5.1. Test Function Simulation
In order to verify the effectiveness of the improved algorithm in this paper, three test functions (single objective function: De jong, Schaffer) simulated and compared the fourdifferent optimization algorithms: the improved immune moth flame optimization algorithm (IIMFO) proposed in this paper, the improved version of the moth flame optimization algorithm based on Lévy-flight strategy (LMFO), the moth flame optimization algorithm (MFO), differential evolution (DE), and particle swarm optimization (PSO).
The specific simulation comparison results are as follows:
(I) The sphere function (real optimal minimum function value is 0.0) is expressed as follows. .
The specific simulation results of the sphere function are shown in
Figure 6 and
Table 1.
As shown in
Figure 6 and
Table 1, compared with LMFO, MFO, DE and PSO, the improved immune moth flame optimization algorithm is most ideal, and its optimal minimum function value is
, the optimal function value is
.
(II) De jong function (real optimal minimum function value is 0.0), it is expressed as follow. .
The specific simulation results about De jong function are shown in
Figure 7 and
Table 2.
As shown in
Figure 7 and
Table 2, compared with LMFO, MFO, DE and PSO, the improved immune moth flame optimization algorithm is most ideal, and its optimal minimum function value is
, the optimal function value is
.
(III) The Schaffer function (real optimal minimum function value is 0.0) is expressed as follows. .
The specific simulation results of the Schaffer function are shown in
Figure 8 and
Table 3.
As shown in
Figure 8 and
Table 3, compared with LMFO, MFO, DE and PSO, the improved immune moth flame optimization algorithm is most ideal, and its optimal minimum function value is
, the optimal function value is
.
5.2. Intelligent Automatic Parking Simulation
The setting situation of coordinate axis for intelligent automatic parking in this paper is as follows: the bottom edge line of the vehicle garage is the x-axis, the side line of the vehicle garage away from the vehicle and vertical to the x-axis is the y-axis, the bottom corner of garage edge away from the vehicle is the reference origin O, and the coordinate of reference origin O is (0,0). The two automatic parking scenarios are chosen: Volkswagen UP and Honda XR-V are the simulation object, and the parallel distance between the initial coverage area and vehicle garage near the corner is 2.2 m, respectively. The specific setting situation of scenario for Volkswagen UP is described as follows: the parking space is , the vehicle coverage area is , and the distance between initial coverage area and the side line of vehicle garage is 1 m. The scenario for Honda XR-V is as follows: the parking space is , the vehicle coverage area is , and the distance between initial coverage area and side line of vehicle garage is 0.8 m.
The parking path optimization method adopts the improved immune moth flame optimization algorithm proposed in this paper (IIMFO), improved version of the moth flame optimization algorithm based on Lévy-flight strategy (LMFO), the moth flame optimization algorithm (MFO), differential evolution (DE) and particle swarm optimization (PSO). The specific automatic parking path curves and optimization results using Volkswagen UP and Honda XR-V are shown in
Figure 9 and
Figure 10 and
Table 4 and
Table 5.
As shown in the automatic parking path curves and related results using Volkswagen UP and Honda XR-V (
Figure 9 and
Figure 10 and
Table 4 and
Table 5), compared with MFO, DE and PSO, under the premise of no collision avoidance of the side line of the vehicle garage during the parking process, the automatic parking path obtained by IIMFO is smoother and shorter. This indicates that IIMFO proposed in this paper has a stronger optimization effect and has more advantages in intelligent parking.
5.3. Intelligent Automatic Parking Semi-Automatic Experiment
Because the ideal automatic experiment environment is not easy to be obtained, a semi-automatic experiment environment is chosen as the verification environment in this paper. A commonly used and favored intelligent semi-automatic parking mode was adopted in the semi-automatic experiment environment. The specific details about the limitations of the intelligent automatic parking semi-automatic experiment are shown as follows.
(I) The parking system contains the identification function of extremely bad weather and road conditions. When it knows that the vehicle is in extremely bad weather and under different road conditions such as rainstorm, blizzard, heavy uphill and heavy downhill, it will automatically disable the intelligent semi-automatic parking function and inform the driver.
(II) The parking system is equipped with both a parking path optimization function and parking path tracking control performance. In other words, in general, parking systems have the potential to realize unmanned autonomous parking.
