This section concentrates on examining the validity of the algorithm for risk detection in autonomous vehicles. This paper tries to discuss the emulation experiment from three perspectives, including experiment scene, experiment design, and experiment result.
5.3. Analysis on Result of Emulation Experiment
On the premise of not losing generality, this experiment should use the verification experiment shown in
Figure 8b. In the simulation experiment, in order to better observe the experiment, the obstacles in the figure are expanded without data deviation. Therefore, the following basic conditions are set: the length of the vehicle is 4 m, the width is 1.8 m, the maximum turning angle is 40 degrees, and the expansion reaction size of the obstacle is 0.9 m.
Figure 9 shows the map after swelling.
This paper assumes that the coordinates of the initial point are (1,1), and that the targeting point is at (499,499). Under this circumstance, this paper implements experiment and comparison by virtue of controlling variables.
The RRT algorithm is used for calculation. As shown in
Figure 10, in the simulation experiment, the path planning time is 54 s, and the number of extended nodes reaches more than 2000; the number of nodes in the return path is 252. The overall calculation efficiency is low, and the final path is not a more scientific and reasonable path.
- (1)
Path planning based on AV-RRT accords to the kinematical constraint condition.
From
Figure 11, it can be seen that when using the AV-RRT algorithm to pass through a curve with a turning angle of 40 degrees, the required path planning time is 44 s, and the number of expanded nodes is more than 1300, of which the maximum turning angle is 37 degrees, which means the result of path planning is ideal.
- (2)
Functional examination for AV-RRT algorithm
In
Figure 12 it can be seen that because the control of step size is based on principle of rapid growth, the number of summary points in the simulation experiment is 454, the number of nodes in the path is 122, the path planning time is 28 s, and the entire path planning time is reduced by nearly half, which proves that the dynamic step size of the algorithm is effective.
- (3)
Functional Examination of Algorithm Based on AV-RRT
Figure 13 shows the result of path planning based on the AV-RRT algorithm. During the experiment, it takes 48 s to carry out path planning, the number of extended nodes in the space is 965, the number of nodes in the return path is 132, and the length of path planned is 861 m. In particular, comparing with path planning based on RRT, a conclusion can be drawn that extended nodes in the space decreased by 63%, path nodes decreased by 49%, consumption of time decreased by 11%, and length of path decreased by 17%. Furthermore, the maximum steering angle is 39.87 degrees, which appears on the position of 11th node, that is to say, the result of path planning is ideal.
To sum up, the result of the functional examination is ideal, and this paper will be devoted to carrying out a performance examination in the following section.
From the above simulation results, we can see that the AV-RRT algorithm is significantly better than the RRT algorithm in terms of path planning time and dynamic step size. The number of expansion nodes in space is reduced by more than 60%, the time of path planning is reduced by about 50%, and the maximum turning radius also conforms to the vehicle’s kinematic constraints.
5.4. Analysis on Performance Examination Based on AV-RRT Algorithm
This paper defines the number of extended nodes, number of nodes of path planning, and time consumption of path planning as the key performance indexes.
In order to maintain the universality of the algorithm, this paper divides the experiment into three conditions, including a two-dimensional plane with sparse obstacles, a plane with moderate obstacles, and a plane with dense obstacles. The experiment is conducted 30 times, which paves the way for comparison. In addition, this paper selects the experiment scene randomly, and defines (0,0) and (499,499) as the initial point and final point, respectively, on the premise of having no influence on the result of the experiment.
- (1)
Comparison of Extended Nodes [
27] Based on AV-RRT and based on RRT
The difference between the two is shown in
Figure 14,
Figure 15 and
Figure 16. The blue represents the number of expansion nodes of the basic RRT algorithm, and the orange represents the number of expansion nodes of the AV-RRT algorithm.
From
Figure 14,
Figure 15,
Figure 16 and
Figure 17, it can be seen that in each scene, the performance is affected by random growth in the space time of extension, meaning that the number of extended nodes based on both the RRT and AV-RRT is bigger. However, the latter algorithm is more stable than the former, and the time of extension of extended nodes based on the AV-RRT is smaller compared to RRT, especially in the scene with sparse obstacles, which is caused by dynamic step size.
- (2)
Comparison of Path Nodes based on AV-RRT and based on RRT
From
Figure 18,
Figure 19,
Figure 20 and
Figure 21, it can be seen that in each scene, the number of path nodes based on AV-RRT is smaller than RRT, especially in the scene with sparse obstacles. This is caused by the dynamic step size.
