**1. Introduction**

In recent years, with the development of virtual reality technology towards practical applications, vehicle driving simulators have gradually become an important development direction in simulating the "people-vehicle-road-environment" system of road traffic research [1,2]. A vehicle driving simulator is a typical representative of a human-vehicleroad-environment simulation system. It exploits electronic computer images, with the support of electronic control and other technical support, to conduct manned simulation and research, including vehicle driving behavior, dynamic performance and traffic systems. The driving simulator has the distinguishing features of high safety, anticipated reproducibility, strong exploitability and low cost [3–6]. It can provide a safe environment

**Citation:** Chen, L.; Xie, J.; Wu, S.; Guo, F.; Chen, Z.; Tan, W. Validation of Vehicle Driving Simulator from Perspective of Velocity and Trajectory Based Driving Behavior under Curve Conditions. *Energies* **2021**, *14*, 8429. https://doi.org/10.3390/en14248429

Academic Editors: Guzek Marek, Rafał Jurecki and Wojciech Wach

Received: 16 October 2021 Accepted: 8 December 2021 Published: 14 December 2021

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for driving research and conveniently formulate a research approach related to driving behavior strategies. In particular, the experimental conditions feature a wide range and can be adjusted, and are also easy to change. Furthermore, the experimental data can be processed online, and classified and stored by a computer, which provides great convenience for the consequent statistical analysis [7,8]. Until now, driving simulators have been widely applied in research on intelligent control of vehicles, road traffic facilities and intelligent transportation systems [9,10]. They have become an effective auxiliary means and research tool for studying human efficiency, civil engineering, traffic engineering, psychology and related fields [11–15]. However, a vehicle driving simulator can only partially simulate an extremely complex transportation system. Meanwhile, each vehicle driving simulator experiment [16–18] involves effectiveness of experimental design, the rationality of content selection and representativeness of the selection of the sample (subjects), as well as the accuracy of the scene design, all of which may affect the experimental results, and even make the simulation results inconsistent with real situations. Therefore, how to validate the performance of a vehicle driving simulator deserves to be further investigated.

Until now, the simulator validation method has changed with the development of techniques and the extension of its applications. In the initial stage, the validation of simulators focuses on the physical characteristics of the vehicle. In the intermediate stage, the validation of simulators focuses on virtual images and vehicle kinematics. At present, the validation of simulators focuses on the characteristics of human-computer interaction, which is mainly due to the leading of cutting-edge technologies, such as humancomputer driving intelligent vehicle and advanced driver assistance systems (ADAS). Bham et al. [7] combined the objective evaluation and subjective evaluation to validate the driving simulator by comparing the simulation results with the real operation data collected by the global positioning system (GPS) along the highway and the video records of specific locations in the specific working area. Meuleners et al. [8] recruited 47 testers to participate in experiments and suggested they drive along a selected route on the real road and a virtual road in the driving simulator. Then, the driving simulator was calibrated by evaluating the behaviors of the driver in observing the left, right, front-viewing behavior, the speed of the intersection, the speed of following the vehicle and the observance of traffic lights and stop signs under two conditions. John A. Groeger et al. [19] compared the drivers' behavior characteristics of simulator driving and the real car driving under different curvature curves based on real vehicle experiment and two simulator simulation experiments. Through the analysis of vehicle speeds, position steering behavior and other parameters on curved road sections with different radii, the correlation of these parameters between the real vehicle and the simulator is attained to complete the effectiveness calibration of the driving simulator. Yanning Zhang et al. [20] calibrated the simulator from the perspective of absolute and relative validity. The simulator calibration was attained by setting up two experimental scenarios of free driving and following driving, and using mathematical statistics, regression methods, Wilcoxon test and non-parametric methods to compare the test point speed, driving distance, vehicle position, reaction time, risk perception and other parameters.

In terms of the current driving simulator validation methods, statistical testing is the main method, especially the Tukey and Anova tests. Speed, vehicle position, acceleration and deceleration are often considered as the validation parameters. By designing experimental scenes, conducting comparative experiments between vehicle and simulators is the main way to validate simulators. However, in the simulator validation experiment of road perception and driving interaction, the representativeness of complex road selection is quite critical. In addition, it is difficult to achieve the selection of complex roads and guarantee the safety of the experiment, as well as the efficiency and spread ability of the experiment being consequently low. According to the analysis of the above methods, considering the role of the road in the overall traffic, this paper selects the curve road as the criterion to evaluate the performance of the vehicle driving simulator, as the curve road condition can preferably evaluate the driving characteristics. In the comparison study of different curve

radii, vehicle speed and trajectory are two main parameters that can comprehensively reflect driving characteristics [21,22]. On this account, this article validates the effectiveness of driving simulators based on speed from reliability and validity aspects, where reliability is an indicator of the consistency of test results, and validity accounts for the accuracy of test results [23]. In the curve test, the driver judges and manipulates the vehicle to pass the curve with different radii at certain speeds, and the speed value of each sampling point on the curve is equivalent to the test on the driver [24]. After that, the experiment's quality, i.e., the reliability of the experimental results, is evaluated. From this point of view, the reliability and validity theory can be used as a reference [25]. The driving trajectory is the specific performance of the driver's strategy and behavior of manipulating the vehicle. The similarity of the trajectory is an important reference index for investigating the steering behavior of the driver [26]. When analyzing the position parameters of the vehicle on the curve, the trajectory similarity model can be used to compare the simulator experiment. After the validation parameters and validation methods are determined, a method of using theoretical models instead of real vehicle experiments is proposed for easy acquisition of calibration data. In summary, this method can solve the problem that real complex scenes are difficult to realize in the simulator validation. Selecting the trajectory as the validation parameter can more comprehensively and intuitively reflect the simulator's curve driving state. Using speed model and trajectory model instead of real car experiment can improve the efficiency of simulator validation and lay a foundation for the standardization of simulator validation [27,28].

Driving simulator technology has the advantage of being able to collaborate with multiple external vehicles at different speeds. It can also provide complex traffic environments and extreme test conditions. It further offers the advantage of safe and fast verification of motion strategies under complex operating conditions. Based on the above advantages, in recent years some car manufacturers and research institutes have started to experiment with driving simulators to promote research into automotive intelligence technologies. In particular, they have played an important role in the development and advancement of driverless car technology. For example, in January 2017, the US Department of Transportation designated 10 pilot units for testing unmanned vehicle technology, four of which were research institutes using driving simulators as a means of testing [29]. Therefore, as the advantages of driving simulators for applications in complex conditions increase, the need for driving simulator effectiveness under equivalent conditions is also increasing. The method proposed in this paper addresses the prediction of vehicle trajectories under extreme curves, small sample size and multi-dimensional metrics conditions. The proposed validation method addresses the reliability, robustness and generalisation of the simulator as a vehicle for the above research. The main contributions of this study adding to the literature are summarized as follows.


The remainder of this paper is structured as follows. Section 2 details the methods, and introduces the whole design framework. Section 3 explains the experimental data, and Section 4 discusses improvement of simulator curve track planning model, followed by the conclusion drawn in Section 5.