(III) In the process of intelligent semi-automatic parking, it is necessary to configure a driver familiar with two simple skills. The details are as follows: I according to the deviation between the optimized path and the tracking control path in the reversing image, manually and gently control the steering wheel to improve the accuracy of the parking path tracking control; II it is able to stop parking or apply emergency braking in combination with the on-site parking situation and the prompt of the parking reminder. In other words, the driver acts as both a safety officer and an enhanced track control corrector.
(IV) The parking system is equipped with strong safety assurance measures. Once an accident occurs, the parking vehicle will be parked immediately to ensure the safety of people and vehicles.
The above intelligent semi-automatic parking mode introduced in this paper will become a major parking mode in China in the future because of its dual advantages of convenience and economy.
In the above semi-automatic parking mode, the rearview camera with an optimization parking path and track trajectory is used for reference, and a driver with the above described simple skills is needed. Specifically, the optimization parking path is the capital driving factor, and the driving experience should not be ignored too. The driving trajectory tracks the optimization parking path by the rearview camera and corrects by the driving experience. So, the experiment vehicle need to configure the rearview camera with the optimization parking path and tracking trajectory, position sensors, driver prompter, tracking controller, parking feasibility decider, emergency parking device and stopping parking device.
In this paper, the No. 148 and No. 146 parking areas of Xinghai Square Shell Museum in Dalian, China are chosen as the semi-automatic experiment area, and the Toyota LeiLing Shuangqing 185T Sportline and First Automobile Works (FAW) Senya r7 are chosen as the semi-automatic experiment object. The two automatic parking scenarios are chosen: Toyota LeiLing Shuangqing 185T Sportline and Honda Accord 15T as semi-automatic experiment objects, and the parallel distance between initial coverage area and vehicle garage near corner is 2.2 m, respectively. The specific setting situation of scenario for FAW Senya r7 is described as follows: the parking space is
, the vehicle coverage area is
, and the distance between initial coverage area and the side line of vehicle garage is 1 m. The specific setting situation of scenario for Honda Accord 15T is described as follows: the parking space is
, the vehicle coverage area is
, and the distance between initial coverage area and the side line of vehicle garage is 1.2 m. The main parameters of the calculus complexity for semi-automatic experiments based on intelligent automatic parking in this paper are as follows: the limit time for collecting parking path optimization data is 4 s, the time for determining the feasibility of simulated parking is 1.5 s, the time for obtaining the parking path by the optimization algorithms is 10.5 s, and the limit of the total time for the parking path optimization is 16 s. In general, the acceptable limit total time is identified as 20 s, thus, the verification for semi-automatic experiment comparison in this paper is believable and realistic. The integral fitting method is used to solve the length of the stopping trajectory curve in the control period of 1000
s (1 ms). In this paper, the Mavic 2 DJI’s unmanned aerial vehicle (UAV) is chosen as the camera equipment. The specific physical diagram of Mavic 2 DJI’s unmanned aerial vehicle is shown in
Figure 11.
In this paper, semi-automatic experiment comparison based on intelligent automatic parking was implemented on several calm, cloudless days. The parking path optimization method adopts the improved immune moth flame optimization algorithm proposed in this paper (IIMFO), improved version of moth flame optimization algorithm based on Lévy-flight strategy (LMFO), moth flame optimization algorithm (MFO), differential evolution (DE) and particle swarm optimization (PSO). The three vital fixed points were filmed using the Mavic 2 DJI’s unmanned aerial vehicle. The specific filmed vital fixed points for the semi-automatic parking process using Volkswagen Toyota LeiLing Shuangqing 185T Sportline and FAW Senya r7 are shown in
Figure 12 and
Figure 13.
As can be seen from the filmed vital fixed points for the semi-automatic parking process using Toyota LeiLing Shuangqing 185T Sportline and FAW Senya r7, compared with LMFO, MFO, DE and PSO, under the premise of no collision avoidance of the side line of the vehicle garage during the parking process, the semi-automatic parking effect obtained by IIMFO is more ideal. It indicates that the IIMFO algorithm is a suitable algorithm with strong optimization ability and can deal with the actual automatic parking problem more effectively.