with obstacles. In this performance evaluation, an autonomous driving system is not applied. This measure simply evaluates the performance of the algorithm itself considering the obstacles without considering of the path-following performance. Moreover, since the input environment toward the proposed algorithm is the same as the output of the autonomous driving system, this evaluation is meaningful. The created path from the proposed MGPF-Hybrid A* is shown in Figure 12. Moreover, all the scenarios are shown in Figure 12, separated as cases 1, 2, and 3. The results of local path planning for each of the algorithms are drawn in the figures as green lines. Case 1 in Figure 12 denotes a similar performance for the generated local path between A* and MGPF-Hybrid A*. However, there are performance gaps for path generating, as shown in case 2 of Figure 12. MGPF-Hybrid A* has a better performance for following reference path points. A* unnecessarily changed the following path quickly. On the other hand, the MGPF-Hybrid A* performs a suitable collision-free operation. The ability to follow multiple goals is evident, as shown in case 3 of Figure 12. A* does not consider the multiple goals. Therefore, on curved roads, A* disregards the reference path points. This could cause lane penetration when an autonomous vehicle is operated on a real road. On the other hand, the MGPF-Hybrid A* successfully follows multiple goals. In addition, since MGPF-Hybrid A* considers the vehicle steering model, the generated route is smoother than A*. The parameters of the MGPF-Hybrid used are, \(n=3,k_{1}=0.5,k_{2}=0.3,k_{3}=1.0e+10\). How to determine these parameters is introduced in the following sections.  
Figure 11: Process flow of the vehicle longitudinal controller.  
Figure 12: Performance evaluation of A* and MGPF-Hybrid A*. The generated paths are drawn on a grid map.  
The numerical evaluation of Figure 12 is shown in Table 1. The table denotes the error consisting of the distance gap between the generated path and the reference path by using the root mean square (RMS). The errors were calculated every 1-m interval. In case 1 which set as a straight path, the RMS of the A* algorithm was better than the proposed algorithm. However, the value does not make much of a difference for the autonomous driving environment. In cases 2 and 3, where obstacles and curve situations are considered, the proposed algorithm significantly outperforms the A* algorithm in regards to RMS values.  
Except for the RMS values, the shortest path distance and the farthest path distance from the reference path were evaluated; the unit was meters. In Table 1, each of these are denoted as D-Min and D-Max. In all situations, in cases 1, 2, and 3, the D-Min values are lower than 10 cm. This means that the algorithms, A* and MGPF-Hybrid A*, successfully converged on the reference path. The D-Max values of A* and MGPF-Hybrid A* in cases 1 and 2 were also similar, while the values in case 3 showed that the value of MGPF-Hybrid A* was lower than that of regular A*.  
As a result of this evaluation, the proposed MGPF-Hybrid A* converged successfully on the reference path and it showed superior performance regarding multiple obstacles and curved road environments compared to the regular A* algorithm.