- (3)
Comparison of Consumption of Time based on AV-RRT and based on RRT
From
Figure 22,
Figure 23,
Figure 24 and
Figure 25, it can be seen that in each scene, consumption of time for both the RRT algorithm and AV-RRT algorithm is greater. However, the latter algorithm is more stable than the former, and the consumption of time by the AV-RRT algorithm is shorter than RRT algorithm, especially in the scene with sparse obstacles, which is caused by the dynamic step size.
Based on the simulation experimental data in the above three scenarios, it is concluded that the AV-RRT algorithm has a higher performance than the basic RRT algorithm in terms of node expansion times in space, number of nodes included in the planned path, and path planning time consumption, and this advantage is more prominent in sparse obstacle scenarios.
In order to maintain the validity of experiment, this paper selects the initial point and targeting point randomly and divides the experiment into three conditions, including a two-dimensional plane with sparse obstacles, a plane with moderate obstacles, and a plane with dense obstacles, and implements the experiment 400 times, which paves the way for comparison.
Table 6 shows the result of experiment, including the AV-RRT algorithm, RRT algorithm [
28], and KB-RRT [
29] algorithm, which was used as a reference for comparison with other studies in the literature.
Generally speaking, although path planning based on AV-RRT accords to kinematical constraint condition and has better practical applicability, it weakens the capability of the path searching aspect of the algorithm and increases the execution time. In addition, according to the data in the table, owing to setting dynamic step size and area sampling, the performance indexes of the AV-RRT algorithm are better than the RRT algorithm. In the three scenes, times of extension for extended nodes based on the AV-RRT algorithm decreased by 30.35%, 31.69%, and 22.52%, respectively, and the total number decreased by 28.19%. Meanwhile, the number of path nodes based on the AV-RRT algorithm decreased by 61.56%, 40.63%, and 35.02%, respectively, and the total number decreased by 45.74%. Moreover, consumption of time based on the AV-RRT decreased by 39.56%, 38,64%, and 48.74%, respectively, and the total consumption of time decreased by 42.31%.
Compared with the KB-RRT algorithm, in sparse, moderate, and dense obstacle scenarios, the number of expansion nodes based on the AV-RRT algorithm is reduced by 22.80%, 35.91%, and 30.37%, respectively, and the total number of expansion nodes is reduced by 29.69%. Meanwhile, the number of path nodes based on the AV-RRT algorithm is reduced by 63.05%, 38.96%, and 33.13%, respectively, and the total number of path nodes is reduced by 45.05%. In addition, the time consumption based on AV-RRT was reduced by 16.74%, 14.53%, and 22.57%, respectively, and the total time consumption was reduced by 17.95%.
Compared with the RRT algorithm and KB-RRT algorithm, the AV-RRT algorithm has obvious performance advantages. No matter whether the obstacles are sparse, moderate, or dense, the number of expansion nodes decreases significantly, the dynamic step size has obvious advantages, and the path calculation time decreases significantly. The experimental results prove the effectiveness of AV-RRT algorithm and allow us to draw conclusions from the number of expansion nodes, dynamic step size, and path calculation time.
In order to facilitate analysis, this paper carries out an emulation experiment for the scene with moderate obstacles.
Figure 26 shows the result of path planning based on AV-RRT and the scene with moderate obstacles. Through detection based on NPCD [
30], it can be seen that a turning point (337.57,400.1046) in the figure does not pass the detection.
From
Figure 27, it can be seen that when the automobile turns from the path from point (332.7231,397.5523) to point (337.57,400.1046) to the path from point (337.57,400.1046) to (346.2173,398), due to driving outside safe cavity, the inside body of the automobile collides with the obstacle. In order to avoid collision, the automobile should firstly turn for maximum steering angle, and, when completing turning, the inside rear wheel is located on the extended curve of the trod line of the inside front wheel without deviation, before it turns with the front wheel for the path steering angle.
Due to that, the safe cavity is a region that extends the planned path based on AV-RRT to two sides for half of the breadth of the automobile; the rectification of the path based on PM lies in the original path as well.
Figure 27 shows the path after rectification. The automobile turns outward on the red path point (332.8721,397.5523) for 40 degrees, and then turn to the side close to the obstacle for 40 degrees when reaching green path point (333.2901,398.5590). When the automobile reaches blue path point (333.8571,399.6457), the rectification of path planning is completed.
As shown in
Figure 28, the result of the experiment mentioned above primarily proves the validity of collision detection based on NPCD and the rectification of the path based on PM. In order to further examine the validity of the algorithm, the author implemented the experiment 100 times, and the results showed that collision detection based on NPCD might forecast whether or not the automobile will collide with an obstacle, and the probability of rectifying path successfully reached 85%.