**2. Methods**

### *2.1. The Whole Design Framework*

By designing curves with different radii as experimental scenes, selecting the speed and trajectory as validation indicators, and exploiting the Kronbach's *α* reliability, split-half reliability, *r* reliability, criterion-related validity and Cohen's *d* exponent as the evaluation criteria [18], this paper completes the validation of the speed indicator of the driving simulator, and leverages the cosine similarity method to complete the validation of the driving simulator's trajectory. After converting the trajectory data into state variables, a body of sequence data of the driver's trajectory characteristics can be obtained. Based on the analysis of experimental data, the establishment of a curve trajectory planning model, i.e., a multi-bidirectional long-short term memory (Mul–Bi–LSTM) recurrent neural network (RNN), driven by human-like operation data is proposed [30,31]. Bi–LSTM is currently widely used in the prediction of sequence data, such as pedestrian trajectory prediction, intrusion detection, traffic speed prediction and traffic flow prediction [32–34]. Since the vehicle trajectory is sequence data and features a strong regularity, the Bi–LSTM neural network data-driven method enables to establish a vehicle trajectory planning model with high performance. The model results manifest that the proposed validation model can better replace the expected trajectory of a vehicle driving under complex road conditions and reduce the cost of collection of actual vehicle parameters. The whole design framework is shown in Figure 1. As can be found, the whole validation is conducted from the perspectives of speed and trajectory, which are respectively evaluated from reliability, validity, similarity and trajectory fit. In addition, a data-driven trajectory planning model is constructed to facility trajectory design.

#### *2.2. Experimental Design*

In this paper, the vehicle data are obtained through experiment under different horizontal curves, including longitudinal vehicle speed, longitudinal displacement, lateral displacement, longitudinal acceleration, vehicle position, accelerator pedal and brake pedal. The analysis of speed under curves, driving trajectory, theoretical vehicle speed and expected trajectory approximation are intensively analyzed to study the effectiveness of driving simulator based on vehicle-road interaction. As Table A1, a total of 27 drivers with different genders, ages, driving years and driving mileages are selected as the test subjects in the experiment, and they are numbered 1–27. Among them, all drivers are with corrected visual acuity of 1.0 and can skillfully complete the driving tasks. The experiment recruited 16 skilled drivers, which were test numbers 1, 2, 3, 4, 5, 7, 10, 11, 13, 15, 16, 17, 18, 19, 21, and 26, including 11 male drivers and 5 female drivers. There are 11 new drivers, and the test numbers are 6, 8, 9, 12, 14, 20, 22, 23, 24, 25, and 27, including 7 male drivers and 4 female drivers. Drivers' age, driving experience, annual vehicle kilometers traveled total mileage, number and gender all meet the basic conditions of driving simulation experiments [35–37]. The experimental section is set as a two-way highway with no central separation zone and a length of nineteen kilometers. The design speed is 40 km/h and the lane width is 3.5 m. The experimental road types are composed of straight road sections and different horizontal curved road sections. The straight-line section is set between each characteristic road section (different horizontal curved sections), with a length of 700 m, so that the driver can adjust their speed to enter the next curve with the expectation speed as the entry speed. The curve consists of a symmetrical basic type and simple type, mainly involving straight lines, circular curves and transition curves.

**Figure 1.** The whole design framework.

The circular curve setting considers the driving characteristics and the design speed to specify the minimum curve radius. According to *Design Specification for Highway Alignment* [38], the design radii include 55 m, 150 m, 250 m, 350 m, 450 m and 550 m and the transition curve is set to 35 m, 85 m, 135 m, 185 m, 235 m and 285 m, considering centrifugal acceleration, driver operation response and reaction time, as well as visual conditions. Finally, a road design software is employed to devise the curve shape of the experimental characteristic curve. The virtual road environment scene is built based on our self-developed software [39]. The driving simulator system consists of two parts: the cockpit and the console. The cockpit portion was composed of an actual Jetta automobile equipped with all the necessary sensors and a monitoring system. Three cameras and one dual voice intercom system were installed in the cockpit, and the facial expressions, movements of the hands and feet, and sounds were transmitted to the recording system and the monitor to be stored for further study. Figure 2 shows the KMRTDS driving simulator and the test while driving. The visual scenario was presented on a large screen, providing an approximately 150◦ horizontal view [40].

**Figure 2.** The KMRTDS driving simulator and the test while driving.

#### *2.3. Experimental Data Preprocessing*

The driving simulator test can collect corresponding experimental data including simulation time, vehicle longitudinal acceleration, longitudinal velocity, lateral velocity, lateral acceleration, displacement, yaw rate, vehicle mileage, steering wheel angle, accelerator, pedal, brake pedal and gear steering. In order to facilitate the analysis of the driver's driving behavior in a curved road, it is necessary to preprocess the collected raw driving data. Since the start and end points of each trajectory data are slightly different, and the difference in vehicle speed leads to misalignment between the different original trajectory data. In the data processing, the form pile number is used as the curve landmark, and the curve landmark is set in each curve. A series of points is marked on the lane dividing line of the experimental road, and thus the distance between adjacent virtual landmarks is equal. The virtual landmarks are only used for calculations. Considering the length of the road and the number of sampling points at the same time, the interval of virtual landmarks in this paper is 1 m. The sampling interval of the tested driving simulator is 50 Hz (20 ms), and the sampling points will be different according to the speed of the vehicle. When analyzing the similarity of the vehicle trajectory, the experimental data should be distinguished according to the speed when entering the corner. As shown in Figure 3, for ease of calculation, a Cartesian coordinate system needs to be established by two mutually perpendicular coordinate axes, usually called the *x*-axis and *y*-axis, and each axis points to a specific direction. The middle *y*-axis is tangent to the lane dividing line, and the *x*-axis is perpendicular to the *y*-axis and points to the inner lane. The intersection of the two coordinate axes is the origin. The coordinate axes of these two different lines determine a plane, called *xy*-plane, i.e., the Cartesian plane. For easier understanding, this paper quotes the concept of lateral offset, which is the distance between the projection point of the vehicle center on the *xy* plane and the form pile number. The specific calculation for the lateral offset can be formulated as:

$$D\_P = \sqrt{(X\_{CAR} - X\_Z)^2 + (Y\_{CAR} - Y\_Z)^2},\tag{1}$$

where *DP* is offset, *XCAR* is Longitudinal displacement of the vehicle, *XZ* is longitudinal displacement of pile number, *YCAR* is vehicle lateral displacement, and *YZ* is longitudinal displacement of pile number.

**Figure 3.** Driving simulation track diagram.
